Embracing this game design philosophy, we considered the component of meaning and the component of play the same for both our serious games. Meaning is reflected on the objective of our research, which, as stated previously in the introduction, is to raise awareness around the challenges associated with implementing innovative systems in transport and logistics in a sustainable way and explore the role of different actors involved. The game materials and dynamics also do not change. The physical game elements of each game include: one game board, four role cards, five action cards per role, event cards, tokens, and pawns. The roles of the players in the two games correspond to the key actors of the truck platooning ecosystem and of the port container ecosystem for Mobinn and Platform4Barge respectively. What changes is the world of reality for the two cases, and thus the content of all the cards involved in each game. A description of how we obtained the critical insights in the reality of each one of the cases, which helped us then unfold the content of the cards, follows.

For the Mobinn game, in order to develop the role cards, as well as the action and event cards of the game, we first needed to understand who are the main actors that are involved in shaping the truck platooning community and what is "at stake" for each one of them; then we translated this information into content of our three types of cards: role cards, action cards and event cards. we started by a comprehensive literature review of scientific papers about truck-platooning (publications in journals and conference proceedings, working papers, theses', e.g., see [54,55,66]). As truck platooning, being a technology-driven innovation, does not have such a large volume of scientific literature available yet, we also decided to study materials such as white papers, reports (e.g., see [52,67], websites and media sources e.g., see [68,69]. Moreover, The Netherlands has organized a few years ago the so-called European Truck Platooning Challenge, when the country was in the EU presidency [70], and we also reviewed the results of this initiative [71,72]. After the online desk research which helped us obtain a better understanding of the truck platooning world and especially of the actors involved, we discussed our initial ideas with actors within the Port of Rotterdam and we concluded that the main categories of actors involved in truck platooning are the following: the transporters, the freight forwarders, the policy-makers and the developers.

Each actor category then helped us in building a role and creating a role card that "brings this role into life"—from the world of reality into the world of play. Each role card briefly explains who the player is and what is his/her mission in the game. For instance, the developer is a representative of an original equipment manufacturer (OEM) company, which is interested in the truck platooning technology and has already invested a significant amount of resources in the research and development process. The objective of this role is to develop the technology before the company's competitors in the field in the most cost-effective way possible. The absence of EU regulations on the topic is a source of concern for this role. The policy-maker's role in the game is represented by an employee with a high-ranking position in the Dutch Ministry of Infrastructure and Water Management. The main dilemma that this role faces is if they should be patient until the EU publishes regulations and then align the national policy accordingly or work towards making The Netherlands a frontrunner country in this field, by introducing country-level policy that would encourage the deployment of truck-platooning. Figure 1a illustrates an example of a role card in Mobinn.

In the case of Platform4Barge, to re-construct the world of reality around it, we followed exactly the same logic in developing the game cards' content; beginning with a thorough literature review on the field of multi-sided digital platforms, with a focus on digital platforms in transport and logistics, and the container ecosystem in particular. As an extra way to gain meaningful insights in this case, we used also our experience from co-developing a set of four teaching cases and a teaching note around the use of multi-sided digital platforms in transport and logistics [73], together with actors from the Port of Rotterdam as well as from the private sector (we worked on the cases' development in parallel with the game development). We organized a number of try-out sessions with master's students in Rotterdam to test and validate the teaching cases, and the feedback we received was also

valuable content wise for the development of the game cards. Following that, we arranged meetings with actors of the Port of Rotterdam who helped us in shaping our ideas and finally deciding the four main categories of actors for this game: the shippers/freight forwarders (in a combined role that represents the demand side), the deep-sea terminal operators, the barge operators and the port authority. For example, the role card of the representative of the port authority implies that the player acts as an orchestrator of the introduction of the digital platform and its operation and as a facilitator of the process. Achieving sustainability through modal shift is of crucial importance for this actor. Figure 1b presents an example of a role card in Platform4Barge.

**Figure 1.** Example of a role card in: (**a**) Mobinn and; (**b**) Platform4Barge.

The same process of exploring the world of reality for both our case studies, helped us also in defining the key performance indicators (KPIs) for both the games, as illustrated in Table 1.

**Table 1.** Key Performance Indicators of Mobinn and Platform4Barge.

The KPIs are illustrated on the game boards, with a 1–9 point scale, using a "traffic light" approach, i.e., dividing the scale in three areas: red, yellow and green, inspired by the work of Van den Ende (2019) (Figure 2a,b). The green area indicates alignment of interests and goals, the yellow area shows only partial alignment, while the red one demonstrates lack of consensus of actors. Each action card, in addition to describing a certain action that can be performed by a certain role, indicates the number of tokens needed to be paid by this role as well as by other(s) in the game in order to be activated. The impact of the card on the three KPIs of the game is also mentioned (Figure 3a,b). The event cards contribute in creating more suspense and fun during the game, as they can indicate either a positive, or a negative event that "disrupts" the players' plan and can make them adapt their strategy (Figure 4a,b).

**Figure 2.** Game board and key performance indicators (KPIs) in: (**a**) Mobinn and; (**b**) Platform4Barge.

**Figure 3.** Example of an action card in: (**a**) Mobinn and; (**b**) Platform4Barge.

**Figure 4.** Example of (**a**) a negative event card in: Mobinn and; (**b**) a positive event card in Platform4Barge.

Both games are played in five rounds. At the beginning of a game session, each player gets one role card, all respective actions cards and an initial number of tokens. When a round begins, each player can either bring to the negotiations table one of the action cards or alternatively he/she can choose to not "act" in this round. After every player shares his/her decision, the players who chose to use an action card, simultaneously place them on the board. Each player has to pay the number of

tokens that is written on the card for his/her own role before requesting other players to support the action with their tokens.

The card is considered valid and has an impact on the KPIs of the game, only in cases when all the roles mentioned on it agree to contribute with the necessary number of tokens—otherwise, the player who suggested the card loses the invested tokens and he/she can keep the card for future use. At the end of each round, an event card is drawn, and each player gets some extra tokens, representing income from their services. The role of other important actors (in addition to the ones represented by the four main roles), such as the European Commission (in the form of regulations or directives), is introduced in the game through the event cards.

The goal of both games is to "make the innovation happen" (in our case the innovation is aimed at the concepts of truck platooning and the multi-sided digital platform respectively), which is translated in achieving to have all three KPIs in the green area of the game board (points 7–9 in the 9-point scale) at the end of game play.

The main learning goal defined for both games is to understand how important an innovation ecosystem perspective is for a successful adoption of innovation in the transportation domain. Actors, decisions and actions within the innovation ecosystem are highly interdependent. Both games aim to highlight this characteristic and make players more aware of the interrelations of decisions and events. The players have the opportunity to influence the innovation ecosystem by (joint) investments and actions, but they must keep in mind that the innovation is also influenced by external events, limited budget and the existence of only five rounds. The game is played by at least four players (one per role). In cases when there are more participants, teams are formed and two or sometimes three players can together play a single role. This enables participants to first discuss choices of actions and it can be seen as a purposeful game element. Every game session is introduced by a short briefing, during which the facilitator explains the concept and the rules of the game. After the completion of the five game rounds, a debriefing follows. The total time of the game play, including briefing and debriefing is approximately 60 to 90 min for each of the games.

### *4.2. Play-Test Sessions and Data Collection*

In order to test the two games and receive valuable feedback for further improvement, several game sessions were organized in which the game prototypes were played. The Mobinn game was tested between October 2018 and November 2019 at game sessions in The Netherlands and the USA (Figure 5a). The Platform4Barge prototype was tested at sessions in The Netherlands between December 2019 and February 2020. (A fourth game session was planned for March 2020, as part of an alumni-student event organized by Transito, the study association for the Bachelor and Master program Urban, Port and Transport Economics (UPTE) of the Erasmus University Rotterdam. This scheduled event was cancelled due to the measures taken to stop the spread of COVID-19 (Corona Virus Disease 2019) in Europe) (Figure 5b).

**Figure 5.** (**a**) Play-test session of Mobinn, during the event for the 10th year-anniversary of RDM (Rotterdam Dry Docks, in Dutch: Rotterdamsche Droogdok Maatschappij) Campus in Rotterdam, 4 July 2019; (**b**) play-test session of Platform4Barge during the Erasmus Port Campus in Rotterdam, 12 December 2019.

All sessions of both games were facilitated by at least one member of the game development group, who was responsible for the briefing, facilitation, debriefing, as well as for the data collection during and after the game. The data collection took place by audio recording if it was feasible to do so, and by observation through the participating researchers. Usually, one researcher took over the role of process facilitator, and one more observed the session. Beyond dedicated game sessions, the game was also played as part of a larger event, where usually background noise made audio recording difficult. During these sessions, data was collected by observation and notes during the game-play. The notes taken included decisions of the players, the cards they chose to use, as well as their game play behavior. After the end of the game, a debriefing phase was conducted based on semi-structured questions regarding the game experience and the take-aways. (The debriefing questions were adapted from the framework described by Kriz [74], in line with the former adaptation of this framework made for the debriefing and workshops of the Plaitra Game Session, which took place in the context of the iTRACK Project, at TU Delft Campus, The Netherlands, in May 2017). The questions aimed at deriving what types of feelings were experienced by the players during the game play and at revealing the lessons learned (if any) by the game. Moreover, the players were asked what, according to their opinion was working well during the game and which elements might need improvement, and how we can achieve this improvement. These questions were used as a trigger to initiate the discussion with the participants, but they were not in any case exclusive—the players were invited to share any kind of feedback, comment, observation or suggestion for change they considered relevant with the game facilitator. Thus, the debriefing phase focused on the game itself as well as the play experience of the players.

The following tables present the number and type of players, as well as the location where each game session took place (Table 2 for Mobinn and Table 3 for Platform4Barge).

The following section discusses the results of the game sessions.

**Table 2.** Play-tests sessions that have been organized for Mobinn.

#### **5. Results and Discussion**

The results discussed in this section represent a summary of the observations of the facilitator and accompanying researcher, collected and analyzed by the researcher team in a qualitative way, based on the in-situ observations during the game play and during the debriefing stage, as well as based on the recordings (when available) and notes for both stages. This approach follows methods as proposed in the field of serious gaming towards solving sustainability-related issues by Den Haan and Van der Voort [77]. Their study found that the majority of publications which fall into the aforementioned category of trying to address sustainability challenges have used qualitative data for the game evaluation, including unstructured observations by the researchers and debriefings.

Both games have been tested by players with a diverse background, knowledge and with different roles; from real actors in the field to professionals and members of the academic and research community; all do have knowledge of the domain of transport and logistics from their respective profession. The facilitator of the game was trying to intervene as little as possible during the game play, to minimize the associated biases and be able to detect and analyze the negotiations and discussions that were taking place among players, and only tried to support the process of play, but not the decision making. High engagement levels were observed during all game sessions, which proved that the games succeeded in creating an enjoyable, comfortable and fun environment for the players.

The negotiations and discussions among players involved more tension when actors with a presence in the field were involved. On the other hand, students and researchers were more curious and keener on learning about the innovation process around truck platooning and multi-sided digital platforms. The professional actors, being already familiar with the concepts, were able to focus more on attributes such as the aspirations of the different roles, and the characteristics of the different actions that could be taken. Students also reported that after the end of the game play, they felt that they obtained a more holistic view and a more comprehensive understanding regarding the challenges for new technologies and innovative concepts to be adopted by the transport and logistics sector. They also realized the value of communication among the stakeholders and organizations in an innovation ecosystem.

As the concept of innovation ecosystem and its importance emerged through the games, the participants appeared afterwards to have realized that nobody can win these games playing alone; it was necessary to discuss, negotiate and collaborate with other parties to increase the KPIs. It was observed that in those game sessions in which the players realized early in time that they needed to collaborate and share information and knowledge with each other to boost the KPIs, almost every game finished with all three KPIs in the green area of the spectrum. On the other hand, in sessions

where the players appeared more reluctant to collaborate and unwilling to have increased visibility of their negotiation strategy in the beginning of the game, they struggled towards the end of the game and often failed to reach the objective of having all KPIs in the green area within the five rounds of the game.

A very interesting observation was made during a Mobinn game session with real actors related to the Port of Rotterdam; at one of the rounds, the resources of one player/role were not enough to invest in an action card that that player would like to use. At that moment, another player suggested to pay his part instead, because he said that this action could really contribute to the direction of "making the innovation happen" and thus it would be a win-win for both the roles they represented if they made this joint investment. The noteworthy point here is that this was never mentioned in the game instructions as an option, but the game play motivated the creative, out-of-the box thinking of the player towards the direction of collaboration.

When players had already some background knowledge on truck platooning, they considered it a plus in better understanding the Mobinn game. As for Platform4Barge, even players which did not have any background knowledge on the specific topic of exchange platforms, did not encounter difficulties in understanding, because they were familiar with the concept of digital multi-sided platforms through very widespread platforms of this kind in other sectors, such as Uber and other on-demand transport services for shared mobility, and Airbnb in housing.

A repeated comment during the Mobinn sessions was about the equal distribution of money (tokens) among roles; several players felt that this is often not the case in real-life, as the authorities' budget is usually considerably higher than the one of private actors. For this reason, for Platform4Barge it was decided to start with a different number of tokens per role to better reflect the situation in reality.

Last but not least, feedback from experts included the view that identifying all actors involved in an innovation ecosystem, along with their potential actions, is already a very powerful characteristic of both the games.

## **6. Conclusions**

Actors from diverse backgrounds participated in a number of play sessions with both games; from experts who represented the real actors in the field, to students, researchers and professionals. This led to very interesting observations and proved that both games can act as triggers to make participants aware of the existing challenges that stakeholders involved in transport and logistics face when implementing innovations to increase sustainability. The games provide useful insights in the benefits of collective goal setting and can support and stimulate discussions towards the importance of collaborative action in innovation processes. The games can be used to trigger a valuable discussion and make actors aware of the value of an innovation ecosystem, and the need for collaboration to achieve sustainability goals.

The results of the game sessions highlight the critical role that each actor can play in an innovation ecosystem, by collaborating on data sharing and improving data visibility and transparency. The study found that using serious games to address the challenge of enhancing awareness, communication and collaboration of actors in innovation ecosystems can be highly effective.

**Author Contributions:** Conceptualization, A.R., H.L., A.V. and R.Z.; methodology, A.R., H.L., A.V. and R.Z. validation, A.R., H.L., A.V. and R.Z.; formal analysis, A.R., H.L., A.V. and R.Z.; investigation, A.R., H.L., A.V. and R.Z.; resources, A.R., H.L., A.V. and R.Z.; data curation, A.R., H.L., A.V. and R.Z.; writing—original draft preparation, A.R., H.L., A.V. and R.Z.; writing—review and editing, A.R., H.L., A.V. and R.Z.; visualization, A.R., H.L., A.V. and R.Z.; supervision, H.L., A.V. and R.Z.; project administration, H.L., A.V. and R.Z.; funding acquisition, H.L., A.V. and R.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** Mobinn game was developed as part of the InDeep (Innovation Network Design Enables Excellent Ports) project, funded by The Netherlands Organization for Scientific Research (NWO). The initial version of the Platform4Barge game was developed in the context of the EU Horizon2020 Project SELIS (Towards a Shared European Logistics Intelligent Information Space). The final version was developed in the context of the project "Digital Platforms for Logistics: Flipping the Classroom by Means of Games and Teaching Cases", funded by the Community for Learning and Innovation (CLI) of Erasmus University Rotterdam as an Educational Innovation project.

**Acknowledgments:** The authors would like to thank the lead developers that were involved in the development of the two games. In the case of Platforrm4Barge, in addition to the authors this includes Donald Baan, Arco Jansen and Maurice Jansen. Game production and visual design was realised by the TU Delft GameLab: for Mobinn, by Linda van Veen and for Platform4Barge, by Linda van Veen and Resy Arts. The authors would also like to thank all the participants of the game sessions for their time and valuable feedback on the game and the anonymous reviewers who helped in improving the manuscript by providing their constructive suggestions and comments.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

## **References**

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## *Article* **Efficiency Assessment of Operations Strategy Matrix in Healthcare Systems of US States Amid COVID-19: Implications for Sustainable Development Goals**

**Aydın Özdemir 1,2,\*, Hakan Kitapçı 1, Mehmet ¸Sahin Gök <sup>1</sup> and Er¸san Ci ˘gerim <sup>1</sup>**

**Abstract:** The objective of this study is to assess the efficiency of the operations strategy matrix in the healthcare system of U.S. states amid COVID-19. Output-Oriented Data Envelopment Analysis was used to assess the efficiency of the operations strategy matrix. Strategic Decision Areas (Capacity, Supply Network, Process Technology, and Development and Organization) were considered inputs while competitive priorities (Quality, Cost, Delivery, and Flexibility) were considered outputs. According to results; Alaska, Alabama, Arkansans, Florida, Hawaii, Iowa, Idaho, Louisiana, Minnesota, Missouri, Mississippi, Montana, North Carolina, New Jersey, New York, Oklahoma, South Carolina, South Dakota, Texas, Vermont, Wisconsin, and Wyoming are relatively efficient. Additionally, Connecticut, Louisiana, Minnesota, New Jersey, Rhode Island, Tennessee, Utah, Vermont, Washington, and Wyoming are fully efficient while South Dakota is the state that needs the most improvement in terms of strategic decision areas and competing priorities. On the other hand, inefficient states have larger population and GDP than efficient states. Based on these results, implications for sustainable development goals (SDGs) are drawn.

**Keywords:** efficiency assessment; operations strategy matrix; data envelopment analysis; healthcare systems; COVID-19

## **1. Introduction**

A novel coronavirus named COVID-19 was identified in Wuhan/China on 31 December 2019, and the World Health Organization (WHO) assessed that COVID-19 could be characterized as a pandemic on 11 March 2020. The first case was confirmed on 22 January 2020 and as of 27 June 2021, due to COVID-19, there were 34,494,677 confirmed cases and 619,424 confirmed deaths in the USA [1].

Centers for Disease Control and Prevention (CDC), a service organization that protects the public's health, has prepared a global response to COVID-19. It includes the goals limiting human-to-human transmission, minimizing the impact of COVID-19 in some states with limited healthcare delivery capacity, and reducing certain threats that pose a risk to the United States' healthcare system [2]. In this context, public health, and social measures have been implemented to prepare and respond to the pandemic [3]. Although there have been many actions implemented to cope with the pandemic, the increasing number of COVID-19 cases poses a major threat to healthcare delivery [4].

WHO has provided comprehensive guidance to community and service providers to minimize the spread of the disease [5]. Since the early experience shows that COVID-19 requires unprecedented mobilization of health systems, it is recommended to assess the health systems to mitigate the outbreak's impact [6].

Although health is only one of the UN Sustainable Development Goals (SDGs), many other health-related goals comprise determinants of health [7]. The SDGs represent a

**Citation:** Özdemir, A.; Kitapçı, H.; Gök, M. ¸S.; Ci ˘gerim, E. Efficiency Assessment of Operations Strategy Matrix in Healthcare Systems of US States Amid COVID-19: Implications for Sustainable Development Goals. *Sustainability* **2021**, *13*, 11934. https://doi.org/10.3390/ su132111934

Academic Editors: Golam Kabir, Sanjoy Kumar Paul and Syed Mithun Ali

Received: 1 September 2021 Accepted: 20 October 2021 Published: 28 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

unique opportunity to promote and assess public health [8]. The healthcare assessment process seeks to measure how care affects individuals or populations' health and wellbeing [9]. The assessment is also vital for achieving the SDGs, especially Goal 3, described as ensuring healthy lives and promoting well-being for all at all ages [10]. because sustainability is a managerial trend that plays an important role [11], and implications drawn based on healthcare assessment help to help policymakers for favorable policymaking [12]. Mentioned assessment depends on the development of standards [13]. There are some standards and tools for assessing healthcare systems such as effectiveness, efficiency, humanity, and equity [14]. As a novel evaluation tool, Operations Strategy Matrix describes the operations strategy as the intersections of an organization's performance objectives (competitive priorities) with its decision areas [15]. According to Slack and Lewis (2017); the matrix can be considered a checklist of the issues required to be assessed and helps operations to be extensive. Additionally, all intersections on the matrix don't have equal importance. Some intersections are more critical than others. This depends on the nature of operations. The matrix has four strategic decision areas (capacity, supply network, process technology, and development and organization), and four competitive priorities (quality, cost, delivery, and flexibility) [15].

The research question of this study is as follows: are US states efficient in the healthcare system amid the COVID-19 pandemic, and how do the efficient or inefficient conditions affect Sustainable Development Goals (SDGs).

The objective of this study is (i) to assess the efficiency of the operations strategy matrix in the healthcare system of US states amid COVID-19. For this purpose, 50 US states were considered as Decision Making Unit (DMU), and output-orientated Data Envelopment Analysis (DEA) was used; and (ii) to draw implications for sustainable development goals (SDGs) based on DEA results. The unique contribution of this study lies in the use of the Operations Strategy Matrix to assess the healthcare system of US states and to draw the implications for Sustainable Development Goals (SDGs). To validate the Operations Strategy Matrix, Data Envelopment Model was used.

The research paper is organized as follows. The following section presents the exiting literature review associated with COVID-19 and the healthcare system. Section 3 describes the DEA methodology. Section 4 presents the results. Section 5 discusses the findings and draws implications for sustainable development goals (SDGs). The final section portrays the conclusion and opportunities for future work.

## **2. Related Research**

The section presents the existing literature about COVID-19 and the healthcare system. O'Leary et al. (2021) have documented the healthcare policies developed during the initial wave of widespread COVID-19 transmission in Ireland, and they have developed six category headings to describe to focus VOVID-19 policies: (i) infection prevention and control, (ii) residential care settings, (iii) maintaining non-COVID-19 healthcare services, and supports, (iv) testing and contact tracing, (v) guidance for healthcare workers concerning COVID-19, and (vi) treating COVID-19 [16]. Tsai and Yang (2020) have examined the impact of the COVID 19 outbreak on voluntary demand for non COVID-19 healthcare, and their research has indicated a substantial decline in healthcare use is caused by the prevention of measures for COVID-19 [17]. Adwibowo (2020) has recorded the daily COVID-19 cases and has continued with the forecasting of the average daily demand (ADD) of healthcare facilities including beds, ICUs, and ventilators using the ARIMA model, and the model has shown that the healthcare ADD is different in each population [18]. Alshammari et al. (2021) have evaluated the potentiality of emerging technologies for controlling the COVID-19 transmission and ensuring health safety and their study has revealed that most people receive information from social networking sites, health professionals, and television without facing any challenges [19]. Brodie et al. (2021) have explored how adopting a service ecosystem perspective provides insight into the complexity of healthcare systems during times of COVID-19, and they have provided an understanding of the relevance

of managerial flexibility, innovation, learning, and knowledge sharing [20]. Arlotti and Ranci (2021) have argued that the negative impact of COVID-19 stems from the poor development of long-term care policy and the marginality of residential institutions within the Italian healthcare system [21]. Rodríguez and Hignett (2021) have presented a model for integrating Human Factors/Ergonomics into healthcare systems to make them more robust and resilient during the COVID-19 pandemic, and they have argued that it is crucial to have a systems vision focused on optimizing the interactions people and other healthcare systems elements [22]. Akiyama et al. (2020) have described how their experience with inpatient care has changed in the wake of COVID-19 and they have determined that COVID-19 hospital discharge rates surpass admission rates [23]. Tasri and Tasri (2020) have analyzed the competency influence of medical records and health information management on the planning and decision making of healthcare services, and they have concluded that the new tools or systems can be an alternative to improve healthcare management [24]. Bel et al. (2021) have built a theoretical model and used it to develop an empirical strategy, analyzing the drivers of policy-response agility during the outbreak, and according to their model, healthcare system capacity and cost-related variables have a significant influence on reaction time; therefore, this situation has negatively affected government strategy [25]. Chamboredon et al. (2020) have presented a brief history of the development of the pandemic in France, including the political decisions that have been taken to combat the outbreak, and they have argued that the history of the development of the pandemic helps explain the establishment of the state of health emergency and containment of the population. [26]. Leite et al. (2020) have evaluated the impact of the COVID-19 pandemic on healthcare systems' demand, resources, and capacity. Then they have discussed that the sustainability of lean post-pandemics is a new modern operational issue [27].

Currently, the world is facing a global health crisis COVID-19; however, ensuring healthy lives and promoting well-being at all ages is essential to sustainable development, and the pandemic provides a milestone for health emergency preparedness and investment in critical 21st-century public services [28]. The SDGs aim to be relevant to all countries to promote prosperity, and almost all of the other 16 goals are related to health, or their achievement will contribute to health implicitly [29]. The SDGs are a tremendous opportunity to improve the health of the people of the world, and to make progress on the SDGs, states/countries must invest more heavily in health services research [30]. To meet the SDG targets and improve health system quality, states/countries need to undertake a measurement agenda [31]. Measuring and assessing the efficiency of health systems has been explored to ensure the sustainability of countries'/states' health and social systems [32]. Furthermore, gaps in the efficiency of the healthcare system will interrupt achieving SDGs [33].

All of these research findings reveal that there is a close relationship between the efficiency of the healthcare system and the implications for sustainable development goals amid the COVID-19 pandemic.

### **3. Materials and Methods**

#### *3.1. Background of Data Envelopment Analysis (DEA)*

DEA is a nonparametric method of evaluating the relative efficiency of DMUs that use the same inputs to produce the same outputs, such as firms or public sector agencies [34–36]. DEA is widely used in many areas such as healthcare, banking, education, auditing, market research, and agriculture [37–40].

DEA has been used as a benchmarking and assessment tool in healthcare worldwide [21]. In addition, DEA is considered one of the most effective techniques for relative efficiency assessments, as it can evaluate multiple inputs and outputs simultaneously [22]. According to Ozcan (2009), since it is a multi-dimensional construct, the assessment of efficiency is often troublesome. Nevertheless, DEA addresses the limitations of ratio analysis and regression. Additionally, DEA uses multiple outputs and multiple inputs to identify efficiencies and inefficiencies and also to project how inefficient DMUs can become more

efficient, by identifying reference sets (best practices). A reference set function can be built from observed inputs and outputs [23].

DEA models can be divided into two main types; constant returns to scale (CRS), also known as CCR (Charnes-Cooper-Rhodes) model, was initially introduced by Charnes et al. in 1978 [41], and variable returns to scale (VRS), also known as BCC (Banker-Charnes-Cooper) model, was later developed by Banker et al. in 1984 [42]. While the CCR (CRS) model yields an objective assessment of overall efficiency, identifies the sources, and estimates the number of inefficiencies in this way, the BCC (VRS) model distinguishes between technical and scale inefficiencies by estimating pure technical efficiency and identifying possible increasing, decreasing, or constant returns to scale [20]. Unlike CCR (CRS) models, input and output efficiency are equal, BCC (VRS) models yield different input and output efficiencies [21]. In addition, while CCR (CRS) models can assume that economies of scale don't change as the size of service facility increases, BCC (VRS) models cannot assume that economies of scale don't change as the size of service facility increases [26].

DEA models can be either input-orientated or output-orientated. In the input-orientated case, the DEA method defines the frontier by seeking the maximum possible proportional reduction in input usage, with output levels held fixed for each DMU; in the output orientated case, the DEA method seeks the maximum proportional increase in output production, with input levels held constant for each DMU [43,44].

There are four DEA model classifications, also known as Basic Envelopment Models: CCR (CRS)-Input Orientation, CCR (CRS)-Output Orientation, BCC (VRS)-Input Orientation, and BCC (VRS)-Output Orientation [26].

The BCC (VRS) efficiency scores are considered pure technical efficiency scores, while CCR (CRS) efficiency scores are considered technical efficiency scores. On the other hand, scale efficiency can be calculated by dividing CCR (CRS) efficiency scores by BCC (VRS) efficiency scores [28].

The efficiency of each DMU is evaluated relative to optimal production patterns, which are computed from the performance of DMUs with input and output combinations that are the best of any peer DMU [40]. These evaluations result in an efficiency score that represents the degree of efficiency [45]. When the efficiency score for each DMU is a score of 1, it represents efficiency [40]. While DMUs with an efficiency score ranging from zero to one are defined as inefficient in the input-oriented models, DMUs with an efficiency score greater than 1 are defined as inefficient in the output-oriented models [43]. Once the efficiency frontier is set, the performance of inefficient DMUs can be improved by increasing the outputs quantities or decreasing the inputs quantities [46]. For this purpose, a reference set, also known as best practices, is identified for each inefficient DMUs [40,43].

According to Ozcan (2014), the performance of DMUs can be assessed either as fully efficient or weakly efficient. If one DMU's efficiency score is 1 and slack values (both input slack and outputs slacks) are 0, it is considered fully efficient [26]. On the other hand, while the slack value in an input "i" represents an additional inefficient use of input "i", the slack value in an output "r" represents an additional inefficient in the production of output "r" [21].

The basic efficiency measure is the ratio of total outputs to total inputs [17,21]. The mathematical structure and formulations of Basic Envelopment Models can be found in the studies of Cooper et al. (2006), Ozcan (2014), and Emrouznejad and Cabanda (2014) [20,22,24].

#### *3.2. Sample*

DMUs used in this study consist of 50 US states. The correct selection of DMUs to be compared is essential and DMUs should be homogeneous. In other words, DMUs should be performing the same tasks with similar objectives using the same inputs and outputs under the same set of market conditions [47]. The sample size is expected to be at least 2 or 3 times larger than the sum of the number of inputs and outputs [34]. This requirement was met, as the study has 50 DMUs, 4 inputs, and 4 outputs. Descriptive statistics of the sample are presented in Table 1.

**Table 1.** Descriptive statistics of the sample.

**Table 1.** *Cont.*

In this table, population data were provided from CovidActNow [48], and gross domestic product (GDP) and region data were provided Bureau of Economic Analysis (BEA) [49].

## *3.3. Inputs, Outputs, and Data*

Since the input-output combination preferred by DMUs should produce an output bundle from the input bundle, it should be technically feasible [35]. In these bundles, both good (desirable) and bad (undesirable) inputs and outputs factors may be available [24]. When evaluating DMUs' efficiency, the desirable and undesirable factors should be addressed differently. Because in the standard DEA model, increases in undesirable inputs and desirable outputs are allowed, similarly, decreases in undesirable outputs and desirable inputs are allowed [50].

The operations strategy matrix mentioned earlier was used as the primary measurement tool.

Data used for inputs and outputs were collected from many databases, public and private agencies, web pages, etc. in the US for 17 months (from 22 January 2020 to 27 June 2021). The data source of each input and output is mentioned in its description.

There are four inputs used in the analysis; these are Decision Areas/Strategic Decision Areas in the Operations Strategy Matrix adapted from Slack and Lewis (2017) and Karuppan et al. (2016) as the main input framework [15,51].

Capacity (i1): An operation's capacity is the maximum level of value-added activity that it can perform under normal conditions [15]. Capacity measures can be based on outputs or the availability of inputs [52]. Most healthcare facilities' capacity indicators are composed of volume measures per reporting period [53]. The capacity of healthcare systems is determined by the capacity of each server and the number of servers being used [40]. According to the CDC, as an essential disease control measure used by local and state health department personnel for decades, contact tracing is a key strategy for preventing the further spread of COVID-19. Thus, it requires people with the training [54]. On the other hand, Donabedian's Model has argued that personnel is an input measure of healthcare quality [13]. The Capacity, therefore, is represented by the "Contact Tracer Capacity Ratio" in this study. Data were provided from CovidActNow [48].

Supply Network (i2): Since a supply network perspective is defined as setting an operation with all the other operations, it interacts with materials, parts, ideas, information, data, knowledge, and people all flow through the supply network formed by all these operations [55]. The Supply network involves the design and management of seamless inter and intra-organizational processes [39]. Moreover, material, information, and capital flows must be sustainable [40]. However, COVID-19 has created trouble to manage a sufficient supply network [41]. Since COVID-19 vaccines reduce the risk of people spreading the virus, vaccinations are vital to get population immunity [56–59]. COVID-19 vaccines and

ancillary supplies are procured and distributed by the US federal government at no cost to jurisdictions (states, territories, tribes, and local entities) [60,61]. The transportation ecosystem provides the technologies, services, and processes necessary to facilitate market penetration [44]. According to CDC, distribution is the process of shipping vaccines to provider locations, as directed by jurisdictions, federal agencies, and pharmacy partners who are enrolled in the COVID-19 Vaccination Program. Vaccine delivery is the last part of the distribution process. Deliveries represent the vaccine doses that have arrived at their destination [62]. The Supply Network, therefore, is represented by the "Distributed Vaccine Amount/Per Capita" in this study. Data were provided from CovidActNow [48].

Process Technology (i3): Process technology refers to the machines, devices, and equipment that create and deliver products and services [55]. Process technologies can be classified into three types: material processing technologies such as flexible manufacturing systems, information processing technologies such as optical character-recognition machines, and customer processing technologies such as medical equipment/devices [15]. The successful delivery of health care depends on medical devices; therefore, the Management of Medical Equipment (MME) is considered the most critical component within Health Systems [63]. The SEIR model attempts to predict how a disease will evolve in a population. Accordingly, all of the COVID-19 deaths have progressed from ICU cases [64]. On the other hand, Donabedian's Model has argued that facilities and equipment are input healthcare quality measures [13]. The Process Technology, therefore, is represented by the "Intensive Care Unit (ICU) Bed Capacity/Per 100,000 Population" in this study. Data were provided from CovidActNow [48].

Development and Organization (i4): This input is concerned with a broad and longterm set of decisions governing how the operation is run continuingly due to different employees having different tolerance for risk and ambiguity [15]. Additionally, it includes the workforce organization, planning and control, and improvement activities as an infrastructural decision [55]. Since COVID-19 has swept across the USA, it became clear that certain factors—such as healthcare systems—make some states more vulnerable to its impact [65]. Vulnerability is a state of sensitivity to disaster [66]. States with higher vulnerability have pre-existing economic, social, and physical conditions that may make it hard to respond to the COVID-19 outbreak [67]. According to Surgo Ventures, the COVID-19 Community Vulnerability Index (CCVI), developed by Surgo Ventures, evaluates how well any state could respond to the health, economic and social consequences of COVID-19 without appropriate response and additional support. It ranges from 0 to 100 and constitutes seven themes: Socioeconomic Status, Minority Status & Language, Household & Transportation, Epidemiological Factors, Healthcare Systems Factors, High-Risk Environments, and Population Density. Theme 5, Healthcare System Factors, measure the capacity, strength, accessibility, and preparedness of the healthcare system to respond to the COVID-19 outbreak [68]. Development and Organization, therefore, is represented by the "The COVID-19 Community Vulnerability Index (Theme 5: Healthcare System Factors)" in this study. Data were provided from Surgo Ventures (Precision for COVID) [68].

There are four outputs, two of which undesirable output, used in the analysis: these are Competitive Priorities or Performance Objectives in the Operations Strategy Matrix adapted from Slack and Lewis (2017) and Karuppan et al. (2016) as the main output framework [15,51].

Quality (o1): Since quality usually means the high specification of a product or service [15], it can be defined as consistent conformance to customers' expectations [15,55]. Because quality has two dimensions, high-performance design and, goods and services consistency [69], in the healthcare area, quality means that patients receive the most appropriate treatment and that their treatment is carried out correctly [55]. Adopting the most effective prevention and treatment practices for the leading causes of mortality, and enabling healthy living are healthcare systems' priorities [51]. On the other hand, Donabedian's Model has argued that patient experience, restoration of function, recovery, and survival are the output measure of healthcare quality [13]. Therefore, as an undesirable

output, Quality, is represented by the "Deaths/1M Population" in this study. Data were provided from Worldometers [1].

Cost (o2): As a competitive priority, cost means offering a product or a service at a low price relative to the substitute's product or service prices [69]. Even organizations that compete on things other than price are interested in keeping their costs low [15]. Economic efficiency considers whether a given output is produced at a low cost [13]. In the healthcare area, the total cost includes the costs of resources such as material, equipment, people, facilities, and the costs inherent in the transformation process [51]. According to USASpending.Gov; in early 2020, the U.S. Congress appropriated funds in response to the COVID-19 pandemic. These funds were made possible through the Coronavirus Aid, Relief, and Economic Security (CARES) Act and other supplemental legislation. In March 2021, additional funds were appropriated through the American Rescue Plan Act. Once the federal government has determined that an individual, organization, business, or state, local, or tribal government will receive an award, the money is obligated (promised) and then outlay (paid) according to the terms of the contract or financial assistance [70]. Therefore, as an undesirable output, the cost is represented by the "Award Outlays/Per Capita Spending" in this study. Data were provided from USASpending.Gov [70].

Delivery (o3): Delivery, as a competitive priority, refers to the ability to provide services on time (on-time delivery) or to deliver the services faster (rapid delivery) than the competitors [51]. Rapid delivery means how quickly an order is received, while on-time delivery means how often deliveries are made on time [69]. Healthcare delivery includes many repetitious workflows, such as filling prescriptions, reporting laboratory test results, and completing radiology images [71]. Donabedian's Model has argued that preventive management, coordination, and continuity of care, acceptability of care to the recipient are the process measure of healthcare quality [13]. Immunization with a safe and effective COVID-19 vaccine is a critical component of the United States strategy to reduce COVID-19-related conditions [60]. Vaccines are widely accessible in the United States and are available for everyone at no cost [59]. Percent vaccinated is the percentage of the total population of a state that has started the vaccination process by receiving at least their first dose [67]. Therefore, delivery is represented by the "Vaccinated Rate (+1 Dose)" in this study. Data were provided from CovidActNow [48].

Flexibility (o4): Flexibility means being able to change the operation anywise [55]. Competing on flexibility refers to responding to changes with minimal penalties [51]. One operation that can exhibit a wide range of abilities is more flexible than another [15]. As customer demand is increasing, organizations are increasingly promoting different models of their products and service [72]. A flexible system can rapidly increase or decrease the quantity of production to meet demand fluctuations [69]. Some operational uncertainties can be balanced by systematic flexibility [73]. In the healthcare area, excess capacity or a flexible workforce is often required to meet demand fluctuations [52]. An essential metric for coping with demand fluctuations caused by COVID-19 is whether hospitals can handle the increased load of new COVID-19 cases without resorting to crisis standards of care [64]. Flexibility, therefore, is represented by the "Available ICU Capacity (by percentage)" in this study. Data were provided from CovidActNow [48].

According to the explanations above, it is assumed that the input bundle used by DMUs can produce the output bundle in the Operations Strategy Matrix.

Summary statistics of inputs and outputs are presented in Table 2.

**Table 2.** Summary statistics of inputs and outputs.

## *3.4. Analysis Design*

The analysis consists of two stages. In the first stage; since there are two undesirable (bad) outputs in the dataset, BCC (VRS)-Output Orientation DEA model was employed in this study. The model proposed by Seiford and Zhu (2002) was applied for undesirable outputs [50]. Then, DMUs were evaluated using pure technical efficiency scores, a reference set was identified for each inefficient DMUs, and improvement options of inefficient DMUs were calculated. In addition to this, fully efficient DMUs are determined based on efficiency scores and slack values. All analyses were performed using the deaR package in the R project [74].

In the second stage; an independent-samples *t*-test was conducted to compare DMUs' populations in the efficiency and inefficient conditions and an independent-samples *t*-test was conducted to compare DMUs' gross domestic product (GDP) in the efficiency and inefficient conditions.

## **4. Results**

Pure technical efficiency scores and inputs/outputs values of US states are shown in Table 3.

**Table 3.** Pure technical efficiency scores and input/output values.

**Table 3.** *Cont.*

According to Table 3, Alaska, Arkansans, Arizona, Connecticut, Hawaii, Idaho, Kentucky, Louisiana, Massachusetts, Maine, Minnesota, Missouri, Mississippi, Montana, North Carolina, North Dakota, Nebraska, New Jersey, New Mexico, Nevada, Oregon, Rhode Island, South Carolina, Tennessee, Utah, Virginia, Vermont, Washington, Wisconsin, West Virginia, and Wyoming have a score of 1, and they are relatively efficient.

Based on Ozcan (2009) and Ozcan (2014), a reference set, also known as best practices, was identified for each inefficient DMUs to become efficient [40,43]. Improvement options for the inefficient states are shown in Table 4.

**Table 4.** Improvement options for the inefficient states.

According to Table 4:

As shown in Table 5, independent samples *t*-tests were conducted to compare DMUs' populations and gross domestic product (GDP) in the efficiency and inefficient conditions.

According to Table 5:

## **5. Discussion**

COVID-19 pandemic is a complex and unprecedented public health crisis worldwide. It is crucial to evaluate health systems for mitigating the impact of the COVID-19 pandemic [6].

Although all countries are affected by the pandemic, the United States is the country with the highest number of COVID-19 cases and deaths reported as of 27 June 2021. Therefore, both the CDC and each state's health department are committed to stopping its spread.

CDC's global COVID-19 response works toward the goals mentioned above by meeting the following objectives: strengthening healthcare system capacity to prevent, detect, and respond to local COVID-19 cases; mitigating COVID-19 transmission in the community, across borders, and in healthcare facilities; contributing to the scientific understanding of COVID-19; ensuring readiness to implement and evaluate vaccination programs [2].

Since healthcare systems rely heavily on scientific analysis to find results that can be generalized to a larger context [9], the evaluation should be both critical and as objective as possible [14]. Operation Strategy Matrix is a novel and objective evaluation tool. The matrix deal with how Strategic Decision Areas (Capacity, Supply Network, Process Technology, Development and Organization) affect Competitive Priorities (Quality, Cost, Delivery, Flexibility) [15].

DEA has been used widely in assessing healthcare efficiency in the United States and around the world at different levels of decision-making units [43]. Therefore, each U.S State's Operation Strategy Matrix was evaluated using DEA in the context of the COVID-19 pandemic. During the analysis, Strategic Decision Areas (Capacity, Supply Network, Process Technology, and Development and Organization) were considered as inputs while competitive priorities (Quality, Cost, Delivery, and Flexibility) were considered as outputs. Capacity was represented by "Contact Tracer Capacity Ratio". Supply Network was represented by "Distributed Vaccine Amount/Per Capita". Process Technology was represented by "Intensive Care Unit (ICU) Bed Capacity/Per 100,000 Population". Development and Organization was represented by "The COVID-19 Community Vulnerability Index (Theme 5: Healthcare System Factors)". Quality was represented by "Deaths/ 1M Population". The cost was represented by "Award Outlays/Per Capita Spending". Delivery was represented by "Vaccinated Rate (+1 Dose)". Flexibility was represented by "Available ICU Capacity (by percentage)". Additionally, since there are two undesirable (bad) outputs in the dataset, BCC (VRS)-Output Orientation Data Envelopment Analysis model was employed. Inputs (Capacity, Supply Network, Process Technology, and Development and Organization) are essential components of any operations including healthcare operations while outputs (Quality, Cost, Delivery, and Flexibility) are results of the inputs.

According to the results, 31 states are efficient, while 19 states are inefficient. Additionally, Connecticut, Louisiana, Minnesota, New Jersey, Rhode Island, Tennessee, Utah, Vermont, Washington, and Wyoming are fully efficient DMU based on efficiency scores and slack values.

A reference set was identified for each inefficient DMUs to become efficient. In the reference sets:

Additionally, the DMUs that need the most improvement are New York, Maryland, Pennsylvania, South Dakota, Alabama, and Texas.

It is relatively hard limiting the human-to-human transmission of COVID-19 in large communities because independent samples *t*-test results demonstrate that inefficient states have more population than efficient states. Moreover, 62.25% of the total US population lives in inefficient states, and 9 out of 12 states in the 3rd Population Quartile (7,845,049.50) are inefficient, while 9 out of 12 states in the 1st Population Quartile (1,790,876.50) are efficient. Furthermore, only 10.70% of the total US population lives in fully efficient states.

Economic and human mobility is maximum in the states with high GDP. For this reason, the spreading of the virus is fast. Hence, independent samples *t*-test results demonstrate that inefficient states have more GDP than efficient states. Moreover, 64.14% of the total US GDP is formed by inefficient states and 8 out of 12 states in the 3rd GDP Quartile (587,874.25) are inefficient, while 9 out of 12 states in the 1st GDP Quartile (91,862.25) are efficient. Additionally, only 13.69% of the total U.S GDP is formed by fully efficient states. From the perspective of BEA region grouping [49]:

New England and Far West are the most efficient regions while Mideast and Great Lakes are the least efficient regions by percentages. These results are in line with the population and GDP findings mentioned above. Additionally, three out of six states are fully efficient in the New England Region and 1 of 6 states is fully efficient in the Far West Region.

The SDGs are a universal agenda taking various aspects in development into account and applying them to all countries [75–77]. According to the United Nations Department of Economic and Social Affairs, SDG 3 is described as ensuring healthy lives and promoting well-being for all at all ages, and COVID-19 has shortened life expectancy [10]. United Nations has called the COVID-19 pandemic, beyond being a health emergency, as a systemic crisis that is already affecting economies and societies in unprecedented ways [72]. United Nations has created so that the countries cope with the pandemic, and the dashboards include some indicators such as the capacity of the healthcare system, vulnerability, and poverty [73]. These indicators are also included in our research model with the same or close names.

This study had some limitations. Since COVID-19 is a global pandemic, it is difficult to assess its effect on health systems. Additionally, data used for inputs and outputs were collected from many databases, public and private agencies, web pages, etc., in the US mentioned above. As such these databases were considered to be correct. Furthermore, data include 17 months from 22 January 2020 to 27 June 2021.

### **6. Managerial Implication and Conclusions**

This study provides the first overview of the healthcare systems of U.S. states in the context of COVID-19, based on the first 17 months of the pandemic. The use of a novel evaluation tool named Operation Strategy Matrix constitutes the unique aspect of the study. Thus, the study is important for healthcare operations research literature.

The study results might contribute to both the federal and state health authorities; while the inefficient states can become efficient by applying our improvement suggestions, the federal government can develop new strategies to mitigate the COVID-19 pandemic considering our findings especially inductive statistical findings regarding population, GDP, and region.

Since SGDs address the global challenges we face, it could be yielded some critical projections for the future from the study's findings. Moreover, our research findings might help to ensure healthy lives in the context of COVID-19. The reference sets identified for each inefficient DMUs to become efficient can be used for both the US and other countries to achieve SDG Goal 3 amid COVID-19. Especially, fully efficient states (Connecticut, Louisiana, Minnesota, New Jersey, Rhode Island, Tennessee, Utah, Vermont, Washington, and Wyoming) can be served as a model to achieve Targets 3.8, 3. c, and 3.d.

Further studies can be developed new models applying different DEA approaches (Fuzzy DEA, Two-Stage DEA, Network DEA, etc.) to prioritize issues, challenges, drivers, and barriers related to healthcare systems and SDGs in the context of the COVID-19 pandemic.

**Author Contributions:** Conceptualization, A.Ö., H.K., M. ¸S.G., and E.C.; methodology, A.Ö., H.K., M. ¸S.G., and E.C.; software, A.Ö., H.K., M. ¸S.G., and E.C.; validation, A.Ö., H.K., M. ¸S.G., and E.C.; formal analysis, A.Ö., H.K., M. ¸S.G., and E.C.; investigation, A.Ö., H.K., M. ¸S.G., and E.C.; resources, A.Ö., H.K., M. ¸S.G., and E.C.; data curation, A.Ö., H.K., M. ¸S.G., and E.C.; writing—original draft preparation, A.Ö., H.K., M. ¸S.G., and E.C.; writing—review and editing, A.Ö., H.K., M. ¸S.G., and E.C.; visualization, A.Ö., H.K., M. ¸S.G., and E.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

72. Mamun, A.A.; Khaled, A.A.; Ali, S.M.; Chowdhury, M.M. A heuristic approach for balancing mixed-model assembly line of type i using genetic algorithm. *Int. J. Prod. Res.* **2012**, *50*, 5106–5116. [CrossRef]

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**4.1 Color sensing by Cphs and CBCRS**

Cyanobacterial proteins contain the accompanying regions PAS-GAF-PHY [48]. Entire genome sequencing of cyanobacterial species, for example, *Microcoleus* IPAS B373 [49], *Euhalothece* Z-M001 [44], and *Tolypothrix* PCC7910 [50] are devoid of gene HY2, for phytochromobilin (PФB) synthase. Further, these cyanobacteria have pcyA gene that encodes phycocyanobilin (PCB): ferredoxin oxidoreductase that catalyzes the conversion of biliverdin (BV) to PCB, a significant cofactor of Cphs and CBCRs [32, 51]. The quantity of Cphs and CBCRs differ among cyanobacteria, *Euhalothece* has 3 numbers, *Synechocystis* (8), *Microcoleus* IPAS B353 (9), *Acaryochloris marina* (12), *N. punctiforme* (18), and *Tolypothrix* PCC 7910 (36). In cyanobacterium, the complete number of bilin photoreceptors relies upon the size of its genome [49]. Besides, CBCRs are more plentiful in cyanobacteria, than Cphs, and the proportion of CBCRs for blue to red is corresponding to the environmental light conditions. For example, *Microcoleus* IPAS B353 grown in UV light developed only violet CBCRs than red/green and green/red CBCRs. Generally, UV light is recommended to develop and improve the quantity of short wavelength responsive CBCR [49].


**1. Introduction**

According to the 2020 Global Status Report for Buildings and Construction published in 2019, the sector moved away from the Paris Agreement goals by causing the highest CO2 emissions ever recorded: around 10 Gt CO2, or 28% of total global energy-related CO2 emissions [1,2]. The increase is mainly related to the carbon-intensive manufacturing processes of building construction materials; therefore, it is crucial to develop novel material strategies to mitigate carbon emissions during the lifecycle of buildings.

Although using renewable raw materials, e.g., wood, presents itself as a logical strategy to withstand CO2 emissions, the main problem lies in their production, or, more precisely, their growing time. Looking for alternative renewable materials, recent research has suggested that fast-growing organisms such as Fungal mycelium can be engineered to produce novel construction materials [3–6]. Mycelium-based composite production is based on the use of lignocellulosic substrates in combination with the natural growth of the vegetative component of the mycelium of filamentous fungi. As filamentous fungi grow, they form hyphae, which result in a close-meshed network and give the resulting material a solid structure. Such composites have many advantages, such as good thermal insulation, low dry density, and sound absorption. These properties make them suitable for use as building materials (e.g., as insulating materials), but they represent a challenge in their load-bearing capacity.

Our team has been conducting research experiments by developing methods for influencing hyphal growth with the primary objective to provide a mycelium-based composite

**Citation:** Saez, D.; Grizmann, D.; Trautz, M.; Werner, A. Exploring the Binding Capacity of Mycelium and Wood-Based Composites for Use in Construction. *Biomimetics* **2022**, *7*, 78. https://doi.org/10.3390/ biomimetics7020078

Academic Editors: Andrew Adamatzky, Han A.B. Wösten, Phil Ayres and Stanislav N. Gorb

Received: 19 March 2022 Accepted: 9 June 2022 Published: 11 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

with particular stability and increased strength [7–11]. In this paper, we describe a manufacturing method of mycelium and wood-based composites where the binding capacity of mycelium plays a crucial role. The fabrication process leads to the fungal mycelium forming predominantly skeletal hyphae at the joint interface of the composite material, which, due to its morphology, leads to increased material strength (Figure 1). This increased strength opens up new application possibilities that go beyond the applications as insulation material or leather substitute [12]. posite with particular stability and increased strength [7–11]. In this paper, we describe a manufacturing method of mycelium and wood-based composites where the binding capacity of mycelium plays a crucial role. The fabrication process leads to the fungal mycelium forming predominantly skeletal hyphae at the joint interface of the composite material, which, due to its morphology, leads to increased material strength (Figure 1). This increased strength opens up new application possibilities that go beyond the applications as insulation material or leather substitute [12].

Our team has been conducting research experiments by developing methods for influencing hyphal growth with the primary objective to provide a mycelium-based com-

*Biomimetics* **2022**, *7*, 78 2 of 8

**Figure 1.** (**a**) The conceptual illustration describes the systematical formation of skeletal hyphae: the dashed line symbolizes the material interfaces (1); the rectangles, substrate consisting of coarse (2) and fine (3) wood chips; and the blue lines, the dense network of mycelial threads (4). The photos show the growth of mycelial cross-linked growth over time (**b**) after two weeks, (**c**) after three weeks, and (**d**) after four weeks. **Figure 1.** (**a**) The conceptual illustration describes the systematical formation of skeletal hyphae: the dashed line symbolizes the material interfaces (1); the rectangles, substrate consisting of coarse (2) and fine (3) wood chips; and the blue lines, the dense network of mycelial threads (4). The photos show the growth of mycelial cross-linked growth over time (**b**) after two weeks, (**c**) after three weeks, and (**d**) after four weeks.

### **2. Materials and Methods 2. Materials and Methods**

### *2.1. Fungal–Substrate Composition 2.1. Fungal–Substrate Composition*

The findings of this study concern a specific fungal–substrate composition: the fungal mycelium is derived from *Ganoderma lucidum* (GL) and *Pycnoporus sanguineus* (PS), and the substrate is beechwood. Fungi belonging to the genus *Basidiomycetes*, such as GL, *Ganoderma applanatum*, *Trametes hirsuta*, *Trametes versicolor*, or *Fomes fomentarius*, are mostly found in forests and fulfill, among other things, the task of decomposing deadwood. Consequently, we chose timber as the lignocellulosic substrate. Wood consists of approx. 25–30 wt % lignin, 25–30 wt % pentosans (hemicellulose), 40–50 wt % cellulose, and other components such as resinous substances, terpenes fats, fatty acids, proteins, and minerals. Fungi can decompose lignin, hemicellulose, and cellulose into their subunits by releasing enzymes such as cellulases, laccases, amylases, proteases, or lipases into the immediate environment to degrade the substrate. Subsequently, the degradation products are absorbed by the hyphae and used to grow the fungus [10]. The selection of beechwood as the substrate is a consequence of this research team's previous investigations [2,4,10]. Although the methodology we are about to describe could be transferred to other fungal– substrate compositions, the test results may differ. The findings of this study concern a specific fungal–substrate composition: the fungal mycelium is derived from *Ganoderma lucidum* (GL) and *Pycnoporus sanguineus* (PS), and the substrate is beechwood. Fungi belonging to the genus *Basidiomycetes*, such as GL, *Ganoderma applanatum*, *Trametes hirsuta*, *Trametes versicolor*, or *Fomes fomentarius*, are mostly found in forests and fulfill, among other things, the task of decomposing deadwood. Consequently, we chose timber as the lignocellulosic substrate. Wood consists of approx. 25–30 wt% lignin, 25–30 wt% pentosans (hemicellulose), 40–50 wt% cellulose, and other componentssuch as resinous substances, terpenes fats, fatty acids, proteins, and minerals. Fungi can decompose lignin, hemicellulose, and cellulose into their subunits by releasing enzymes such as cellulases, laccases, amylases, proteases, or lipases into the immediate environment to degrade the substrate. Subsequently, the degradation products are absorbed by the hyphae and used to grow the fungus [10]. The selection of beechwood as the substrate is a consequence of this research team's previous investigations [2,4,10]. Although the methodology we are about to describe could be transferred to other fungal–substrate compositions, the test results may differ.

### *2.2. Binding-Specific Manufacturing 2.2. Binding-Specific Manufacturing*

As mentioned before, we seek to provide a mycelium-based composite with a particularly stable and increased strength for use in construction. The manufacturing method proposed consists of the following steps: As mentioned before, we seek to provide a mycelium-based composite with a particularly stable and increased strength for use in construction. The manufacturing method proposed consists of the following steps:

(5) Placing the obtained incubated mixture from Step (4) in shaping containers defining the shape of the base unit of the composite material, and incubating the mixture in a second incubation phase for a time between 3 and 10 days, at a temperature ranging from 20 ◦C to 30 ◦C, and at humidity ranging from 80% to 95% in order to obtain the cross-linked growth of the mycelium around the substrate. (5) Placing the obtained incubated mixture from Step (4) in shaping containers defining the shape of the base unit of the composite material, and incubating the mixture in a second incubation phase for a time between 3 and 10 days, at a temperature ranging from 20 °C to 30 °C, and at humidity ranging from 80% to 95% in order to obtain the cross-linked growth of the mycelium around the substrate.

ranging from 80% to 95% to achieve the cross-linked growth of the mycelium around

*Biomimetics* **2022**, *7*, 78 3 of 8

the substrate.

**Figure 2.** Conceptual illustrations describing the manufacturing process**:** (**a**) incubation phase II of basic units; (**b**) basic units with binding interface after incubation; (**c**) joining of two basic units; (**d**) incubation phase III of the composite test specimen. **Figure 2.** Conceptual illustrations describing the manufacturing process: (**a**) incubation phase II of basic units; (**b**) basic units with binding interface after incubation; (**c**) joining of two basic units; (**d**) incubation phase III of the composite test specimen.

(8) Denaturizing the specimen at a temperature range of 65 °C to 90 °C and obtaining a mycelium-based lignocellulosic composite with a residual moisture content of 10% to 12% by weight based on the total weight of the composite. (8) Denaturizing the specimen at a temperature range of 65 ◦C to 90 ◦C and obtaining a mycelium-based lignocellulosic composite with a residual moisture content of 10% to 12% by weight based on the total weight of the composite.

Steps (1)–(4) of the manufacturing process are similar to those described in the previous publications of this research team [10]. It is in Step (5) that upon completion of the second incubation phase, at least one base unit of the composite material with at least one binding interface is obtained. A "binding interface" in the present research context refers to the surface to which a different base unit of the composite material can be attached. In the subsequent Step (6), at least two base units of the composite material are provided and subsequently joined so that the binding interfaces of the subunits are joined, as well. Steps (1)–(4) of the manufacturing process are similar to those described in the previous publications of this research team [10]. It is in Step (5) that upon completion of the second incubation phase, at least one base unit of the composite material with at least one binding interface is obtained. A "binding interface" in the present research context refers to the surface to which a different base unit of the composite material can be attached. In the subsequent Step (6), at least two base units of the composite material are provided and subsequently joined so that the binding interfaces of the subunits are joined, as well.

A proper joining configuration is achieved by placing at least two basic units against each other, even though more basic units are able to be attached to form the compound units. Subsequently, the joined basic units are incubated in a third incubation phase (Step (7)). The fungal mycelium grows within the binding interface and couples the two basic units of the composite material. A proper joining configuration is achieved by placing at least two basic units against each other, even though more basic units are able to be attached to form the compound units. Subsequently, the joined basic units are incubated in a third incubation phase (Step (7)). The fungal mycelium grows within the binding interface and couples the two basic units of the composite material.

Finally, the composite material obtained in Step (8) is denaturized to bulk consistency. A mycelium and wood-based lignocellulose composite material is obtained with 10% to 15% residual moisture content. Finally, the composite material obtained in Step (8) is denaturized to bulk consistency. A mycelium and wood-based lignocellulose composite material is obtained with 10% to 15% residual moisture content.

All manufacturing process steps described above result in the fungal mycelium forming predominantly skeletal hyphae at the joint interface of the composite material, which, due to its morphology, leads to the increased strength of the material in the binding interface. All manufacturing process steps described above result in the fungal mycelium forming predominantly skeletal hyphae at the joint interface of the composite material, which, due to its morphology, leads to the increased strength of the material in the binding interface.

## *2.3. Planar and Non-Planar Binding Interface*

The present research developed a method wherein the binding interface of at least two basic units has a non-planar surface and wherein a factor between 1.2 and 5 enlarges the binding interface compared to that of a planar surface. Whether the surface area of the bonding interfaces is increased by non-planar joint means that the surface of the connection interface has teeth-like interlocking. It could be arranged symmetrically or asymmetrically, which can be connected by the interface of at least two basic units with teeth-like interlocking in the longitudinal section. rically, which can be connected by the interface of at least two basic units with teeth-like interlocking in the longitudinal section. The surface of the connecting interface of the base units is enlarged with teeth-like

The present research developed a method wherein the binding interface of at least two basic units has a non-planar surface and wherein a factor between 1.2 and 5 enlarges the binding interface compared to that of a planar surface. Whether the surface area of the bonding interfaces is increased by non-planar joint means that the surface of the connection interface has teeth-like interlocking. It could be arranged symmetrically or asymmet-

*Biomimetics* **2022**, *7*, 78 4 of 8

*2.3. Planar and Non-Planar Binding Interface*

The surface of the connecting interface of the base units is enlarged with teeth-like interlocking with jagged (see test specimens Sch2 and Sch3) or rounded protrusions (see test specimens Sch4 and Sch5). These protrusions may be continuous or have at least one short planar section between each jag or curve. interlocking with jagged (see test specimens Sch2 and Sch3) or rounded protrusions (see test specimens Sch4 and Sch5). These protrusions may be continuous or have at least one short planar section between each jag or curve. Six different shaping containers were developed to compare, on the one hand, a sin-

Six different shaping containers were developed to compare, on the one hand, a single test specimen as a single solid unit (Sch0), without binding interface, with at least two base units test samples (Sch1–5). On the other hand, different geometries of the binding interface were developed to compare the influence of the planar and non-planar binding interfaces. gle test specimen as a single solid unit (Sch0), without binding interface, with at least two base units test samples (Sch1–5). On the other hand, different geometries of the binding interface were developed to compare the influence of the planar and non-planar binding interfaces.

Each container had a 134.4 cm3 capacity. Figure 3 and Table 1 describe the exact shapes and sizes of the junction interfaces. Each container had a 134.4 cm3 capacity. Figure 3 and Table 1 describe the exact shapes and sizes of the junction interfaces.

**Figure 3.** Meso-scale samples for shear tests*.*  **Figure 3.** Meso-scale samples for shear tests.

**Table 1.** Surface and geometry of the binding interface of the test specimens described in Figure 1. **Table 1.** Surface and geometry of the binding interface of the test specimens described in Figure 1.

### *2.4. Shear Tests 2.4. Shear Tests*

Test methods determined the shear strength of the test specimens according to DIN-EN 12090:2013 test standards as illustrated in Figure 4. The test specimens were manufactured as described in Section 2.2 with a consistent filling density of 0.5 g/cm3 in a cubelike container (a × a × h). Due to the exploratory character of the testing, two different substrate–fungus combinations were tested: beechwood–GL and beechwood–PS. This variation led to a total amount of 24 Sch test specimens. The shear tests were conducted under laboratory conditions with the corresponding setup, using a Zwick Zmart.Pro testing machine with a testing speed of 3 mm/min. The tests were documented with the help of photographs, and the force deformation curve was digitally recorded with ZickRoell software. The recorded data were subsequently edited and graphically represented in strength diagrams. Test methods determined the shear strength of the test specimens according to DIN-EN 12090:2013 test standards as illustrated in Figure 4. The test specimens were manufactured as described in Section 2.2 with a consistent filling density of 0.5 g/cm3 in a cube-like container (a × a × h). Due to the exploratory character of the testing, two different substrate–fungus combinations were tested: beechwood–GL and beechwood–PS. This variation led to a total amount of 24 Sch test specimens. The shear tests were conducted under laboratory conditions with the corresponding setup, using a Zwick Zmart.Pro testing machine with a testing speed of 3 mm/min. The tests were documented with the help of photographs, and the force deformation curve was digitally recorded with ZickRoell software. The recorded data were subsequently edited and graphically represented in strength diagrams.

**Figure 4.** (**a**) Conceptual illustration describing the testing setup. Test specimens being tested under DIN-EN Standards: (**b**) Sch0, specimen with no binding interface; (**c**) Sch1, specimen with planar binding interface; and (**d**) Sch3, specimen with big jagged interface. **Figure 4.** (**a**) Conceptual illustration describing the testing setup. Test specimens being tested under DIN-EN Standards: (**b**) Sch0, specimen with no binding interface; (**c**) Sch1, specimen with planar binding interface; and (**d**) Sch3, specimen with big jagged interface.

### **3. Results 3. Results**

The obtained material was examined to determine its shear strength. As mentioned before, the tests were carried out on Sch0 to Sch5 test specimens under DIN-EN 12090:2013. The force–displacement curve was recorded for each test, and the shear strength was derived from it (Figure 5). The obtained material was examined to determine its shear strength. As mentioned before, the tests were carried out on Sch0 to Sch5 test specimens under DIN-EN 12090:2013. The force–displacement curve was recorded for each test, and the shear strength was derived from it (Figure 5).

The first set of analyses presented an apparent variation in fracture behavior. As shown in Figure 5, the blue curves reported significantly less resistance than the rest. Therefore, we can conclude an increase in the material strength of the test specimens developed under binding-specific manufacturing (described in Section 2.2, tests Sch1–5) against those produced under single manufacturing without a binding interface [10]. By repeating the shear tests, this observation was confirmed. These tests were conducted with two different substrate–fungi variations: My8, to beechwood–GL, and My9, to beechwood–PS. Compared with My8, the tests on My9 present significantly less shear re-The first set of analyses presented an apparent variation in fracture behavior. As shown in Figure 5, the blue curves reported significantly less resistance than the rest. Therefore, we can conclude an increase in the material strength of the test specimens developed under binding-specific manufacturing (described in Section 2.2, tests Sch1–5) against thoseproduced under single manufacturing without a binding interface [10]. By repeatingthe shear tests, this observation was confirmed. These tests were conducted with two different substrate–fungi variations: My8, to beechwood–GL, and My9, to beechwood–PS. Compared with My8, the tests on My9 present significantly less shear resistance.

sistance. Non-homogeneous growth on the test specimens may have contributed to the increased variation in the curves in both My8 and My9. The growth variety may result from non-proper environmental conditions in one or more of the cultivation stages during man-Non-homogeneous growth on the test specimens may have contributed to the increased variation in the curves in both My8 and My9. The growth variety may result from non-proper environmental conditions in one or more of the cultivation stages during manufacturing.

ufacturing. From the observation of the red curve (Sch1 = planar binding interface) in contrast to the rest of them (Sch0 = no binding interface; Sch2–5 = non-planar binding interface), an influence on the geometry of the inner binding interfaces can be deduced. Consequently, different interface geometries influence the material's behavior in terms of failure mode, stiffness, and shear strength. The force–displacement curve of specimen Sch1 (red curves) with a planar connection interface, for example, demonstrates an early start of material fracture, which is indicated by a sharp drop in the curve. However, due to the significant curve variation, it has not been possible to determine whether the surface area increase or geometry variation in the binding interface has increased the resistance. Additionally, it would be necessary to repeat the tests with a more significant number of test specimens From the observation of the red curve (Sch1 = planar binding interface) in contrast to the rest of them (Sch0 = no binding interface; Sch2–5 = non-planar binding interface), an influence on the geometry of the inner binding interfaces can be deduced. Consequently, different interface geometries influence the material's behavior in terms of failure mode, stiffness, and shear strength. The force–displacement curve of specimen Sch1 (red curves) with a planar connection interface, for example, demonstrates an early start of material fracture, which is indicated by a sharp drop in the curve. However, due to the significant curve variation, it has not been possible to determine whether the surface area increase or geometry variation in the binding interface has increased the resistance. Additionally, it would be necessary to repeat the tests with a more significant number of test specimens to determine if the variation between jagged and rounded geometry plays a role in the binding capacity.

to determine if the variation between jagged and rounded geometry plays a role in the binding capacity. The results show that by using the binding ability of the mycelium, it is possible to influence the material properties of composites through the targeted arrangement of joining surfaces with higher stiffness. In this way, direction-dependent material behavior can also be generated. It is also interesting to note that the study of shear strengths reveals that both the interface arrangement and the shear strength are essentially derived from The results show that by using the binding ability of the mycelium, it is possible to influence the material properties of composites through the targeted arrangement of joining surfaces with higher stiffness. In this way, direction-dependent material behavior can also be generated. It is also interesting to note that the study of shear strengths reveals that both the interface arrangement and the shear strength are essentially derived from the interface configuration.

the interface configuration.

**Figure 5.** Diagrams showing the recorded force–displacement curves of conducted tests: (**a**) My8 specimen of beechwood–ganoderma lucidum; (**b**) My9—specimen of beechwood–pycnoporus sanguineus. **Figure 5.** Diagrams showing the recorded force–displacement curves of conducted tests: (**a**) My8—specimen of beechwood–ganoderma lucidum; (**b**) My9—specimen of beechwood– pycnoporus sanguineus.

### **4. Discussion 4. Discussion**

The attractiveness of mycelium as a matrix material lies on the one hand in its biological origin, which due to its chemically untreated state, can be easily integrated into the biological material cycle for the circular economy [13]. Due to its manufacturing process, mycelium-based materials have a minimal CO2 footprint compared to the vast majority of standard building materials. A wide variety of mycelium-based products have been developed, such as packaging [12] or insulation materials [14]. In general, mycelium-based materials have gained popularity by exploiting the rapid virtual growth of hyphae, which allows the production of conglomerate materials. On the contrary, the positive results on mycelium and wood-based material binding interfaces present this material as an ideal candidate for manufacturing laminar materials. According to the data recorded in Figure 5, the application of binding-specific manufacturing clearly increases the shear strength of the test specimens by at least 50% (average for Sch1 = 0.173 N/mm2). Although nonplanar binding interfaces present higher shear strength (up to 83%), the results obtained by planar binding interfaces have significant implications for mycelium-based materials. This process could allow the production of multi-laminar elements and could replace oilbased glue materials. Binding-specific manufacturing will doubtless be much scrutinized, The attractiveness of mycelium as a matrix material lies on the one hand in its biological origin, which due to its chemically untreated state, can be easily integrated into the biological material cycle for the circular economy [13]. Due to its manufacturing process, mycelium-based materials have a minimal CO2 footprint compared to the vast majority of standard building materials. A wide variety of mycelium-based products have been developed, such as packaging [12] or insulation materials [14]. In general, mycelium-based materials have gained popularity by exploiting the rapid virtual growth of hyphae, which allows the production of conglomerate materials. On the contrary, the positive results on mycelium and wood-based material binding interfaces present this material as an ideal candidate for manufacturing laminar materials. According to the data recorded in Figure 5, the application of binding-specific manufacturing clearly increases the shear strength of the test specimens by at least 50% (average for Sch1 = 0.173 N/mm2 ). Although non-planar binding interfaces present higher shear strength (up to 83%), the results obtained by planar binding interfaces have significant implications for mycelium-based materials. This process could allow the production of multi-laminar elements and could replace oil-based glue materials. Binding-specific manufacturing will doubtless be much scrutinized, but due to the increase in the shear strength, we can conclude that the production process presents advantageous conditions for conglomerates and laminar mycelium and wood-based materials.

With the investigations presented in this paper, it could be assumed that several basic units' laminar composition can positively influence the load-bearing behavior of myceliumbased materials. However, multiple basic unit composition is not the only factor to consider to achieve building standard requirements. Other factors that positively influence the strength and stiffness properties of mycelium-based materials are mycelium–substrate combinations which could lead to optimal growth or optimal mechanical qualities, and the increase in the material's density by compression [15]. Further studies that take the latter variables into account will need to be undertaken in combination with binding-specific manufacturing processes. With the investigations presented in this paper, it could be assumed that several basic units' laminar composition can positively influence the load-bearing behavior of mycelium-based materials. However, multiple basic unit composition is not the only factor to consider to achieve building standard requirements. Other factors that positively influence the strength and stiffness properties of mycelium-based materials are mycelium– substrate combinations which could lead to optimal growth or optimal mechanical qualities, and the increase in the material's density by compression [15]. Further studies that take the latter variables into account will need to be undertaken in combination with binding-specific manufacturing processes.

but due to the increase in the shear strength, we can conclude that the production process presents advantageous conditions for conglomerates and laminar mycelium and wood-

*Biomimetics* **2022**, *7*, 78 7 of 8

based materials.

One of the most important findings of this research is that the geometry of the interfaces can influence fracture behavior. Figure 6 shows how the non-planar binding interfaces show an increased strength. These findings contribute in several ways to a deeper understanding of the binding capacity of mycelial hyphae in combination with wood substrate and provide a basis for further development of mycelium-based material properties. One of the most important findings of this research is that the geometry of the interfaces can influence fracture behavior. Figure 6 shows how the non-planar binding interfaces show an increased strength. These findings contribute in several ways to a deeper understanding of the binding capacity of mycelial hyphae in combination with wood substrate and provide a basis for further development of mycelium-based material properties.

**Figure 6.** Shear strength to geometry diagram. Test specimen geometries from left to right: Sch0, Sch1, Sch2, Sch3, Sch4, and Sch5. **Figure 6.** Shear strength to geometry diagram. Test specimen geometries from left to right: Sch0, Sch1, Sch2, Sch3, Sch4, and Sch5.

### **5. Patents 5. Patents**

The work reported in this manuscript resulted in the Patent Application No. (DRN)<PHONE_NUMBER>010200DE. The work reported in this manuscript resulted in the Patent Application No. (DRN)<PHONE_NUMBER>010200DE.

**Author Contributions:** Conceptualization, D.S., M.T., and D.G.; methodology, A.W., D.S., and D.G.; validation, M.T., A.W., D.S., and D.G.; investigation, D.S. and D.G.; data curation, D.S.; writing original draft preparation, D.S.; writing—review and editing, D.S. and D.G.; visualization, D.S. and D.G.; photos in Figure 4, Ibac; supervision, M.T.; project administration, D.S. and D.G. Manufacturing steps (1) to (4) were developed and conducted by A.W. at AG Enzymtechnik, Dresden University of Technology. Manufacturing steps (5) to (7) were developed and conducted by Trako, led by M.T., Faculty of Architecture, RWTH Aachen University. All tests were conducted at the Institute and Chair of Building Materials Research (Ibac), RWTH Aachen University. Test analysis and interpretation by D.S. and D.G. All authors have read and agreed to the published version of the manu-**Author Contributions:** Conceptualization, D.S., M.T. and D.G.; methodology, A.W., D.S. and D.G.; validation, M.T., A.W., D.S. and D.G.; investigation, D.S. and D.G.; data curation, D.S.; writing original draft preparation, D.S.; writing—review and editing, D.S. and D.G.; visualization, D.S. and D.G.; photos in Figure 4, Ibac; supervision, M.T.; project administration, D.S. and D.G. Manufacturing steps (1) to (4) were developed and conducted by A.W. at AG Enzymtechnik, Dresden University of Technology. Manufacturing steps (5) to (7) were developed and conducted by Trako, led by M.T., Faculty of Architecture, RWTH Aachen University. All tests were conducted at the Institute and Chair of Building Materials Research (Ibac), RWTH Aachen University. Test analysis and interpretation by D.S. and D.G. All authors have read and agreed to the published version of the manuscript.

script. **Funding:** This research received no external funding. **Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable. **Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This paper and the research behind it would not have been possible without the support of our colleagues at Ibac, RWTH Aachen University: Clarissa Glawe, Hendrik Morgenstern, and Cynthia Morales Cruz. The authors would like to extend special thanks to Trako's assistant team members: Raman Suliman, Steliyana Yancheva, Lea Scholz, Helena Krapp, and Hlib Novosolov.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.


**4. Conclusions**

In this paper, a numerical study of transient states for the process of limiting current in inductive FCLs is proposed. The model is based on the coupling of multiphysics finite element simulation and a circuit model. By optimization, the number of iterations is reduced, and operational speed is greatly increased. The overall model calculation process, submodel setting, and analysis of the macroscopic characteristics (voltage, current) and microscopic characteristics (distribution of magnetic field, electrodynamic force, and temperature) of the SFCL under the current-limiting state are introduced. In SFCL design, more attention should be paid to the large outward force acting on the primary winding, and it is necessary to enhance the structure; the heat dissipation problem should be considered, while ensuring that the support strength and the contact area between the winding and the liquid nitrogen are increased as much as possible. The short-circuit experimental data of an air core inductive superconducting current limiter (SFCL) prototype was compared with the simulation results to verify the reliability of the simulation and provides a theoretical basis for the future design and manufacture of SFCL. Further, inductive SFCL applied in a short test of a large capability transformer under the grid operating condition can be designed. In this paper, some parameters in electromagnetic model and heat transfer model can be further refined and the simulation accuracy is improved. Similarly, better optimization method can be used to accelerate convergence.

**Author Contributions:** Conceptualization, J.S.; methodology, J.S. and W.L.; validation, D.Q.; data curation, J.C., H.Y.; writing—original draft, W.L.; writing—review and editing, W.L., D.Q., J.C., H.Y.; supervision, Z.H.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 51807118. **ConflictsofInterest:** Theauthorsdeclarenoconflictof interest.