N M D S 1

Figure 5. The gut microbiomes of traditional hatchery-reared steelhead differ compositionally compared to their wild broodstock counterparts. NMDS plot showcasing the differences between hatchery broodstock and wild broodstock gut microbial samples (PERMANOVA R2 = 0.29, p < 0.01) as well as differences between Cedar Creek Hatchery and North Fork Alsea Hatchery locations (PERMANOVA R2 = 0.07, p < 0.001). Stress = 0.13. Visually, there is separation between wild steelhead gut microbial composition and hatchery steelhead gut microbial composition within their respective river basins. **Figure 5.** The gut microbiomes of traditional hatchery-reared steelhead differ compositionally compared to their wild broodstock counterparts. NMDS plot showcasing the differences between hatchery broodstock and wild broodstock gut microbial samples (PERMANOVA R2 = 0.29, *p* < 0.01) as well as differences between Cedar Creek Hatchery and North Fork Alsea Hatchery locations (PERMANOVA R2 = 0.07, *p* < 0.001). Stress = 0.13. Visually, there is separation between wild steelhead gut microbial composition and hatchery steelhead gut microbial composition within their respective river basins.

#### *3.3. Combination of Both Studies*

After combining all our available wild-born, wild broodstock, and hatchery broodstock gut microbiome samples, we found that the river basin, broodstock history, and weight remained associated with the beta diversity of the steelhead gut microbiome (PER-MANOVAbasin, Bray–Curtis, R2 = 0.1223, *p* = 0.001; PERMANOVAbroodstock, Bray– Curtis, R2 = 0.0479, *p* = 0.0001; PERMANOVAweight, Bray–Curtis, R2 = 0.1170, *p* = 0.0001). Additionally, the dimensions displayed in the NMDS show two all-encompassing potential clusters that we confirmed with a partitioning around medoids (PAM) cluster-based analysis (Figure 8). Despite their separation, these clusters are not explained by any of our

measured variables, suggesting some other variables underlie this observed structure in the diversity of the steelhead gut microbiome. Microorganisms 2022, 10, x FOR PEER REVIEW 10 of 16 Microorganisms 2022, 10, x FOR PEER REVIEW 10 of 16

> Figure 6. Examples of gut bacterial clades that are more abundant in either traditional hatchery or wild broodstock fish. Asterisk (\*) indicates a statistically significant result using Kruskal-Wallis tests and false discovery rate multiple test correction. (A) This Peptonophilus clade example is more abundant in wild broodstock fish guts. (B) The Pluerocapsa clade example is more abundant in traditional hatchery broodstock fish. **Figure 6.** Examples of gut bacterial clades that are more abundant in either traditional hatchery or wild broodstock fish. Asterisk (\*) indicates a statistically significant result using Kruskal-Wallis tests and false discovery rate multiple test correction. (**A**) This *Peptonophilus* clade example is more abundant in wild broodstock fish guts. (**B**) The *Pluerocapsa* clade example is more abundant in traditional hatchery broodstock fish. Figure 6. Examples of gut bacterial clades that are more abundant in either traditional hatchery or wild broodstock fish. Asterisk (\*) indicates a statistically significant result using Kruskal-Wallis tests and false discovery rate multiple test correction. (A) This Peptonophilus clade example is more abundant in wild broodstock fish guts. (B) The Pluerocapsa clade example is more abundant in traditional hatchery broodstock fish.

Figure 7. Examples of gut bacterial clades that are more abundant in all Cedar Creek Hatchery samples compared to all East Fork Alsea Hatchery samples. Asterisk (\*) indicates a statistically significant result using Kruskal-Wallis tests and false discovery rate multiple test correction. (A) A clade from the genus Flavobacterium that is more abundant in Cedar Creek Hatchery fish guts. Different Bacteriodes clades that are (B) more abundant in East Fork Alsea Hatchery fish guts and (C) more abundant in Cedar Creek Hatchery fish guts. Figure 7. Examples of gut bacterial clades that are more abundant in all Cedar Creek Hatchery samples compared to all East Fork Alsea Hatchery samples. Asterisk (\*) indicates a statistically significant result using Kruskal-Wallis tests and false discovery rate multiple test correction. (A) A clade from the genus Flavobacterium that is more abundant in Cedar Creek Hatchery fish guts. Different Bacteriodes clades that are (B) more abundant in East Fork Alsea Hatchery fish guts and (C) more abundant in Cedar Creek Hatchery fish guts. **Figure 7.** Examples of gut bacterial clades that are more abundant in all Cedar Creek Hatchery samples compared to all East Fork Alsea Hatchery samples. Asterisk (\*) indicates a statistically significant result using Kruskal-Wallis tests and false discovery rate multiple test correction. (**A**) A clade from the genus *Flavobacterium* that is more abundant in Cedar Creek Hatchery fish guts. Different *Bacteriodes* clades that are (**B**) more abundant in East Fork Alsea Hatchery fish guts and (**C**) more abundant in Cedar Creek Hatchery fish guts.

Figure 8. NMDS plots and PAM cluster analysis reveal two clusters that may represent two steelhead gut microbiome types. (A) shows the combined NMDS visualization of all wild-born and hatchery-reared steelhead gut microbiome samples. The samples aggregate into two groups separated by space in the ordination. The coloring based on river basins and the shapes based on management type indicate that neither of these variables separates out into these two clusters. (B) colors each microbiome sample based on the PAM cluster designation and shows that PAM cluster assignment corresponds with the two speculated clusters. **Figure 8.** NMDS plots and PAM cluster analysis reveal two clusters that may represent two steelhead gut microbiome types. (**A**) shows the combined NMDS visualization of all wild-born and hatcheryreared steelhead gut microbiome samples. The samples aggregate into two groups separated by space in the ordination. The coloring based on river basins and the shapes based on management type indicate that neither of these variables separates out into these two clusters. (**B**) colors each microbiome sample based on the PAM cluster designation and shows that PAM cluster assignment corresponds with the two speculated clusters.

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

Pacific salmonid fisheries have the task of keeping up with consumer demands as wild and hatchery population numbers decline. Understanding how the Pacific salmonid gut microbiome varies based on broodstock ancestry or geographic location will provide insight into how gut bacteria may be manipulated to improve fish health and survival. This study defines how the steelhead trout gut microbiome varies across three river basins and as a function of their broodstock background. In particular, this study reveals geographic, geographic by phylogenetic lineage, and ancestry effects on the steelhead gut microbiome. Additionally, this study found an association between the steelhead gut microbial community and weight, which may have fitness implications for these fish. We document several bacterial clades that stratify groups with differing gut microbial diversity. Finally, a combined analysis revealed two predominant types of steelhead gut microbiome composition. This work clarifies how geographic location and broodstock affect the steelhead gut microbiome and informs our understanding of how the gut microbiome manifests in declining fish populations, which may lead to improved management practices or conservation efforts. This study highlights the existence of geographic effects that influence the composi-Pacific salmonid fisheries have the task of keeping up with consumer demands as wild and hatchery population numbers decline. Understanding how the Pacific salmonid gut microbiome varies based on broodstock ancestry or geographic location will provide insight into how gut bacteria may be manipulated to improve fish health and survival. This study defines how the steelhead trout gut microbiome varies across three river basins and as a function of their broodstock background. In particular, this study reveals geographic, geographic by phylogenetic lineage, and ancestry effects on the steelhead gut microbiome. Additionally, this study found an association between the steelhead gut microbial community and weight, which may have fitness implications for these fish. We document several bacterial clades that stratify groups with differing gut microbial diversity. Finally, a combined analysis revealed two predominant types of steelhead gut microbiome composition. This work clarifies how geographic location and broodstock affect the steelhead gut microbiome and informs our understanding of how the gut microbiome manifests in declining fish populations, which may lead to improved management practices or conservation efforts.

tion of the gut microbiome. These observations generally agree with prior studies of wildlife gut microbiomes in terrestrial systems [21,22], and a recent meta-analysis revealed differences in the gut microbiome of over 85 species of fish based on the five Korean water sources they were sampled from [23]. Another study, though, found that the wild gut microbiome of Atlantic salmon did not associate with geographic location [24]. However, our study was conducted with a larger sample size of Pacific salmonids, suggesting a This study highlights the existence of geographic effects that influence the composition of the gut microbiome. These observations generally agree with prior studies of wildlife gut microbiomes in terrestrial systems [21,22], and a recent meta-analysis revealed differences in the gut microbiome of over 85 species of fish based on the five Korean water sources they were sampled from [23]. Another study, though, found that the wild gut microbiome of Atlantic salmon did not associate with geographic location [24]. However, our study was conducted with a larger sample size of Pacific salmonids, suggesting a larger effect size many be needed to reveal geographic patterns in salmonids or that differences between Atlantic and Pacific salmonids—such as differences in physiology, ecology, or geography may account for these distinct results.

Importantly, cryptic variation in host physiology or genetic background may shape the gut microbial composition in this study observing wild-born gut microbes. Salmonids show evidence of subpopulations and genetic differences even within the same river system, and genetic differences have been seen in trout with spawning habitats as low as 2 km apart [25,26]. Given that the host genotype plays a role in shaping gut microbial composition in other fish hosts, the differences seen in the gut microbiome across geographic locations may be related to the accompanying differences in host genetics [27]. However, the steelhead genetics of the wild samples were not explicitly documented in this study, and future work should attempt to correlate gut microbial members with genetic differences in wild steelhead trout.

We uncovered that specific bacterial clades were more abundant in one of the three river basins, which supports the hypothesis that gut microbes may be useful for assessing salmonid biogeography. For example, a clade belonging to the genera *Ferruginibacter* was more abundant in the Alsea Basin, a Sphingomondaceae clade was more abundant in the Nestucca Basin, and *Novosphingobium* was more abundant in the Siletz Basin. In a previous study, *Novosphingobium* abundance varied by geographic location in the gut of another fish species, suggesting that members of this bacterial genera typically show geographic patterns within the fish gut microbiome [28]. While the function of *Ferruginibacter* in the fish gut is unknown, bacteria from this genus are often isolated from freshwater sediment, suggesting that these bacteria are dispersing from sediment to fish gut or from fish gut to sediment [29]. Regardless, given the cross-sectional nature of our study, it is not clear if these geographic associations are maintained over the course of a fish's lifespan, a topic that should be explored in future work.

An additional analysis revealed several clades that display correlations between geographic distance and phylogenetic distance in the steelhead gut microbiome, suggesting that these gut bacterial members co-diversified with their hosts. Alternatively, these bacterial clades may manifest a geographic distribution in the environment and then occupy the fish host. Clades demonstrating this geographic and phylogenetic correlation include clades from the bacterial families Rhodobacteraceae and Sphingomonodaceae. Rhodobacteraceae may play a role in fish health, as this family was previously found to be more abundant in the guts of healthy shrimp compared to diseased shrimp [30], but future studies should explicitly test its role in steelhead health. Also, bacterial clades from Sphingomonodaceae produce sphingolipids, which are organic compounds that can modulate *O. mykiss* mucosal homeostasis and B cell abundance [31]. Although we did not sample mucosal-associated bacteria, mucosal membranes and digesta share some microbial members and microbes in the digesta and lumen can still produce compounds that affect host immune responses [32]. Additionally, Sphingomonadaceae possess sphingolipids in their cell membranes that improve chances of successful colonization and survival in the gut, which can be advantageous for both commensal and pathogenic organisms [33,34]. This speculative role of Rhodobacteraceae and Sphingomonadaceae may be the reason for a potentially prolonged association between these bacterial families and steelhead that gave rise to this geographic lineage sorting.

Despite differences in gut microbial structure across basins, we discovered bacterial clades that are prevalent in all steelhead guts of our first study. Bacterial clades from the genera *Flavobacterium*, *Hyphomicrobium*, and *Singulisphaera* represent such core taxa. The ubiquitous presence of these bacteria suggest steelhead physiology selects for these specific clades, as they may have critical functions within the steelhead gut, or that these bacterial clades are also commonly found in the surrounding aquatic meta-communities. The function of *Hyphomicrobium* and *Singulishpaera* in the gut are unknown, but they have been found in aquatic systems as well as other fish guts [35,36]. Several members of the *Flavobacterium* genus are pathogenic to fish, although some *Flavobacterium* are commensal [37]. The pathogenicity of the *Flavobacterium* clades in this study is unclear but could have widespread consequences, as these clades were found in every fish of our first study. Given

their ubiquitous distribution, future investigations should seek to discern the physiological impacts of these taxa.

In addition, this study clarifies the impact of hatchery broodstock on the gut microbiome. Previous work suggested that hatcheries elicit strong selective pressure on Pacific salmonids that differentiate fish reared in hatcheries for several generations from fish reared in hatcheries for one generation, who are both different from wild-born salmonids. For example, the relative fitness levels and rates of reproductive success of fish with greater hatchery ancestry are significantly lower than those of fish with wild ancestry [38]. Also, the expression of several genes from the first generation of hatchery steelhead trout (i.e., previously wild trout) are heritably altered after a single generation in a hatchery environment [39]. The differences in the diversity of traditional hatchery and first-generation hatchery gut microbiomes suggest this selective pressure is also applied to steelhead gut microbial communities. Other heavily managed animals are known to have different gut microbial communities compared to their wild counterparts, as is the case with animals in captivity [40].

The fact that the first-generation hatchery stock and traditional hatchery stock were reared in the same hatchery environment suggests that the differences in the gut microbiome between these two groups is due to differences in genetics. Genotype has previously affected gut microbial composition in fish and other hosts [27,41]. Future conservation efforts may use the identification of specific clades that stratify or are indicative of a hatchery or wild steelhead gut microbiome to identify a fish as early generation or traditional hatchery-reared. Additionally, our resolution of clades that differentiate traditional hatchery and first-generation hatchery fish microbiomes may help hatcheries develop management practices that ultimately normalize the composition of hatchery-reared microbiomes closer to their wild counterparts. This study only focused on the gut microbiome of juvenile steelhead as this is the life stage steelhead are contained in hatcheries, and more mature steelhead undergo a great deal of physiological changes in preparation to travel out to the ocean, which may induce changes in the gut microbiome.

A combined analysis using all steelhead gut microbiome samples from our two studies revealed two robust clusters that demonstrate densely populated areas in the multidimensional space of steelhead gut microbiome beta diversity. These two clusters may be evidence of two different steelhead gut microbiome types. However, an unknown covariate that we did not measure, such as the sex of the fish, may be responsible for the clustering. Future studies may find these two clusters are robust among other populations of steelhead gut microbiomes and they should focus on measuring more variables that may be causing these clusters. If these two clusters are robust, future researchers should consider that the effectiveness of microbial interventions may be different based on the steelhead microbiome type measured in future studies. Therefore, microbiome type should be another variable considered when studying the steelhead gut microbiome.

Our results indicate that the steelhead gut microbiome varies as a function of geography and broodstock ancestry. Additionally, several steelhead gut bacterial clades show geographic lineage sorting across western Oregon, and a collective analysis showed two gut microbiome types. Given the declining populations of wild salmonids and the comparatively poor fitness of successive generations of hatchery-reared supplementation stock, characterizing the gut microbial communities across these populations is critical in learning 1) how the steelhead gut microbiome plays a role in the health and fitness of these fish and 2) how we can use steelhead gut microbiota or microbial interventions to improve conservation and supplementation efforts.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/microorganisms10050933/s1, Table S1: Number of reads before and after rarefaction for the geography study; Table S2: Table of clades that were correlated with phylogenetic distance and geographic distance. The table includes mantel test *p*-values and associated bacterial taxa identification; Table S3: Number of reads before and after rarefaction for the broodstock study; Table S4: Gut microbial clades significantly different across traditional hatchery broodstock

and wild broodstock fish; Table S5: Gut microbial clades significantly different between North Fork Alsea Hatchery and Cedar Creek Hatchery.

**Author Contributions:** Conceptualization, N.S.K., S.C. and T.J.S.; data curation, N.S.K., T.C. and S.S.; methodology, N.S.K., S.C. and T.J.S.; resources, T.C., S.S., S.C. and T.J.S.; formal analysis, N.S.K. and T.J.S.; writing—original draft preparation, N.S.K. and T.J.S.; writing—review and editing, N.S.K., T.C. and T.J.S.; visualization, N.S.K.; supervision, T.J.S.; funding acquisition, N.S.K. and T.J.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by The National Science Foundation (grant 1557192), institutional funds to T.J.S., and an Oregon Department of Fish and Wildlife fellowship to N.S.K.

**Institutional Review Board Statement:** Animal handling, sampling, and necropsy were conducted by the Oregon Department of Fish and Wildlife as part of their routine management and conservation efforts in accordance with state permits. Microbiome samples were collected from animals that were otherwise subject to these efforts; no animals were handled, sampled, or sacrificed specifically for this study.

**Data Availability Statement:** DNA and R code generated during this research is located on the Sharpton Lab Repository (http://files.cqls.oregonstate.edu/Sharpton\_Lab/Papers/Kirchoff\_Microorganisms\_ 2022/ accessed on 22 April 2022).

**Acknowledgments:** We would like to thank Mark Dasenko at the Center for Quantitative Life Sciences for sequencing samples and providing advice on sample preparation. We thank Jerri Bartholomew for helpful discussions. We would also like to thank the employees at North Fork Alsea Hatchery and Cedar Creek Hatchery for allowing us to sample fish and Jamie Anthony for providing additional historical information about the two hatcheries.

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

### **References**


*<IP_ADDRESS> Antibiotic sensitivity test*

This experiment was carried out to determine antibiotic sensitivity. Antibiotics such as amoxicillin, penicillin, erythromycin, ciprofloxacin, gentamicin, and cefixime were used for this. First, the freshly cultured bacterial isolates were dispersed over the sterile filled Nutrient Agar plates. The antibiotic discs were then put on petri plates at identical distances and incubated at 37°C for 18 h. The creation of a clean zone surrounding the discs was seen after 18 h.


**6. Composites of Nanocellulose with Other Carbon Nanoparticles**

In addition to fullerenes, graphene, nanotubes and nanodiamonds, other important carbon nanoparticles used in industrial, biotechnological and biomedical applications include carbon nanofibers, carbon quantum dots and nanostructures formed by activated carbon and carbon black. All these nanomaterials can be used in nanocellulose/nanocarbon composites. The biomedical applications of these composites are summarized in Table 1.


**Author details**

Matsumiya Yoshiki, Horii Sachie, Matsuno Toshihide and Kubo Motoki

Department of Biotechnology, College of Lifesciences, Ritsumeikan University Nojihigashi 1-1-1, Kusatsu, Shiga 525-8577, Japan

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**1. Introduction**

Gas hydrate is an ice-like crystalline solid, formed by water molecules and methane molecules under low temperature and high pressure. It is mainly distributed in seabed sediments on continental margins and permafrost regions. Gas hydrate can cause seabed geo-hazards and atmospheric environmental problems [1], but is also a clean energy with huge reserves [2]. Gas hydrate saturation is an important index for evaluating gas hydrate reservoirs. Well logs are widely used to estimate gas hydrate saturation due to their fast speed and low cost. The common methods for estimating the saturation of gas hydrate by using well logs mainly include resistivity methods and velocity methods [3]. Resistivity-based methods use resistivity logs to estimate gas hydrate saturation according to Archie's law [4,5], while velocity-based methods use the theoretical or empirical relationship between gas hydrate saturation and velocity to estimate gas hydrate saturation by using velocity logs. The frequently used relationships between gas hydrate saturation and velocity include time-average equations [6], the effective medium theory [7,8], and three-phase Biot-type equations [9,10].

The close relationship between gas hydrate saturation and well log machine learning technology provides a new idea for using well logs to estimate gas hydrate saturation. Singh et al. [11,12] used different combinations of well logs to predict gas hydrate saturation through unsupervised and supervised machine learning algorithms. They obtained a higher accuracy of gas hydrate saturation than in classic resistivity and velocity methods, showing the advantages of machine learning technology in gas hydrate saturation predictions. As the most vigorous branch of machine learning, deep learning technology can achieve more accurate prediction and classification than traditional technology. This is

because it builds a deep neural network model with multiple hidden layers and uses a lot of data to train the model to learn complex and e ffective information. Therefore, to use well logs better to estimate gas hydrate saturation and to establish the deep internal connections and laws of the data, we propose a method of estimating gas hydrate saturation from well logs by using deep learning technology.

The concept of deep learning first proposed by Hilton et al. [13] has been successfully applied in image, audio, and natural language processing, and its unique advantages have attracted increasing attention from geoscientists. Deep learning technology is being gradually applied to well log interpretation and reservoir prediction, such as in rock facies classification [14–19] and the prediction of shale content [20] and porosity [21]. Well logs are sequence samples, so to estimate the gas hydrate saturation, we adopted the long short-term memory (LSTM) recurrent neural network, which is suitable for processing sequential data to apply to the well logs that are sensitive to gas hydrate. This method brought good application results in the Shenhu area, South China Sea. It demonstrated the unique advantages of deep learning technology in gas hydrate saturation estimates, and laid the foundation for its further application in gas hydrate research.

#### **2. Long Short-Term Memory (LSTM) Recurrent Neural Network**

#### *2.1. Recurrent Neural Network (RNN)*

A recurrent neural network (RNN) is a neural network model with memory function that can discover the interrelationships between samples. It is especially used to process data with sequential characteristics. Unlike other network structures, an RNN introduces the idea of self-loop, which can input the output of the previous and next samples into the model for operation (Figure 1). The feature information processed by the model contains not only the information of the sequence data before the current sample, but also the information of the current sample itself. However, an RNN cannot effectively deal with long-term dependency problems (neurons that are far away in the hidden layer) because in the process of using the stochastic gradient descent method to train the RNN, the partial derivative of the loss function to the weight matrix will tend toward zero or infinity as the number of input sequence samples increases. This will bring problems of gradient vanishing or gradient exploding, limiting its wide application.

**Figure 1.** Unfolded form of recurrent neural network [22].

#### *2.2. LSTM Recurrent Neural Network*

The LSTM network is a special recurrent neural network proposed by Hochreiter and Schmidhuber in 1997 [23]. It improves and perfects the loop body repeated in a chain in the conventional RNN. By adding a forget gate layer, an input gate layer, and an output gate layer in the network cell, continuous write, read, and reset operations on memory cells can be performed [24]. This enables LSTM to have long-term learning capabilities, and e ffectively solves the problems of gradient vanishing and gradient exploding, making it one of the most successful RNN networks. Figure 2 shows the basic network structure of LSTM, while Figure 3 shows the structure of an LSTM neuron.

**Figure 2.** The basic network structure of the long short-term memory (LSTM) network [22].

**Figure 3.** The structure of an LSTM neuron [22]: (**a**) the forget gate layer, (**b**) the input gate layer, (**c**) the cell status, and (**d**) the output gate layer.

The forget gate layer of the LSTM network determines which information needs to be discarded (Figure 3). The expression is:

$$f\_t = \sigma(\mathcal{W}\_f \cdot [h\_{t-1}, \mathbf{x}\_t] + b\_f) \tag{1}$$

The input gate layer determines which new information is stored in the cell state (Figure 3b). The expression is:

$$\dot{\mathbf{u}}\_t = \sigma(\mathbb{W}\_i \cdot [h\_{t-1}, \mathbf{x}\_t] + b\_i) \tag{2}$$

$$\overline{\mathcal{C}}\_t = \tanh(\mathcal{W}\_\mathbb{C} \cdot [h\_{t-1}, \mathbf{x}\_t] + b\_\mathcal{C}) \tag{3}$$

Then, the current cell status (Figure 3c) is updated to:

$$\mathbf{C}\_{t} = f\_{t} \cdot \mathbf{C}\_{t-1} + i\_{t} \cdot \overline{\mathbf{C}}\_{t} \tag{4}$$

The cell state of LSTM runs through the whole process, so that information is transmitted in a fixed and unchanging way. The output gate layer determines the information that needs to be output at that moment (Figure 3d). The expression is:

$$h\_t = \sigma(\mathbb{W}\_o \cdot [h\_{t-1}, \mathbf{x}\_t] + b\_o) \cdot \tanh(\mathbb{C}\_t) \tag{5}$$

where *xt* is the input vector of the LSTM neuron; *ft* is the activation vector of the forget gate layer; *it* is the activation vector of the input gate layer; *ht* is the output vector of the LSTM neuron; *Ct* is the

neuron cell state vector; *W* is weight matrix; *b* is the bias term; σ is the sigmoid function; (tanh) is the hyperbolic tangent function; the subscript *t* indicates di fferent moments.

#### **3. Gas Hydrate Saturation Estimate**

## *3.1. Geological Background*

The Shenhu area is in the Pearl River Mouth Basin, in the middle of the northern slope of the South China Sea (Figure 4), and it is a key area for gas hydrate exploration. The water depth is 500–1500 m, the seabed topography is complicated, and the topographic slope varies greatly [25]. Since the late Miocene, with its gravity flow having developed and its high deposition rate, several kilometers of Mesozoic and Cenozoic sediments have accumulated to form enough organic matter to provide a source for gas hydrates [26]. In previous geological surveys of the area, many geophysical and geochemical markers indicating the existence of gas hydrates were discovered. In 2007, the Guangzhou Marine Geological Survey conducted the first gas hydrate drilling expedition in this area, and successfully drilled gas hydrate samples.

**Figure 4.** The Pearl River Mouth Basin in the northern slope of the South China Sea; the Shenhu area is shown by the red rectangle.

## *3.2. Well Logs*

Eight sites were drilled in the expedition area in 2007 (Figure 4). Gas hydrates were found in the cores of sites SH2, SH3, and SH7, but no hydrates were found at sites SH1 and SH5. The other three sites, namely, SH4, SH6, and SH9, were drilled for logging without cores.

Figure 5 shows the well logs of site SH2. The cores at this site confirmed that the gas hydrate-bearing sediments were in the range of 190–220 m, and the hydrate saturation could reach 47.3% [27].

In the well logs of site SH2, the resistivity and acoustic velocity in the gas hydrate-bearing formations showed apparent high value anomalies, while the density and gamma showed no obvious changes. The well logs of site SH7 (Figure 6) showed that the depth of the gas hydrate-bearing formation was approximately 152–177 m, and the hydrate saturation could reach 43% [27]. The well log characteristics of the gas hydrate-bearing formation at site SH7 were completely consistent with those at site SH2.

Gas hydrate causes the chloride concentration of the formation pore water to decrease, so the saturation of gas hydrate can be calculated by measuring the chloride concentration of pore water from cores [28] using:

$$S\_{\rm li} = \frac{1}{\rho\_{\rm li}} \left( 1 - \frac{C l\_{\rm pw}}{C l\_{\rm sw}} \right) \tag{6}$$

.

where ρ*h* = 0.924 is the value of the density of pure gas hydrate in g/cm3. Here, *Clsw* is the in situ baseline pore water chloride concentration and *Clpw* is the measured chloride concentration in core water after gas hydrate dissociation. The baseline chloride concentration can be determined by smoothly fitting the chloride data above and below the gas hydrate zone [3].

**Figure 6.** Well logs at site SH7.

Because the chloride concentration of the formation pore water was relatively less disturbed, and the chloride concentration measured by the cores was more accurate, the gas hydrate saturation calculated by the pore water chloride concentration had a higher accuracy [28]. Figure 7 shows the gas hydrate saturations calculated by using the chloride concentration measured by cores in the gas hydrate-bearing formation at sites SH2 and SH7. There were 41 gas hydrate-bearing cores at site SH2, and 21 cores containing gas hydrate at site SH7 [3,29].

**Figure 7.** Gas hydrate saturations calculated by the chloride concentration of the pore water from the cores at sites SH2 and SH7.

## *3.3. Data Preparation*

To use the LSTM recurrent neural network to estimate the gas hydrate saturation, site SH2 was used as a training well to train the LSTM recurrent neural network, while site SH7 was used as a verification well to verify the accuracy of the network model. In site SH2, the resistivity and acoustic velocity, which are more sensitive to gas hydrate, were used as the input of the network model. The gas hydrate saturations calculated by the chloride concentration of the pore water in the cores were used as the output to train the LSTM recurrent neural network.

Because there were only 41 gas hydrate saturation values calculated from the chloride concentration at site SH2, too little training data would seriously affect the training effect of the LSTM recurrent neural network model. Therefore, the interpolation of the gas hydrate saturation was performed at the sampling interval of the well logs to obtain 1400 sample datasets in the range of 191–219 m (Figure 8) where the resistivity and the acoustic velocity were the input of the network model, and the interpolated gas hydrate saturation were output. Before the dataset was input to the LSTM recurrent neural network for training, 1000 consecutive samples were selected as the training dataset, with the remaining samples used as the test dataset. To eliminate the dimensional influence between the parameters, and to ensure that each parameter was within a reasonable distribution range, data standardization processing was required. The expression is:

$$z\_i = \frac{\mathbf{x}\_i - \mu\_i}{\delta\_i} \tag{7}$$

where *zi* refers to the log parameters after standardization, *xi* refers to the input log parameters, μ*i* and δ*i* are the mean and standard deviation of the parameters, respectively.

#### *3.4. The Prediction Framework of the LSTM Recurrent Neural Network*

We constructed an LSTM network prediction model that included an LSTM recurrent layer and two dense layers (Figure 9), where *xi* is the standardized input sequence sample of the resistivity and *p*-wave velocity; *yi* is the output saturation sample; LSTMi is the LSTM neuron that makes up the LSTM recurrent layer, which has the exact structure in Figure 3; *oi* is the output of the LSTM neuron; *Ci* and *hi* have the same meanings as in Equations (1)–(5). Because the actual data were not particularly complicated, to improve the calculation efficiency, the number of nodes of the two fully connected layers was set to 20 and 10, respectively. The optimization algorithm adopted the Adam algorithm, and the dropout regularization method was used to prevent over-fitting.

**Figure 8.** Training dataset of the network model.

**Figure 9.** The prediction framework of LSTM recurrent neural network.

The training process of the LSTM recurrent neural network was similar to that of a conventional fully connected neural network, namely: (1) Use feedforward propagation to input training data into the network, calculate the output of the LSTM unit, and then extract features through the two fully connected layers. This trains it layer by layer to the output layer to obtain the predicted estimate of this sample. (2) Back-calculate the error term of each neuron. The backward propagation of the error term of the LSTM recurrent neural network includes two directions: the first is the back propagation along time, that is, starting from the current *t* time, calculating the error term at each time; the second is propagating the error term to the upper layer. (3) Use the Adam optimization algorithm based on gradient descent to adjust the model parameters by calculating the gradient of each weight according to the corresponding error item, so that the prediction is close to the optimization target. (4) Through the above iterations, train until it meets the required optimization target, then the LSTM recurrent neural network prediction model that meets the error requirements is established.


**1. Introduction**

With the decreasing of oil resources and the worsening of the natural environment, most countries have developed new/renewable energy systems and are trying to change their existing energy structure [1–3]. The proton exchange membrane fuel cell (PEMFC) has had considerable attention paid to it due to its excellent performance, including high energy conversion efficiency, low operating temperature, short start-up time, high power density and small size, etc. As a reliable power source, it has been widely used in the field of traffic engineering.

A conventional low-temperature proton exchange membrane fuel cell (LT-PEMFC) operates at 40–80 ◦C. Liquid water produced by the reaction affects conductivity and gas transmission, which makes the water management and gas management more complicated. In addition, the Nafion membrane at low temperature has low tolerance to CO and S. The high-temperature proton exchange membrane fuel cell (HT-PEMFC) equipped with phosphoric acid-doped polybenzimidazole membrane (PA/PBI) can increase the operating temperature to over the water boiling point (100–200 ◦C) and maintain high proton conductivity under high temperature operating conditions. Therefore, the corresponding water management system can be simplified greatly and the reaction rate of the cathode and anode can be improved, with a cell efficiency that is higher than LT-PEMFC [4].

In terms of modeling HT-PEMFCs, Cheddie et al. [5] established the output voltage and power density model of HT-PEMFC based on PBI membrane which considered the irreversibilities of activation polarization and ohmic polarization. The results found that the voltage loss was caused by activation polarization and ohmic polarization, and membrane

**Citation:** Xu, B.; Li, D.; Ma, Z.; Zheng, M.; Li, Y. Thermodynamic Optimization of a High Temperature Proton Exchange Membrane Fuel Cell for Fuel Cell Vehicle Applications. *Mathematics* **2021**, *9*, 1792. https:// doi.org/10.3390/math9151792

Academic Editor: Maria Luminit,a Scutaru

Received: 9 June 2021 Accepted: 20 July 2021 Published: 28 July 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/).

conductivity and catalyst performance affected the polarization loss greatly. Hu et al. [6] presented a two-dimensional model of HT-PEMFC with PA/PBI membrane, in which the polarization loss on the cathode side was mainly considered. The mathematical model of the cathode exchange current density was established by linear sweep voltammetry (LSV) and the ohmic polarization of the cathode is estimated by electrochemical impedance spectroscopy (EIS). Numerical simulation results were in good agreement with the experimental results. Scott et al. [7,8] developed the output voltage and power model of HT-PEMFC and investigated the influence of operating temperature and operating pressure on open-circuit voltage, exchange current density and diffusion coefficient. Kim et al. [9,10] studied the influence of operating conditions on performance degradation of HT-PEMFC. The results showed that the doping level and current density had a significant effect on the durability of HT-PEMFC.

The above mathematical models consider the influence of polarization losses on cell output and degradation, but the influence of irreversibility of leakage current on cell operation is neglected. In addition, in the application of a fuel cell engine, not only the amount but also the quality of energy should be considered, so the efficiency model should be added into the model to study the overall optimization performance.

The fundamental purpose of finite time thermodynamics is to seek ultimate performance of thermodynamic processes and systems with the goal of reducing irreversibility in finite time or under the constraints of finite size [11–16]. In terms of thermodynamic optimization research of fuel cells, Watowich et al. [17] applied the optimal control theory to determine the limit of the fuel cell operation process, and the current path and optimal terminal state of the constrained cell in a limited time, so as to provide maximum output power, maximum efficiency and maximum profit. Li et al. [18] utilized finite time thermodynamics in HT-PEMFC performance analysis to investigate the effects of kinds of parameters. Although leakage current was considered, concentration potential was not contained in the reversible potential. Sieniutycz et al. [19,20] established the steady-state model of PEMFC based on finite time thermodynamics. The influence of design and operation parameters on the performance of fuel cells was analyzed, and the power limit was predicted from the perspective of thermodynamic optimization. Li et al. [21] conducted ecological analysis on LT-PEMFC and derived ecological coefficient of performance. In addition to the studies of HT-PEMFC model, lots of development was devoted to materials [22–25] and component degradation issues [26].

Firstly, aiming at the lack of irreversible factors, this paper established a thermodynamic model that considered various polarizations and leakage current. Secondly, the influences of operating temperature on *Pmax* and thermodynamic efficiency *ηmax* were studied. The influences of operating temperature, membrane thickness, phosphoric acid doping level, hydrogen and oxygen intake pressure on the optimal performance are discussed. Finally, the optimal relationship between power density and thermodynamic efficiency is analyzed, and the optimal interval of power density and thermodynamic efficiency is obtained.

### **2. Thermodynamic Model**

#### *2.1. Internal Processess of HT-PEMFC*

As shown in Figure 1, HT-PEMFC converts chemical energy into electrical energy through electrochemical reaction of hydrogen and oxygen.

The mass transfer mechanism of HT-PEMFC is much different from LT-PEMFC. LT-PEMFC basically uses the Nafion membrane and the proton transport carrier sulfonic acid functional group can separate hydrogen ions and form hydronium ions with water molecules under humidified conditions; while in HT-PEMFCs, phosphoric acid replaces the humidified water and chemical reaction and mass transfer are based on a so-called Grotthuss mechanism. The chemical reaction and mass transfer within the anode, the cathode and the membrane can be expressed as Equations (1)–(3):

$$\text{Anode} : \text{H}\_2\text{PO}\_4^- + \text{H}^+ = \text{H}\_3\text{PO}\_4 \tag{1}$$

$$\text{Membbrane}: \text{H}\_3\text{PO}\_4 + \text{PBI} = \text{H}\_2\text{PO}\_4^- + \text{PBI} \cdot \text{H}^+ \tag{2}$$

$$\text{Cathode} : \text{PBI} \cdot \text{H}^+ = \text{PBI} + \text{H}^+ \tag{3}$$

When supplying hydrogen to the anode and oxygen to the cathode, hydrogen atoms are separated into hydrogen ions and electrons under the action of anodic catalyst. Hydrogen ions pass through proton exchange membrane and electrons flow to the cathode through the external circuit load; hydrogen ions combine with oxygen atoms and electrons at the cathode to form water molecules at relative higher temperatures over water boiling point. Therefore, water molecules are discharged in the gas phase avoiding water management systems like LT-PEMFCs. The total electrochemical reaction of HT-PEMFC can be formulated as Equations (4)–(6):

$$\text{Anode reaction}: \text{H}\_2 \to 2\text{H}^+ + 2\text{e}^-\tag{4}$$

$$\text{Cathodic reaction}: 2\text{H}^+ + \frac{1}{2}\text{O}\_2 + 2\text{e}^- \rightarrow \text{H}\_2\text{O}(\text{gas}) + \text{heat} \tag{5}$$

$$\text{Total reaction}: \text{H}\_2 + \frac{1}{2}\text{O}\_2 \rightarrow \text{H}\_2\text{O}(\text{gas}) + \text{heat} + \text{electricity} \tag{6}$$

**Figure 1.** Working principle of HT–PEMFC.

#### *2.2. Reversible Output Voltage of HT-PEMFC*

For HT-PEMFC, the reversible output voltage can be written as Equation (7),

$$E\_r = E\_r^0 + \frac{\Delta S}{nF}(T - T\_0) + \frac{RT}{nF} \ln(\frac{p\_{H\_2} p\_{O\_2}^{0.5}}{p\_w}) \tag{7}$$

where, *Er* is obtained under isothermal conditions; *E*0 *r* [18] is the reference standard voltage at ambient temperature and pressure (298.15 K, 1 atm), and its value is 1.185 V; Δ*S* is the change of standard molar entropy, *T* is operating temperature of the HT-PEMFC, *T*0 is the ambient temperature, *R* is the gas constant, *pH*2 is the intake pressure of hydrogen, *pO*2 is the intake pressure of oxygen, and *pw* is the pressure of discharging water vapor.

The entropy change is related to the operating temperature, Equation (8) [27]:

$$\frac{\Delta S}{n} = -18.449 - 0.01283(T)\tag{8}$$

#### *2.3. Irreversible Loss of HT-PEMFC*

#### 2.3.1. Polarization Phenomenon

For a single electrode, the electrode potential with no current passing through is the equilibrium potential (*Er*), and the electrode potential with current passing through is *Ecell*. In general, *Ecell* < *Er*, the absolute value of electrode potential difference (|*Er* − *Ecell*|) is overpotential.

The activation overpotential can be written as Equation (9) [5,28]:

$$E\_{act} = \frac{RT}{2\alpha F} \ln(\frac{I + I\_{lank}}{I\_0}) \tag{9}$$

where, *I* is current density, *I*0 is exchange current density, *Ileak* is leakage current density, *α* is transfer coefficient, *Eact* is activation overpotential. Exchange current density can be expressed as Equation (10) [7]:

$$
\ln(I\_0) = 2.2266 \times \frac{1000}{T} - 0.4959 \tag{10}
$$

Ohmic overpotential can be calculated as the following Equation (11) [27]:

$$E\_{\rm ohm} = I \left( \frac{l\_{\rm m}}{K\_{\rm m}} + \frac{2l\_d}{\sigma\_d^{eff}} \right) \tag{11}$$

where, *lm* is membrane thickness, *Km* is proton conductivity in the membrane phase, *ld* is thickness of diffusion layer, *σeff d* is electron conductivity. The proton conductivity can be presented as Equation (12) [8]:

$$K\_m = \frac{100}{T} \exp\left[8.0219 - \left(\frac{2605.6 - 70.1X}{T}\right)\right] \tag{12}$$

where, *X* is the doping level of phosphoric acid of the proton exchange membrane.

If the reactant gas or oxidant is not supplied in time, the electrode surface cannot maintain the reactant concentration, and concentration polarization will occur. In HT-PEMFC, the value of the concentration overpotential is already included in the reversible potential.

#### 2.3.2. Leakage Current

Theoretically, the electrolyte is an ionic conductor and has no electron transport. However, in actual operation, some hydrogen and electrons will diffuse from the anode to the cathode through the electrolyte, and a small number of electrons will flow outward through the proton membrane. Such leakage current includes internal current and cross current [29]. Therefore, the total current density generated by the fuel cell is equal to the sum of the output current density and leakage current density,

$$I\_{\rm gross} = I + I\_{\rm leak} \tag{13}$$

where *Igross* represents the total current density generated on the fuel cell electrode, *I* is the working current density that can be measured through the external load, and *Ileak* represents the leakage current density.

Haji [30] found that the leakage current increased with the rise of operating temperature and concluded that leakage current density and operating temperature met the functional relationship:

$$
\ln I\_{lank} = \left(-2342.9 \frac{1}{T} + 9.0877\right) \times \ln 10 \tag{14}
$$

#### *2.4. Irreversible Output Voltage*

The irreversible output voltage of HT-PEMFC can be expressed as Equation (15),

$$\begin{array}{c} E\_{cell} = E\_r - E\_{act} - E\_{ohm} - E\_{con} \\ = 1.185 - \left( 1.91 \times 10^{-4} + 1.33 \times 10^{-7} T \right) \left( T - 298.15 \right) + 4.13 \\ \times 10^{-5} T \ln \frac{P\_{H\_2} P\_{O\_2}}{0.0243} - 1.72 \times 10^{-5} T \ln \frac{I + 88458.17 \exp\left( \frac{-2342.9}{I} \right)}{3.95 \times 10^{-6} T^3 - 0.00424 T^2 + 1.523 - 183} \\ \end{array} \tag{15}$$

$$+ I \left( \frac{l\_{\text{tr}} T}{304696.11 \exp\left( \frac{0.11 X - 2665.6}{I} \right)} \right)$$

#### *2.5. Power Density and Efficiency of HT-PEMFC*

The power density [31] of HT-PEMFC can be expressed as Equation (16),

$$\begin{array}{l} P = E\_{cell} \cdot I \\ = E\_{cell} \cdot I \\ = \left[1.185 - \left(1.91 \times 10^{-4} + 1.33 \times 10^{-7}T\right)\right] \left(T - 298.15\right) \\ + 4.13 \\ \times 10^{-5} T \ln \frac{P\_{H\_2} P\_{O\_2}}{0.00243} \\ - 1.72 \times 10^{-5} T \ln \frac{I + 88458.17 \exp\left(\frac{-2342.9}{I}\right)}{3.95 \times 10^{-6} T^3 - 0.00424 T^2 + 1.523 - 183} \\ + I \left(\frac{l\_{\text{m}} T}{304696.11 \exp\left(\frac{0.01X - 26058}{I}\right)}\right) \left| I \times 10^{-3} \end{array} \tag{16}$$

The total energy absorbed from hydrogen and oxygen is enthalpy of reaction [32],

$$
\Delta H = \sum\_{k} \left| \frac{d\_t n\_k}{d\_t} \right| h\_k(T) - \sum\_{j} \left| \frac{d\_t n\_j}{d\_t} \right| h\_j(T) = \frac{I}{nF} \Delta h(T) \tag{17}
$$

where Δ*h*(*T*) is molar enthalpy at temperature *T*, *j* is component of the reactants, *k* is component of the products in the reaction.

For the energy conversion device, the basic definition of thermodynamic efficiency is the ratio of actual useful work to the total energy input [33]. Therefore, thermodynamic efficiency of HT-PEMFC can be expressed as Equation (18),

$$\begin{array}{l} \eta = -\frac{P}{\Delta}H \\ = -\frac{P}{\Delta}H \\ = -192970 \times \left[1.185 - \left(1.91 \times 10^{-4} + 1.33 \times 10^{-7}T\right)(T - 298.15)\right] \\ + 4.13 \\ \times 10^{-5} T \ln \frac{P\_{H\_2}P\_{O\_2}}{0.0243} \\ - 1.72 \\ \times 10^{-5} T \ln \frac{I + 88458.17 \exp\left(\frac{-2342.9}{I}\right)}{9.95 \times 10^{-6} T^3 - 0.00424 T^2 + 1.523 - 183} \\ + I \left(\frac{l\_m T}{30466.11 \exp\left(\frac{-201.5}{I}\right)}\right) \left[I \times 10^{-3}/\cdot h(T)\right] \end{array} \tag{18}$$

### *2.6. Thermodynamic Optimization*

For HT-PEMFC, *P* is related to *I*, *T*, *lm*, *pH*2 , *pO*2 and *X*, so *P* can be expressed as Equation (19) [34–37]:

$$P = f\left(l, T, l\_{m'} p\_{H\_{2'}}, p\_{O\_{2'}}, X\right) \tag{19}$$

When the membrane thickness (*lm*), hydrogen intake pressure (*pH*2 ), oxygen intake pressure (*pO*2 ) and membrane acid doping level (*X*) are determined, the power density (*P*) is only related to current density (*I*) and cell operating temperature (*T*), so *P* can be expressed as Equation (20):

$$P = \mathbb{g}(I, T) \tag{20}$$

In Equation (22), when *T* = *T*1, the power density (*P*) is only related to the current density (*I*), the maximum power density *Pmax* (*P*1) is obtained; when *T* = *T*2, the power density (*P*) is only related to the current density (*I*), the maximum power density *Pmax* (*P*2) is obtained. By analogy, when *T* = *Tn*, the maximum power density *Pmax* (*Pn*) can be obtained. And the relationship between *Pmax* and *T* can be acquired.

Similarly, when operating temperature *T*, film thickness *lm*, oxygen intake pressure *pO*2 , and film acid doping level *X* are determined, the corresponding curve between *Pmax* and *pH*2 can be obtained.

When the operating temperature *T*, film thickness *lm*, hydrogen intake pressure *pH*2 and film acid doping level *X* are determined, the corresponding curve between *Pmax* and *pO*2 can be obtained.

Similarly, thermodynamic efficiency (*η*) is related to current density (*I*), cell operating temperature (*T*), membrane thickness (*lm*), hydrogen intake pressure (*pH*2 ), oxygen intake pressure (*pO*2 ) and membrane acid doping level (*X*), so it can be expressed as formula (21):

$$\eta = h(I, T, l\_{m'} p\_{H\_2 \prime} p\_{O\_2 \prime} X) \tag{21}$$

When the membrane thickness (*lm*), hydrogen intake pressure (*pH*2 ), oxygen intake pressure (*pO*2 ) and membrane acid doping level (*X*) are determined, the thermodynamic efficiency (*η*) is only related to current density (*I*) and cell operating temperature (*T*), so *η* can be expressed as Equation (22):

$$\eta = j(I, T) \tag{22}$$

In Equation (22), when *T* = *T*1, the thermodynamic efficiency (*η*) is only related to the current density (*I*), the maximum thermodynamic efficiency *ηmax* (*η*1) is received; when *T* = *T*2, the thermodynamic efficiency (*η*) is only related to the current density (*I*), the maximum thermodynamic efficiency *ηmax* (*η*2) is received. By analogy, when *T* = *Tn*, the maximum thermodynamic efficiency *ηmax* (*ηn*) can be obtained. And the relationship between *ηmax* and *T* can be acquired.

Similarly, when operating temperature *T*, film thickness *lm*, oxygen intake pressure *pO*2 , and film acid doping level *X* are determined, the corresponding curve between *ηmax* and *pH*2 can be obtained.

When the operating temperature *T*, film thickness *lm*, hydrogen intake pressure *pH*2 and film acid doping level *X* are determined, the corresponding curve between *ηmax* and *pO*2 can be obtained.

#### **3. Results and Discussion**

The relevant parameters in the HT-PEMFC model are shown in Table 1.

**Table 1.** Relevant data of HT-PEMFC.

As shown in Table 1, some parameters referenced in this paper are from the literature [27,38]. The choice of any type of fuel cell as the vehicle power is mainly based on the application scenario of the vehicle and the demand of the power plant. Power density, dynamic response, output efficiency, durability and life, fuel form, emission and other aspects are selected as key indicators for passenger vehicles. PEMFC is superior to other fuel cells in terms of efficiency, dynamic response, durability and life, fuel form and emission.

#### *3.1. Model Validation*

Figure 2 compares model Formula (15) prediction and experimental data at 398 K and 448 K (*lm* = 20 μm; *X* = 6; *pH*2 = 1 atm; *pO*2 = 1 atm). The experimental studies in the literature [8] and model studies in the literature [27,38] are both based on HT-PEMFC equipped with PA/PBI membrane and have the same specifications. The results show that the curve predicted by the cell output voltage model has a good agreement with the experimental data. When leakage current is not considered in the model, the output voltage is significantly higher than that predicted by the model, especially in the low current density region. This is mainly because leakage current mainly affects the activation polarization, as shown in Figure 3, the activation polarization potential changes most significantly in the low current density region.

Figure 3 shows the variation curve of reversible voltage, polarized overpotential and irreversible output voltage versus current density of HT-PEMFC. It can be seen that the reversible voltage is a constant independent of current density. The activation overpotential and ohm overpotential increase with the increase of current density, and the activation overpotential changes greatly in the area of low current density. The irreversible output voltage decreases as the current density increases.

**Figure 2.** Comparison of model curve and experimental data.

**Figure 3.** Reversible voltage, polarized overpotential and irreversible output voltage of HT-PEMFC.

#### *3.2. Maximum Output Performance at a Given Temperature*

Figure 4 reflects the influence of operating temperature on *Pmax* and *ηmax* of HT-PEMFC. As can be seen from the figures, *Pmax* and *ηmax* raise with the increase of temperature. From the perspective of electrochemical kinetics, the increase of operating temperature enhances the proton conductivity of the membrane and reduces the electrochemical polarization of the HT-PEMFC. Moreover, the increase of operating temperature can improve the exchange current density and reduce the activation overpotential, so *Pmax* and *ηmax* will be boosted.

Figure 4a shows the impact of operating temperature on *Pmax* and *ηmax* of HT-PEMFC under different *lm*. It can be seen that with the decrease of proton membrane thickness, *Pmax* and *ηmax* will increase. If the thickness of proton membrane is reduced, the barrier of ions passing through proton membrane and the ohmic overpotential decrease. Therefore, *Pmax* and *ηmax* will be improved. When the temperature is 433 K, *Pmax* increases by 50% and the *ηmax* raises by 1.8% under the change of membrane thickness, which indicates that the membrane thickness has little influence on *ηmax*. The reduction of membrane thickness can improve the performance, but fuel penetration, short circuit and other problems always limit the thickness.

Figure 4b reveals the effect of operating temperature on *Pmax* and *ηmax* of HT-PEMFC under different *X*. It is obvious that with the increase of the acid doping level of the membrane, *Pmax* and *ηmax* will improve, and the variation range of the low temperature zone is greater than that of the high temperature zone. The doping level directly affects the proton conductivity of the membrane. The increase of doping level enhances the proton conductivity of the membrane, thus reducing ohmic overpotential. Therefore, *Pmax* and *ηmax* will be improved. When the temperature is 373 K, *Pmax* increases by 84% under the change of doping level; while when the temperature is 473 K, *Pmax* improves by 52% under the change of doping level. When the temperature is 433 K, the *ηmax* raises by 0.8% under the change of acid doping level. This indicates that doping level has little effect on *ηmax*.

Figure 4c displays the influence of operating temperature on *Pmax* and *ηmax* of HT-PEMFC under different *pH*2 . Obviously, with the increase of hydrogen intake pressure, *Pmax* and *ηmax* will improve. The increase in pressure, on the one hand, increases the diffusion rate of the gas and improves the mass transfer of the reaction gas, which increases the reversible electromotive force of the HT-PEMFC; on the other hand, it increases the gas concentration and reduces the effect of concentration polarization on the reversible electromotive force. At the temperature of 433 K, *Pmax* boosts by 12.5% and the *ηmax* enhanced by 4.5% under the influence of hydrogen intake pressure.

Figure 4d shows the effect of operating temperature on *Pmax* and *ηmax* of HT-PEMFC under different *pO*2 . It can be seen that with the increase of oxygen intake pressure, *Pmax* and *ηmax* will increase. At the temperature of 433 K, *Pmax* and the *ηmax* raises by 6.7% and 2.9% respectively under the change of oxygen intake pressure.

**Figure 4.** Effect of operating temperature on *Pmax* and *ηmax* of HT-PEMFC under different parameters. (**a**) Different *lm*; (**b**) different *X*; (**c**) different *pH*2 ; (**d**) different *pO*2 .


*Article* **Evaluation of an Early Intervention Model for Child and Adolescent Victims of Interpersonal Violence**

**Claudia Calvano 1,2,\* , Elena Murray 1 , Lea Bentz 1 , Sascha Bos 1 , Kathrin Reiter 1 , Loretta Ihme 3 and Sibylle M. Winter 1**

**Abstract:** Only the minority of youth exposed to traumatic events receive mental health care, as trauma-informed clinical services are lacking or are poorly accessible. In order to bridge this gap, the Outpatient Trauma Clinic (OTC) was founded, an easily accessible early, short-time intervention, with onward referral to follow-up treatment. This report presents the OTC's interventional approach and first outcome data. Using a retrospective naturalistic design, we analyzed trauma- and interventionrelated data of the sample (*n* = 377, 55.4% female, mean age 10.95, SD = 4.69). Following drop-out analyses, predictors for treatment outcome were identified by logistic regression. The majority (81.9%) was suffering from posttraumatic stress disorder (PTSD) or adjustment disorders. Around one forth dropped out of treatment; these cases showed higher avoidance symptoms at presentation. In 91%, psychological symptoms improved. Experience of multiple traumatic events was the strongest predictor for poor treatment outcome (B = −0.823, SE = 0.313, OR = 0.439, 95% CI 0.238–0.811). Around two thirds were connected to follow-up treatment. The OTC realized a high retention rate, initial improvement of symptoms and referral to subsequent longer-term psychotherapeutic treatment in the majority. Further dissemination of comparable early intervention models is needed, in order to improve mental health care for this vulnerable group.

 Introduction**

According to epidemiological studies, around 30% of children and adolescents experience at least one form of interpersonal trauma [1,2]. In a substantial number of cases, this is associated with an increased risk for disturbances in mental and physical development [3–5]. Post-traumatic stress-disorder, affective and anxiety disorders as well as behavioral problems are among the most frequent trauma-related mental disorders in children and adolescents [1,6]. Besides a child's female gender [7–9] and a young age at the first traumatic event [10], victims of sexual abuse [4,11] and victims of multiple trauma [12] are particularly at risk for poor prognosis.

In light of the high prevalence, poor prognoses and the substantial costs for the health system [13], effective treatment is urgently needed. Comprehensive meta-analyses show that trauma-focused psychological interventions are effective for the reduction of PTSD, depression and anxiety in children and adolescents, across age groups and trauma types, in controlled and uncontrolled trials [14], with promising results for long-term effects [15].

**Citation:** Calvano, C.; Murray, E.; Bentz, L.; Bos, S.; Reiter, K.; Ihme, L.; Winter, S.M. Evaluation of an Early Intervention Model for Child and Adolescent Victims of Interpersonal Violence. *Children* **2021**, *8*, 941. https://doi.org/10.3390/ children8100941

Academic Editor: Matteo Alessio Chiappedi

Received: 24 September 2021 Accepted: 18 October 2021 Published: 19 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/).

In light of this evidence, translation of trauma-informed intervention into clinical practice is warranted. In order to attain this goal and to improve the health care situation of trauma victims, different approaches and structures of trauma care have been established across Europe in recent years, with variations due to cultural backgrounds and (health-)economic situations [16,17]. However, the countries face similar challenges in the translation of evidence-based intervention into practice and in the promotion and dissemination of trauma-informed treatment models. In Germany, counseling services, crisis intervention and outpatient clinics for victims of interpersonal violence, often affiliated with psychiatric hospitals, have been emerging [16].

Despite these efforts, there is still a discrepancy between the need, the accessibility and the availability of trauma-informed clinical services [16]. For children and adolescents, there is an especially pronounced gap in health care provision and only the minority of children and adolescents exposed to traumatic events receive adequate treatment [18–21]. Data published in 2017 illustrate the situation of trauma care for children and adolescents in Germany: Münzer et al. analyzed the health care utilization of 241 children aged 4–17 years with a history of maltreatment in Germany and point out that 65% of the sample did not receive any psychotherapeutic intervention—and among the cases who did, only a few received trauma-focused psychotherapy [19]. Barriers for seeking and accessing mental health care for affected children and adolescents are by large part structural, e.g., lack of coordination and integration of services, service costs and long waiting times [22]. In a qualitative study [18], internet posts by young people in online trauma forums were analyzed. Their data suggest that structural barriers are not only at work when seeking care, but also at the end of treatment, when guidance for the patients through the pathways within the health care system seems warranted [18].

The Berlin Outpatient Trauma Clinic (OTC) for children and adolescents aims to bridge the void in both the availability of early trauma-informed care and in the connection to longer-term psychological intervention, if needed. In line with the approaches outlined in [16], the Berlin Outpatient Trauma Clinic is affiliated with the Department for Child and Adolescent Psychiatry, Charité—Universitätsmedizin Berlin, Germany. It was founded in 2012 in order to establish an easily accessible, early and specialized outpatient treatment setting for child and adolescent victims of interpersonal violence. Within a short-term early intervention setting, the OTC offers clinical assessment, stabilization and first psychotherapeutic support, as well as an onward referral to longer-term follow-up treatment. The OTC is the first treatment center the affected families consult after the traumatic event. Besides self-referrals by the families, a variety of institutions like the pediatric clinic, social services or the police refer the families to the clinic. The treatment in the OTC is independent of health insurance status as it is funded by the Crime Victims' Compensation Act, which defines the entitlement for compensation for victims of a violent crime [23]. So far, the OTC represents the only trauma-specific early intervention clinic for both children and adolescents in Berlin, financed by the Berlin Senate.

While the need for further implementation of trauma care for children and adolescents is consistently underlined in the literature [18–21], and approaches have been emerging [16], up to now, little is known about the unselected, treatment-seeking samples of children and adolescents [22,24]. However, knowledge on trauma characteristics, mental health, the need for treatment and the families' further pathways through the healthcare system among a naturalistic sample [16,17] will provide valuable contributions to the development and implementation of treatment approaches for this vulnerable group. While for adult populations, few studies with unselected clinical samples are available [25,26], for children and adolescents, comparable data are scarce.

This clinical report intents to fill the gaps in the existing literature by presenting the approach and the data from the health care seeking sample of the OTC in Berlin, Germany, affiliated with the Department of Child Psychiatry and Psychotherapy. The first aim of this clinical report is to systematically describe the sample of the OTC with respect to sociodemographic variables, trauma-related and intervention-related variables. The second

aim is to explore the range of trauma-related mental disorders across all age groups. The third aim is to conduct systematic dropout analyses followed by a presentation of treatment outcome and an analysis of its predictors. In line with the literature, we hypothesized that female gender, younger age, a longer time span untreated, the experience of sexual abuse and the experience of multiple traumatic events were associated with poor outcome.

## **2. Materials and Methods**

## *2.1. Procedure in the OTC*

The formal requirements for treatment in the OTC are child age <18 years, Berlin residency and the experience of interpersonal violence. All cases are assessed and treated by child and adolescent psychotherapists specialized in trauma-focused psychotherapy. With a contingent of up to 18 sessions, the OTC conducts a comprehensive psychological assessment, provides psychosocial support (e.g., a clearance of the situation, and the support of the family with formal steps), and first psychological interventions (e.g., stabilization, psychoeducation, provision of coping skills, parental counseling and, depending on the progress and stability, trauma exposure resp. trauma narratives). The intervention in the OTC follows an adaptive, tailored approach, mirroring the concept of trauma-informed care [22]. At the end of the treatment, individual recommendations for further interventions are stated and longer-term follow-up-intervention for the patients is initiated, if needed.

For this paper, data of all the cases who have consulted the clinic since its foundation are presented (April 2012–March 2020). Data are derived from the internal documentation and from the final letter, which is required for funding. The letter needs to include the anamnesis, results of the psychological assessment together with an evaluation whether or not the psychological symptoms are causally related to the experience of the traumatic event(s), descriptions of the interventions, of treatment outcome and, if applicable, a description of specific recommendations for further treatment.

The concomitant research of the OTC has been approved by the Ethics Committee of the Charité—Universitätsmedizin Berlin (number EA2/145/18, date of approval 30 July 2018).

#### *2.2. Measures*

## 2.2.1. Sociodemographic and Trauma-Related Data

With the use of a structured questionnaire, sociodemographic data and descriptive data on the traumatic event (type of trauma, single vs. multiple events, offender, time span until first visit in the clinic) were collected. The types of traumatic events represented in the clinic are predefined by the Crime Victim Compensation Act and are categorized into sexual abuse, physical violence, witnessing violence, being victim of an attack, and other interpersonal trauma like psychological distress due to indirect involvement in violence, e.g., the information of a sudden death of a close person.

#### 2.2.2. Mental Disorders According to ICD-10, Axis 1

For each case, at the beginning of treatment, comprehensive clinical interviews are carried out in order to evaluate (1) the absence or presence of a mental disorder according to the ICD-10 classification system and (2) whether or not the symptoms were related to the traumatic event.

#### 2.2.3. Intervention-Related Data

We analyzed the number of sessions, the time range of the intervention and the recommendations concerning follow-up treatment on a descriptive level. For each case, the clinicians evaluated whether or not further follow-up intervention was required and if so, whether it should focus on the trauma, on other psychological or psychosocial problems or on a combination of both.

## 2.2.4. Improvement of Psychological Symptoms

The measure for the improvement of psychological symptoms used in the OTC is derived from the standardized, therapist-reported documentation system for all patients in inpatient and outpatient treatment in the Department of Child and Adolescent Psychiatry. Thus, at the end of treatment in the OTC, the overall change of psychological symptoms was assessed in therapist report by the item "improvement of psychological symptoms", rated on a standardized 5-point scale (fully improved, strongly improved, improved a little, no change, worsened). In logistic regression analyses, good outcome was defined as 1 = fully improved or clearly improved.

## *2.3. Data Analysis*

Data were analyzed with SPSS, Version 25. Descriptive data analyses were used for the presentation of sample characteristics as well as trauma-related- and intervention-related characteristics. As the samples cover a broad age group, sensitivity analyses for age were conducted. For the drop out analyses, three groups (completers vs. referrals vs. decliners) were defined and compared on sociodemographic-, trauma- and intervention-related variables. In case of statistical trends (*p* < 0.10) on an overall level, post-hoc-analyses were conducted. Predictors for treatment outcome were first analyzed by univariate logistic regression, providing information on the importance of each predictor by itself. Following an explorative approach, we systematically tested sociodemographic predictors (child age, gender), trauma type (sexual abuse yes/no), other trauma-related characteristics (offender, multiple events yes/no), intervention-related data (number of sessions, time span until first visit) and baseline symptoms of posttraumatic stress (intrusions and avoidance scores derived from the CRIES-8 [27] as predictors. The significant predictors on univariate level were entered in a multivariate regression to gain a more comprehensive picture. For the regression analyses, only data of the completers were used.

## **3. Results**

#### *3.1. Participants*

In total, 377 patients were treated in the OTC till 3/2020, with a mean age of M = 10.95 years (SD = 4.69, range 0.58–18.50 years). 80.3% of the sample was above the age of 6 years (0–5 years *n* = 74, 19.6%; 6–13 years *n* = 169, 44.8%; 14–18 years *n* = 134, 35.5%). 55.4% of the patients were girls. Table 1 summarizes trauma-related descriptive data of the sample. There were no statistically significant differences between the age groups in the trauma-related variables.

In the total sample, the majority presented with one (*n* = 230, 61.0%) or two different trauma types (*n* = 113, 30.0%). The rate of co-occurrence varied across the trauma types (see Figure 1). With the exception of sexual abuse, the co-occurrence of two different trauma types were the most frequent pattern.

#### *3.2. Mental Disorders According to ICD-10*

Structured anamnesis and psychiatric assessment provided an Axis 1-diagnosis according to ICD-10 in 310 cases (82.2%). The clear majority of diagnoses were trauma-related, i.e., the symptoms occurred after the traumatic event(s) (*n* = 288; 92.9%). In 22 cases (7.1%) only, the diagnosis was present already before the trauma. The onset of a broad range of mental disorders was observed. Adjustment disorders and PTSD were the primary traumarelated mental disorder in the majority of cases, across all age groups (81.9% of the total sample). In the age group 14–18 years, depressive disorders were the third most frequent primary trauma-related disorder; while in the age group 6–13 years, externalizing disorders were the third most frequent disorder and in the age group 0–5 years, emotional disorders, respectively. On average, comorbidity was relatively low, with 1.37 diagnoses per patient (SD = 0.70, Median = 1, Modus = 1; range 1–4). Table 2 summarizes the diagnoses on Axis 1 according to ICD-10.

**Table 1.** Descriptive data in relation to the traumatic event.

Notes. † multiple answers possible; ‡ e.g., psychological distress due to indirect involvement in violence, e.g., the information of a sudden death of a close person; § in 3 cases data were missing; ¶ time span between trauma and first visit in weeks. (see Figure 1). With the exception of sexual abuse, the co-occurrence of two different trauma types were the most frequent pattern.

**Figure 1.** Co-occurrence between trauma types. The bars refer to the numbers of other trauma types present for each primary trauma type. **Figure 1.** Co-occurrence between trauma types. The bars refer to the numbers of other trauma types present for each primary trauma type.

#### *3.2. Mental Disorders According to ICD-10 3.3. Drop out Analyses*

Structured anamnesis and psychiatric assessment provided an Axis 1-diagnosis according to ICD-10 in 310 cases (82.2%). The clear majority of diagnoses were trauma-related, i.e., the symptoms occurred after the traumatic event(s) (*n* = 288; 92.9%). In 22 cases (7.1%) only, the diagnosis was present already before the trauma. The onset of a broad range of mental disorders was observed. Adjustment disorders and PTSD were the primary trauma-related mental disorder in the majority of cases, across all age groups (81.9% In total, 242 cases (64.2%) completed the treatment in the OTC ("completers"). 26 cases (6.9%) were referred to inpatient treatment due to the high severity of psychological symptoms ("referrals"). While in 13 cases (3.4%) organizational reasons (e.g., no Berlin residency) prohibited further treatment, 92 cases (24.4%) did not continue their sessions and were lost in follow-up ("decliners"). There was a trend that the time span between trauma and first visit differed between groups (F(2, 257) = 2.972, *p* = 0.053), with the highest

of the total sample). In the age group 14–18 years, depressive disorders were the third most frequent primary trauma-related disorder; while in the age group 6–13 years, exter-

diagnoses per patient (SD = 0.70, Median = 1, Modus = 1; range 1–4). Table 2 summarizes

the diagnoses on Axis 1 according to ICD-10.

time span until the first visit at the OTC for the referrals to inpatient treatment (M = 24.85, SD = 28.24) and the shortest for the completers (M = 13.67, SD = 18.56). There were significant differences between the three groups on the level of avoidance (F(2, 128) = 4.42, *p* = 0.014) and the total PTSD score at baseline (F(2, 140) = 3.909, *p* = 0.022) as measured with the CRIES-8 [27]. Post-Hoc tests showed significant higher avoidance scores in the decliners (M = 3.93, 0.88) than in the completers (M = 3.12, SD = 1.18; see Table 3). Concerning the duration of the intervention till drop out, decliners (M=2.72 months, SD = 4.13) and referrals to inpatient treatment (M = 3.85 months, SD = 4.76) showed a comparable time in intervention, but significantly shorter than the completers (M = 7.51 months, SD = 5.85, *p* = 0.003 and *p* < 0.001, respectively). The three groups did not differ with respect to gender (χ 2 (2) = 2.160, *p* = 0.340), age (F(2, 357) = 0.280, *p* = 0.756) nor trauma type (sexual violence (χ 2 (2) = 5.239, *p* = 0.073; physical violence (χ 2 (2) = 1.024, *p* = 0.599; witness of violence (χ 2 (2) = 1.183, *p* = 0.554; victim of an attack (χ 2 (2) = 1.211, *p* = 0.546). Table 3 summarizes the results of post-hoc tests for those variables with significant overall effects.

**Table 2.** Mental disorders in relation to the traumatic event on axis-1 according to ICD-10, summarized in categories of disorders, for the total sample and the age groups.

Notes. *n* in the table refers to the number of cases with the specific diagnosis, %-score refers to the percentage within the total sample resp. within the age group for each category of diagnoses. The highest proportion of a specific disorder across the three age groups is marked in bold. Table includes comorbidities.

## *3.4. Intervention-Related Data*

#### 3.4.1. Number of Sessions

Analyses on the completers revealed that on average, 10.18 (SD = 6.04) sessions were conducted (Median = 9, Modus = 18, range 1–18). While there were no age or gender effects, victims of sexual abuse received a significantly higher number of sessions than the other trauma types (M = 11.72, SD = 6.45 versus M = 9.05, SD = 5.55, *p* = 0.001). The average time span of intervention was 23.93 weeks (SD = 23.02, range 0–126 weeks, Median = 17 weeks). There were no differences for gender, age or trauma type for the time span of intervention.

*Children* **2021**, *8*, 941

## 3.4.2. Recommendation for Further Treatment

Regarding the 239 completers, in about two thirds (*n* = 153, 64.0%), follow-up treatment was recommended. Outpatient psychotherapy (*n* = 113, 73.9%) was the most frequent recommendation at the end of the intervention, followed by recommendations for outpatient child psychiatry in 35 cases (22.9%), inpatient psychiatric treatment in one case (0.6%) and social measures for child protection in four cases (2.6%). For the clear majority (*n* = 142, 95.3%), further trauma-related psychotherapeutic intervention was recommended. Age groups did not differ in terms of recommendations (results not shown). The majority (69.4%) of the victims of sexual abuse needed further treatment, which was in contrast to victims of an attack (35.4% were recommended further treatment). For the other trauma types, about half of the cases were in need for further intervention (51.7–55.4%).

## *3.5. Analyses of Treatment Outcome*

For the cases completing the intervention (*n* = 235), about half of the cases showed good outcome (*n* = 121, 51.5%), defined as full improvement (*n* = 28), or strong improvement (*n* = 93) of psychological symptoms. The other large part improved a little (*n* = 94; 40.0%). For 19 cases, no change was observed (8.1%) and in one case, worsening of psychological symptoms was stated (0.4%). There were no age or gender effects in the rating (results not shown).

Table 4 summarizes the significant predictors derived from the univariate regression analyses on good treatment outcome (coded with 1 = strong or full improvement of psychological symptoms). Female gender, victims of multiple traumatic events and victims of sexual violence as well as the cases with a higher number of intervention sessions were at risk for poor treatment outcome. The other sociodemographic, trauma-or interventionrelated predictors were not significantly related with the outcome (results not shown).

**Table 4.** Summary of significant predictions in univariate logistic regression on good treatment outcome, defined as "improvement of psychological symptoms" at the end of the intervention (coded with 1, *n* = 121).

Notes. The categorial predictors female gender, multiple traumatic events and sexual abuse all included with 1 = yes in the regression analyses.

Additionally. in multivariate regression, the presence of multiple traumatic events at presentation (B = −0.823, SE = 0.313, *p* = 0.009, OR = 0.439, 95% CI 0.238–0.811) and, with a weaker effect, a higher number of sessions (B = −0.070, SE = 0.025, *p* = 0.006, OR = 0.933, 95% CI 0.887–0.980) were inversely related with good treatment outcome.

#### **4. Discussion**

This report presented the interventional approach and clinical data from the OTC for child and adolescent victims of interpersonal violence. In this paper, we aimed to (1) provide a comprehensive account of trauma-specific characteristics of the treatment-seeking sample, (2) assess the onset and rates of trauma-related mental disorders, (3) describe intervention-related data and (4) evaluate in how far improvements in psychological symptoms can be achieved within the scope of the first-care, short-term naturalistic intervention. Furthermore, factors related to drop out were explored.

Summing up the descriptive analyses, the trauma types were equally distributed across the age groups, an average co-occurrence of one to two trauma types was observed and over one third of the sample experienced multiple events within one trauma type. A high proportion was acutely presenting at the clinic within the first two weeks after trauma. In the majority of cases, the offenders were known from the personal environment, which implies that within this first-care setting, additional measures for safety and child protection were regularly warranted.

The second aim was to give an account on the mental health in the clinical sample. In total, 82.2% were diagnosed with a mental disorder, and of these, in 92.9%, the onset was related to the experience of the trauma. Adjustment disorders and PTSD were the most prevalent diagnoses, in line with epidemiological data [1,6,28]. While adjustment disorders were more frequently diagnosed up to the age of 13 years, the majority of adolescents suffered from PTSD. School-aged children additionally showed externalizing symptoms and onset of enuresis or encopresis while the preschoolers showed a higher rate of childhood emotional disorders like separation anxiety. The broad range of clinical diagnoses and especially the higher variety of comorbid diagnoses like substance abuse and personality disorders in the adolescent subgroup mirror the relevance of transdiagnostic approaches in trauma-focused care [29] and the need for a broad psychiatric assessment. The complexity of the acutely presenting cases also underline the need for an adapted clinical approach with an increased share of psychosocial and psychological stabilization [30].

The third aim was to explore intervention-related data and treatment outcome. The average treatment duration, independent of age, gender or trauma type, covered approximately four to six months and on average, ten sessions were provided. The regression analyses aimed to get a better picture of the characteristics related to treatment outcome. Results replicated findings in the literature, as in our sample, girls [7–9] and victims of sexual abuse [4,11] were at risk for poor treatment outcome. Beyond all other predictors, children and adolescents with a history of multiple traumatic events, independent of the type of trauma, were at highest risk for poor improvement of psychological symptoms, which adds to previous findings as well [12,31]. Noteworthy, in this report, the outcomes only refer to therapists' rating at the end of the intervention. While this measure is an established part of the internal documentation and quality assurance in the university clinic, the one-item measure only captures improvement on an overall level, limiting generalizability for further, more specific psychological symptoms. Further, only therapist ratings are collected and patient-reported data are currently not available. Therefore, for further proceedings of the OTC's and other clinical services' concomitant research, the use of validated and more differentiated measures for treatment outcome, both in therapist and in patient-report need to be implemented. This will increase validity and generalizability, and will facilitate future replication of our findings.

Dropout analyses indicated that the majority of cases regularly finished their treatment in the OTC. At 24%, the rate of decliners in our naturalistic setting was comparable to that of completers in large randomized-controlled trials for the evaluation of trauma-focused cognitive behavioral therapy [32,33]. However and noteworthy, the context conditions (e.g., naturalistic clinical setting vs. standardized research setting; treatment seeking sample vs. participation in a clinical trial) are differing to a high degree, therefore comparisons are limited. Further naturalistic studies are warranted in order to gain more insight into attrition and more knowledge on how to best prevent early drop out. In our sample, the cases who dropped out of treatment showed the highest level of avoidance symptoms. This highlights the relevance of early screening particularly for avoidance symptoms, which will provide valuable information and individual target points for preventive actions. Thus, the screening needs to be followed by an early provision of strategies to target avoidance, e.g., symptom and trigger monitoring and provision of coping skills. These measures may help to identify cases at risk at an early stage and to reduce dropout from trauma-focused intervention. Besides avoidance symptoms, the time span between the traumatic event and presentation in the clinic emerged as relevant factor, too: the decliners showed a

significantly longer time span till their first visit than the completers. In order to reduce the time span untreated, barriers need to be addressed. This calls for better access to care [18], increased availability of clinics [19,20] and trauma-informed approaches [22], in order to reach out to those in need for treatment.

The overlap between trauma types was comparable with the rate reported for other community samples [31,32]. While this is a common phenomenon, conclusions of the trauma type-specific analyses in this paper are limited. Nevertheless, for victims of sexual abuse a more distinct pattern was observed on a descriptive level. While the rate of cooccurrence with other trauma types was comparably low, a higher number of sessions was required than for the other trauma types and the majority was in need for followup-intervention. The data therefore suggest that a tailored approach for the specific requirement of victims of sexual abuse might be warranted, e.g., by offering an extended quota of sessions.

The data from this report entail public health relevancy. First, the need for a specialized and accessible outpatient clinic for traumatized children and adolescents is evidenced by the high number of patients since the foundation of the trauma clinic, with about one new referral per week. Second, by the accessibility of the clinic, the burdened cases did receive an early trauma-informed and individualized intervention, contrasting the otherwise high probability that they were left untreated and not connected to any health services, for a longer time span at least [19,20]. Therefore trauma-informed facilities such as the OTC can play an important bridging role between onset of the trauma and the access to early intervention and the mental health care system: For one third of the patients, the provision of an initial clinical assessment, clearing and stabilization at the OTC led to reduction of psychological distress to the extent that no further follow-up treatment was required (and thereby helping to reduce the pressure on health care overload and costs). For the other two thirds, targeted follow-up treatment could be recommended and initiated by the clinic to contribute to sustained care. Further data on mental health care use and longer-term outcome are not yet available; however, a 3–12-months follow-up study is currently running.

In conclusion, early trauma-informed treatments, like described in the literature [22] and like the early intervention approach of the OTC described in this paper, are able to provide comprehensive and specialized support the families during early stages after the traumatic event; this may mitigate the risk for persistence of symptoms in the vulnerable group of children and adolescents.

Nationwide policies within the health care system need to ensure that trauma care for this vulnerable group is available and accessible [17] in order to facilitate assessment and intervention. Furthermore, knowledge on treatment centers' procedures and on their implementation of care will help to disseminate treatment approaches, which is especially warranted in the area of child and adolescent trauma, where a lack of treatment has been observed [19]. Therefore, enabling fast referral to specialized trauma-informed treatment centers like the OTC, and building up regional networks of trauma-informed care to foster direct follow-up treatment for the affected families are the key efforts which must urgently and widely be undertaken in clinical practice. Thus, we call other psychiatric and pediatric clinics to adapt this early treatment approach for the sake of improving and expanding the care for traumatized children and adolescents.

**Author Contributions:** Conceptualization, C.C., E.M., S.B., K.R., L.I. and S.M.W.; Data curation, E.M., L.B., S.B. and K.R.; Formal analysis, C.C.; Methodology, C.C.; Project administration, C.C., E.M., L.B., S.B., K.R., L.I. and S.M.W.; Supervision, C.C. and S.M.W.; Writing—original draft, C.C.; Writing—review & editing, C.C., E.M., L.B., S.B., K.R., L.I. and S.M.W. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** The study was approved by the Ethics Committee of the Charité—Universitätsmedizin Berlin (EA2/145/18, date of approval 30 July 2018).

**Informed Consent Statement:** The retrospective study was carried out as part of the accompanying clinical research of the Charité—Universitätsmedizin Berlin, which is why no separate consent was obtained for this study.

**Data Availability Statement:** The data that support the findings of this study are available upon reasonable request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

**Acknowledgments:** We wish to thank Anneke Lipinski, Sophie Seja and Jana Kindermann for their encouragement and support in data collection and data entry. We acknowledge support by the Open Access Publication Fund of the Freie Universität Berlin.

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

## **References**


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