2.2.1. FE Modeling and Mesh Generation

Subject-specific 3D anatomical reconstruction of patient's mandible and skull/articular eminence was performed using commercial software Mimics v14.12 (Materialise, Plymouth, MI, USA) from computed tomography (CT) scans of patient's TMJ. Upon importing the patients CT images in Mimics, anatomical model comprising of patient's mandible and fossa eminence was developed from the CT scan by performing a series of operations such as image processing, segmentation, mask formation for bone and teeth, region growing, and calculation of 3D equivalent similar to the 3D reconstruction method described elsewhere [18]. Using the design methodology discussed in previous sections, two patientspecific total TMJ prostheses systems—a 'simple implant' without notches, and another 'implant with notches'—were designed for total reconstruction of the patient's left TMJ (see Figures 24 and 25). For FE simulations, volume bound within surfaces of anatomical components (cortical bone, cancellous bone, and teeth) and prosthetic components (condyle, fossa, and screws) were meshed. Three-D volume mesh was generated for each of these components with ten-node quadratic tetrahedral elements of type C3D10 (see Figures 26 and 27). Mesh convergence was achieved using the technique discussed previously [18]. The finite element analyses were performed using a commercial FE package ABAQUS v6.10 (SIMULIA, Providence, RI, USA).

rotation of the prosthetic condylar head along the medio–lateral axis.

**Figure 25.** A patient-specific total TMJ prosthesis. (**A**,**B**) Show two views of the 'simple' total TMJ prosthesis along with left fossa bone and mandible after removal of left condyle. (**C**,**D**) Show two views of the total TMJ along with screws. **Figure 25.** A patient-specific total TMJ prosthesis. (**A**,**B**) Show two views of the 'simple' total TMJ prosthesis along with left fossa bone and mandible after removal of left condyle. (**C**,**D**) Show two views of the total TMJ along with screws.

**Figure 24.** A patient-specific total TMJ prosthesis with medial notches in fossa and condylar components. (**A**) Shows anterior–lateral view of the 'notched implants' with screw holes. Fossa prosthesis has two medial notches to be fit into host bone (**B**,**C**). The articular surface of fossa implant has medio–lateral openings, and is designed to allow optimal anterior and medial translation along with

## 2.2.1. FE Modeling and Mesh Generation 2.2.2. Model Constraints and Loads

Subject-specific 3D anatomical reconstruction of patient's mandible and skull/articular eminence was performed using commercial software Mimics v14.12 (Materialise, Plymouth, MI, USA) from computed tomography (CT) scans of patient's TMJ. Upon importing the patients CT images in Mimics, anatomical model comprising of patient's mandible and fossa eminence was developed from the CT scan by performing a series of op-As illustrated in Figure 28, the condylar head of the prosthetic TMJ was allowed to rotate along the medio–lateral axis, and translate in anterior-posterior direction. Similarly, for the TMJ on contralateral side, the natural condylar head was allowed to only rotate along the medio–lateral axis, and translate in anterior-posterior direction. The incisor teeth were fixed so that they could not translate in three directions, but could rotate. The entire fossa host bone was constrained in all directions.

erations such as image processing, segmentation, mask formation for bone and teeth, region growing, and calculation of 3D equivalent similar to the 3D reconstruction method described elsewhere [18]. Using the design methodology discussed in previous sections, two patient-specific total TMJ prostheses systems—a 'simple implant' without notches, and another 'implant with notches'—were designed for total reconstruction of the patient's left TMJ (see Figures 24 and 25). For FE simulations, volume bound within surfaces The interface between prosthetic condylar head and articulating surface of fossa prosthesis was modeled as sliding contact with a coefficient of friction of 0.3. The interface between the prostheses and bone in contact was modeled with contact elements having a coefficient of friction of 0.42 as reported in literature [26]. The screw-to-prosthesis and screw-to-bone interfacial conditions were assumed to be bonded. Since use of locking screws eliminates the possibility of movement between screw and prosthesis, the interface condition between screw heads and TMJ prostheses (condylar and fossa) was assumed to be perfect bonding. Two oblique bite forces, each 200 N for normal loading condition and 400 N for over–loading/worst-case scenario, were applied to the mandibular model in the angulus area as shown in Figure 28.

age ABAQUS v6.10 (SIMULIA, Providence, RI, USA).

**Figure 26.** Three-D finite element mesh of the host bone components prepared for total prosthetic replacement of the left TMJ. (**A**) Shows FE surface mesh of left fossa, and (**B**) shows a lateral crosssection of the 3D volume mesh of left fossa bone with screw holes. Similarly, (**C**,**D**) show surface mesh and anterior cross-section of volume mesh, respectively, of the mandible with screw holes and removal of damaged left condyle. **Figure 26.** Three-D finite element mesh of the host bone components prepared for total prosthetic replacement of the left TMJ. (**A**) Shows FE surface mesh of left fossa, and (**B**) shows a lateral crosssection of the 3D volume mesh of left fossa bone with screw holes. Similarly, (**C**,**D**) show surface mesh and anterior cross-section of volume mesh, respectively, of the mandible with screw holes and removal of damaged left condyle. *Materials* **2022**, *15*, x FOR PEER REVIEW 24 of 34

of anatomical components (cortical bone, cancellous bone, and teeth) and prosthetic components (condyle, fossa, and screws) were meshed. Three-D volume mesh was generated for each of these components with ten-node quadratic tetrahedral elements of type C3D10 (see Figures 26 and 27). Mesh convergence was achieved using the technique discussed previously [18]. The finite element analyses were performed using a commercial FE pack-

**Figure 27.** Three-D finite element mesh of the components of patient-specific total TMJ prostheses. (**A**–**C**) Show FE mesh of the condylar/ramal component of the 'simple' TMJ implant (without notches). (**D**,**E**) Show FE mesh of the fossa component, and (**F**) demonstrates FE mesh of a screw for device fixation. 2.2.2. Model Constraints and Loads **Figure 27.** Three-D finite element mesh of the components of patient-specific total TMJ prostheses. (**A**–**C**) Show FE mesh of the condylar/ramal component of the 'simple' TMJ implant (without notches). (**D**,**E**) Show FE mesh of the fossa component, and (**F**) demonstrates FE mesh of a screw for device fixation.

As illustrated in Figure 28, the condylar head of the prosthetic TMJ was allowed to rotate along the medio–lateral axis, and translate in anterior-posterior direction. Similarly,

teeth were fixed so that they could not translate in three directions, but could rotate. The

entire fossa host bone was constrained in all directions.

device fixation.

2.2.2. Model Constraints and Loads

entire fossa host bone was constrained in all directions.

**Figure 27.** Three-D finite element mesh of the components of patient-specific total TMJ prostheses. (**A**–**C**) Show FE mesh of the condylar/ramal component of the 'simple' TMJ implant (without notches). (**D**,**E**) Show FE mesh of the fossa component, and (**F**) demonstrates FE mesh of a screw for

As illustrated in Figure 28, the condylar head of the prosthetic TMJ was allowed to rotate along the medio–lateral axis, and translate in anterior-posterior direction. Similarly, for the TMJ on contralateral side, the natural condylar head was allowed to only rotate along the medio–lateral axis, and translate in anterior-posterior direction. The incisor teeth were fixed so that they could not translate in three directions, but could rotate. The

**Figure 28.** Assembly of all parts of the FE model (including anatomic and prosthetic components), and schematic representation of model constraints and load application for FE simulation of total TMJ prostheses and anatomical components. Green arrows depict the location and direction of bite forces applied in the angulus region on both sides of the mandibular mesh. The asterisks indicate constrained nodes at condyle, fossa, and incisor teeth. Left prosthetic condylar head and right natural condylar head were constrained such that they could only rotate along the medio–lateral axis and translate in anterior-posterior direction. The nodes at incisor teeth were so constrained such that they could only rotate. The entire fossa host bone was constrained in all directions. The interface between prosthetic condylar head and articulating surface of prosthetic fossa was modeled as sliding contact. The prosthesis-to-bone, screw-to-prosthesis, and screw-to-bone interfaces were assumed to be bonded. The interfacial and boundary conditions were kept similar for normal and over–load configurations; and only magnitude of applied forces was changed across the two loading configurations.


**1. Introduction**

The world population is increasing at an exponential rate and available water resources are reducing due to pollution and the effects of the climate change that increase the severity of droughts and favor other extreme events [1]. This places stress on many public services and dramatically increases the gap between water supply and demand. In many countries, urban growth has exceeded, and continues exceeding, the growth of supply infrastructure [2]. This growth generates the conditions necessary for operators of water supply systems to embrace intermittent water supply (IWS) [3]. Many countries in Africa, Asia, and Latin America have IWS [4].

Reducing poverty and improving public health is an important part of the Millennium Development Goals [5]. Achieving this goal is threatened by water shortages, lack of supply guarantees [6] and poor quality of supplied water. Although it is considered that the drinking water supplied through pipeline systems is safe, many studies show that deficiencies in the network, caused by IWS, can create conditions so that water is not safe and reliable [7–13]. The lack of reliable water supply systems in developing countries can undermine much of the hope for improvements in public health [14], and have negative effects for drinking water system objectives [15].

IWS generally seeks to reduce the per capita water demand based on savings in capital and operating costs. However, instead of being smart, this strategy brings negative consequences that outweigh the positive factors [16,17]. Symptoms of system failure include very low levels of pressure, and insufficient supply in the remotest and highest points. Generally, intermittent supply is adopted by necessity rather than by design and results in serious system impairment [18].

The best way to protect water quality is by maintaining positive and continuous pressures throughout the network [13,19]. Thus, continuous water supply ensures security. The supply change from intermittent to continuous is one of the main challenges concerning water and health in developing countries [20].

The cost of risks to the health of users must also be considered (in terms of their incomes, medical treatments, *etc.*) as it is much greater than the cost of replacing deficient pipes [11] that are detrimental to continuous water supply.

According to several studies [21–23], IWS systems produce insufficient pressure in less favored sectors or areas (nodes located on high points and/or far away). Such conditions may be favorable for reducing water losses. However, they also produce inequity in the supply [18].

Insufficient funding and mismanagement [17] are two of the main causes of the origin of IWS. System improvements in these scenarios do not derive from increasing the water supply sources, but from improving system infrastructure and management. However, a shortage of funding does not allow operators to make large investments, so they should look for profitable long term planning strategies. In this sense, phased or gradual improvements can be a good option.

The growth of cities occurs horizontally and/or vertically, as a result of residential, industrial, and commercial developments, and community facilities, *etc.* [24]. This growth requires expanding the network capacity and the correction of anomalies or reduced system performance [25].

When undertaking the expansion of a water supply network, the goal is to supply a much larger demand. However, when this expansion does not take into account the network capacity and the influence of the new expansion, various scenarios may appear that reduce the capacity of the network and threaten the quantity and quality of the service. Reducing the capacity of the network may lead, for example, to intermittent supply.

Generally, the network of an IWS system has insufficient capacity. However, this situation can be imperceptible because the operators manage to cover the demanded flows through differentiation of supply schedules, sectorization, and use of household tanks. Increasing the network capacity in IWS systems that seek to reach continuous water supply (CWS) is a task that must be carefully analyzed.

In this paper, the *theoretical maximum flow* is proposed as an indicator of network capacity. This element is endowed with its true dimension as a quantitative element that is crucial in decision-making, assessment, management, maintenance, exploitation, and design of drinking water distribution systems.

The theoretical maximum flow is important to evaluate the behavior and evolution of a drinking water system and its relationship with intermittent supply. It also serves as a basis for proposing a greedy algorithm that enables the definition of a schedule for pipe modification stages, and thus efficiently expands network capacity.

The case of study has two parts. In the first part, we evaluate the growth of the southern subsystem of the city of Oruro (Bolivia), which was originally built to offer continuous supply. However, various network modifications imposed an ideal environment for intermittent supply. In the second part, we consider the possibility of increasing the current network capacity, as part of various actions to revert to CWS. Based on the IWS classification given by Totsuka *et al.* [17], the system only suffers economic scarcity and management problems, and not physical scarcity. Thus, only the actions related to infrastructure improvement are analyzed.