**3. Strategy for Determining the Function of Unknown Mitochondrial Proteins**

A useful initial step for identifying the biochemical lesion of *pet* mutants is to assign them to one of three broad phenotypic classes based on the spectral properties of their mitochondria. This substantially reduces the number of subsequent assays. For example, a strain showing a normal complement of mitochondrial cytochromes and respiratory chain complexes can be excluded from harboring a mutation in a gene that affects mitochondrial translation, as both COX and the bc1 complex contain subunit polypeptides (cytochromes *a*, *a*3, and cytochrome *b*) that are translated on mitochondrial ribosomes [12]. By the same token, a selective loss of cytochrome *a* generally signals a mutation in a gene required either for:

A similar argument can be made for mutants lacking cytochrome *b*, except that a safe assumption is that the lesion affects some aspect of bc1 biogenesis.

Finally, mutations in genes that are directly or indirectly required for the maintenance of mitochondrial DNA (mtDNA), undergo a large deletion or complete loss of the genome resulting in a population of cytoplasmic petites (̺- and ̺ 0 mutants). Particularly prevalent in this class are mitochondrial protein synthesis mutants, (e.g. aminoacyl tRNA synthases and ribosomal mutants) [13] and mutants with defective ATP synthase [14,15]. Both mitochondrial translation and ATP synthase mutants display the absence of "*a*" and "*b*" type cytochromes for the reasons indicated above. An outline of the screens useful in identifying different classes of *pet* mutants is shown in Figure 1.

**Figure 1.** Genetic and biochemical screening of *pet* mutants. The initial complementation tests are done to identify *pet* mutants with counterparts in the knockout strain collection. This eliminates the need to clone and sequence genes already annotated.


*Article* **A Combined Modal and Route Choice Behavioral Complementarity Equilibrium Model with Users of Vehicles and Electric Bicycles**

**Senlai Zhu 1,\*, Jie Ma 2,\*, Tianpei Tang 1,3 and Quan Shi 1**

Received: 25 April 2020; Accepted: 21 May 2020; Published: 24 May 2020

**Abstract:** The popularity of electric bicycles in China makes them a common transportation mode for people to commute and move around. However, with the increase in traffic volumes for both vehicles and electric bicycles, urban traffic safety and congestion problems are rising due to traffic conflicts between these two modes. To regulate travel behavior, it is essential to analyze the mode choice and route choice behaviors of travelers. This study proposes a combined modal split and multiclass traffic user equilibrium model formulated as a complementarity problem (CP) to simultaneously characterize the mode choice behavior and route choice behavior of both vehicle and electric bicycle users. This model captures the impacts of route travel time and out-of-pocket cost on travelers' route choice behaviors. Further, modified Bureau of Public Roads (BPR) functions are developed to model the travel times of links with and without physical separation between vehicle lanes and bicycle lanes. This study also analyzes the conditions for uniqueness of the equilibrium solution. A Newton method is developed to solve the proposed model. Numerical examples with different scales are used to validate the proposed model. The results show that electric bicycles are more favored by travelers during times of high network congestion. In addition, total system travel time can be reduced significantly through physical separation of vehicle lanes from electric bicycle lanes to minimize their mutual interference.

**Keywords:** traffic behavior; user equilibrium; complementarity problem; electric bicycle; commute mode choice

#### **1. Introduction**

In recent years, electric bicycles (E-bikes) quickly became one of the main nonmotorized travel modes in some developing countries, especially in China [1–3]. E-bikes have many merits over both regular bikes and vehicles, including that they are much faster and can support longer trips compared with regular bikes. Further, despite the lower maximum speed, they are much more flexible and can run at higher speeds than vehicles in congested areas. E-bikes also have other advantages, such as high availability due to low price, efficient energy consumption, and no tailpipe emissions. Due to these characteristics, E-bikes are now one of the main transportation modes in China. Each year, over 35 million E-bikes are sold in China and the installed base of E-bike in use is over 100 million [4].

However, with the increase in traffic volumes for both vehicles and electric bicycles, due to traffic conflicts between these two modes, various urban traffic problems are rising, such as traffic safety, traffic congestion, and parking problems. Recently, extensive research efforts were devoted to address the multiple research needs related to E-bikes, such as estimating cycling capacity, the bicycle equivalent unit for E-bikes, consumption behavior of E-bikes users, and characteristics of traffic accident involving

E-bikes [5–7]. Existing research generally studied the operational characteristics of E-bike from the micro level, such as operations on links or intersections. However, as an important commute mode, few studies investigated the corresponding mode choice and route choice behaviors, which play important roles in designing management strategies and operational decisions related to E-bikes to alleviate the above traffic problems at the traffic-network level.

Similar to the Braess paradox [8], overall performance of the urban transportation network may decrease when improving the operational level of a certain link or intersection for vehicles and E-bikes. To address traffic problems caused by conflicts between vehicles and E-bikes, the mode choice and route choice behaviors of users at the network level require study, alongside the impact of various management strategies (such as separating bicycle lanes and vehicle lanes by physical separations, e.g., parterres and barriers on some links) on these travel behaviors.

Hence, to simultaneously estimate the mode choice and route choice behaviors of vehicles (cars/automobiles) and E-bikes, this paper proposes a combined modal split and route choice model, with the underlying assumption that all users own vehicles and E-bikes and can choose traffic modes based on the congestion level of each mode. Thus, the general flow pattern is estimated using an user equilibrium model which assumes that nobody can reduce their own travel cost by unilaterally shifting their route or mode at the equilibrium state. Considering the well-established complementarity theory, the proposed multimode traffic assignment model is developed as a complementarity problem (CP).

In reality, vehicle lanes and bicycle lanes on some links are separated by physical barriers, while some links have no physical separations. Link cost functions are different under these two cases. In the literature, the Bureau of Public Roads (BPR) cost function [9] was frequently adopted to analyze the link travel time characteristic of vehicles in congested networks. Without loss of generality, modified BPR functions of each mode are developed to capture the interference between vehicles and E-bikes in different scenarios. As discussed before, compared with vehicles, E-bikes can run at higher speeds in congested areas, even though their designed speeds are less than those of vehicles. This characteristic can be captured by setting different parameters in the modified BPR functions. Out-of-pocket costs are considered in the proposed model to capture impacts of factors such as fuel or electricity consumption, vehicle or E-bike depreciation, insurance, the environment, etc., on mode choice.

In summary, the contributions of this paper include:

The rest of the paper is organized as follows. Related literature is reviewed in the next section. In Section 3, the CP model for the multimode traffic assignment problem is presented. Section 4 discusses the uniqueness of the equilibrium solution. In Section 5, a Newton method for solving the proposed model is developed. Section 6 applies the proposed method to two numerical examples. The last section concludes this study.

#### **2. Literature Review**

#### *2.1. Tra*ffi*c Assignment Model*

Traffic assignment models are important tools in the design of effective management strategies and operational decisions to improve network performance, for example, they are usually leveraged to deploy infrastructures optimally to reduce traffic congestion [10–13] and to find optimal traffic signal settings to minimize total travel time [14,15]. Among various traffic assignment models, the user equilibrium problem is perhaps the most common due to its simple assumption of travelers' behavior and the close-form formulation. The user equilibrium problem assumes that at the equilibrium state, nobody can reduce their own travel cost by unilaterally shifting their travel route.

Given Origin–Destination (OD) flows, the user equilibrium problem is treated traditionally as two different methods, namely, deterministic user equilibrium [16] and stochastic user equilibrium [17]. In deterministic user equilibrium methods, all users are assumed to have perfect information about route costs and all choose the routes of minimum cost. In stochastic user equilibrium methods, the traffic costs are considered as random variables and route choices are different among different users. In this paper, the proposed CP model estimates the deterministic user equilibrium condition of traffic flow for both vehicles and E-bikes.

#### *2.2. Tra*ffi*c Assignment Model with Multiple Modes*

In reality, various modes can be chosen by travelers, such as vehicle, public transportation (bus, metro, taxi), bike (E-bike, regular bike), and so on. To estimate the use ratio of each mode, various methods are proposed, such as discrete choice models [18,19]. After giving the ratio of each, to address the traffic assignment problem with multiple modes, many studies attempted to convert the traffic flows of all other modes into standard passenger cars, followed by conversion of total traffic volume to be used as the input of demand for the traffic assignment model. However, each mode has particular characteristics (such as speed, travel time, capacity, security), which may be ignored if all modes are converted to the standard passenger cars.

In the literature, several multimode and/or multiclass traffic assignment models [20,21] and combined modal split and traffic assignment models [22,23] were proposed to model heterogeneous travel behavior. To capture the characteristics of travel cost realistically, these studies used different link cost functions for different traffic modes. However, in this paper, due to interactions between E-bikes and vehicles, travel cost functions may be asymmetric, thereby increasing the difficulty to formulate a mathematical programming problem. In the literature, traffic assignment problems with asymmetry travel cost functions were usually modeled as variational inequality (VI), complementarity, fixed-points, and entropy maximization problems [24–30]. Despite all these efforts, the best approach to this multimode traffic assignment problem is still under debate.

In existing multimode traffic assignment models, the demand of each mode is normally determined (or assumed to be elastic). That is, these models do not consider mode choice behaviors of users. To address this problem, we first need to study factors affecting mode choice behaviors. This paper focuses on studying the travel behaviors considering users of vehicles and E-bikes. In fact, except for travel time, users choose to use vehicles or E-bikes based on factors such as security, weather, distance, fuel and electricity prices, and so on. Similar to Liu and Li [31], we define costs related to these factors as out-of-pocket costs.

In addition, modes such as buses and taxis use the same lanes as vehicles, and modes such as metros do not interfere with vehicles in space at all. Different from these modes, E-bikes are designed to run in bicycle lanes separated from vehicle lanes. On some links, bicycle lanes and vehicle lanes are physically separated, such as by parterres and barriers. However, bicycle lanes and vehicle lanes are separated only by traffic markings instead of physically on some links. In this case, vehicles and E-bikes may occupy each other's lanes. This interference should be considered in the traffic equilibrium problem, and the existing link travel time function cannot capture this interference.

To address the aforementioned gap in the existing research, this paper proposes a combined modal split and route choice model, in which out-of-pocket costs are considered in the mode route cost function and modified BPR functions are adopted to analyze the link travel time of vehicles and E-bikes for links with and without physical separation between vehicle lanes and bicycle lanes.

#### **3. Model Formulation**

Consider a strongly connected network [N, A], where N is the set of nodes and A is the set of directed links. Notations are first given as the following:

*Ta*, *Ta*: Travel time on link *a* ∈ *A* for vehicles and E-bikes, respectively; *T*0 *a* , *T* 0 *a* are the corresponding free-flow travel times;

*Ca*: Capacity of link *a* for vehicles and E-bikes, respectively;

*Pw i* , *P w i* : Travel time on route *i* between OD pair *w* for vehicles and E-bikes, respectively; *i* ∈ *Pw*, *Pw* is the set of routes connecting OD pair *w*;

*f w i* , *w i* : Flow of vehicles and E-bikes on route *i* between OD pair *w*, respectively;

*f f*: *f* = [... , *f w*, ...] *T* with dimension *n*1 equals the total number of routes in the network, (·) *T* denotes the transpose of either a vector or a matrix, and *f w* = ... , *f w i* , ... is the vehicle route flow set of OD pair *w*;

*l w i* , *w* Out-of-pocket costs (costs related to factors such as weather, distance, fuel and electricity prices) of route *i* between OD pair *w* for users of vehicles and E-bikes, respectively;

*i* , *C i* of route *i* between OD pair *w* for users of both vehicles and E-bikes are given, respectively. The multiclass traffic equilibrium problem considering users of vehicles and E-bikes is formulated as the following mixed complementary problem (MCP):

$$0 \le f\_i^w \bot C\_i^w - \pi^w \ge 0 \,\,\forall i \tag{1}$$

$$0 \le \overline{f}\_i^w \perp \overline{C}\_i^w - \pi^w \ge 0, \forall i \tag{2}$$

$$\sum\_{i \in P^w} \left( f\_i^w + \overline{f}\_i^w \right) = q^w \,, \forall w \tag{3}$$

Equations (1) and (2) are the complementary slackness conditions. That is, for each OD pair *w*, if the flow on route *i* satisfies *f w i* ≥ 0 (*f w i* ≥ 0), the route cost *Cw i* (*C w i* ) on route *i* is equal to the minimal route cost π*w*, i.e., *Cw i* = π*w* (*C w i* = π*w*). These complementary slackness conditions are consistent with the Wardrop's user equilibrium (UE) principle, i.e., all used routes have equal and minimum travel costs, and all unused routes have equal or higher travel costs. Equation (3) is the flow conservation constraint.

To reduce the MCP formulated by Equations (1)–(3) to a pure CP, Equation (3) is reformulated as follows (the proof of the equivalent of Equations (3) and (4) is given in Appendix A):

$$0 \le \pi^w \bot \sum\_{i \in \mathbf{P}^w} \left( f\_i^w + \overline{f\_i}^w \right) - q^w \ge 0, \forall w. \tag{4}$$

Then the CP can be formulated in vector form as follows:

$$\mathbf{x} = \begin{pmatrix} f \\ \tilde{f} \\ \pi \end{pmatrix} \ge \mathbf{0},\\ F(\mathbf{x}) = \begin{pmatrix} \mathbf{C} - \sigma \pi \\ \overline{\mathbf{C}} - \sigma \pi \\ \sigma^T (f + \tilde{f}) - q \end{pmatrix} \ge \mathbf{0},\\ \mathbf{x}^T F(\mathbf{x}) = \mathbf{0}. \tag{5}$$

Note that if both *Cw i* and *C w i* are linear functions with respect to traffic flow, CP (5) becomes a linear complementarity problem (LCP), which can be solved using algorithms such as Lemke's method, the projected successive over relaxation iteration method, the general fixed-point iteration method, or the modulus-based matrix splitting iteration method [32–36]. If either *Cw i* or *C w i* are nonlinear, CP (5) becomes a nonlinear complementarity problem (NCP), which can be solved by algorithms such as Newton methods [37–39]. In this paper, route cost functions are assumed to be "convex combinations" of route travel time and out-of-pocket costs, and thus the proposed CP (5) becomes an NCP.

Specifically, route cost functions *Cw i* , *C w i* are defined as

$$\mathbf{C}\_{i}^{w} = P\_{i}^{w} + l\_{i}^{w}, \overline{\mathbf{C}}\_{i}^{w} = \overline{P}\_{i}^{w} + \overline{l}\_{i}^{w}, \tag{6}$$

where *Pw i* , *P w i* denote route travel time for vehicles and E-bikes, respectively, and *l w i* , *l w i* denote the corresponding out-of-pocket costs.

The route travel time is formulated as

$$P\_i^w = \sum\_a \delta\_{ia}^w T\_a \, \overline{P}\_i^w = \sum\_a \delta\_{ia}^w \overline{T}\_a. \tag{7}$$

Out-of-pocket cost relate to fuel or electricity consumption, vehicle or E-bike depreciation, insurance, security, the environment, and so on. Similar to Liu and Li [31], we assume that the out-of-pocket cost is defined as a function of both travel time and travel distance, as follows:

$$I\_i^w = \lambda\_m P\_i^w + q \, \_m L R\_i \tilde{I}\_i^w = \lambda\_e \overline{P}\_i^w + q \, \_e L R\_i \, \_i \tag{8}$$

where λ*m* and λ*e* denote the monetary cost per unit time for vehicles and E-bikes, respectively, and ϕ*m* and ϕ*e* denote the monetary cost per unit distance traveled by vehicles and E-bikes, respectively. Note that values for λ*m*, ϕ*m*, λ*e*, and ϕ*e* depend on factors such as fuel price, weather, and so on. In reality, these parameters can be calibrated by data collected by surveys of stated preference.

According to Equations (6)–(8), route costs *Cw i* , *C w i* are obtained by

$$\mathbf{C}\_{i}^{w} = (1 + \lambda\_{m}) \sum\_{a} \delta\_{a}^{i} T\_{a} + q \rho\_{m} L R\_{i} \\ \overline{\mathbf{C}}\_{i}^{w} = (1 + \lambda\_{\varepsilon}) \sum\_{a} \delta\_{a}^{i} \overline{T}\_{a} + q \rho\_{\varepsilon} L R\_{i}. \tag{9}$$

Note that the linear or nonlinear characteristics of route cost function depend on the function of link travel time (*Ta* and *Ta*). On some urban links, bicycle lanes are separated from vehicle lanes by physical separations, so the flows of vehicles and E-bikes involve almost no interactions. The following modified BPR functions are used to model the link travel time for links with physical separations between bicycle lanes and vehicle lanes:

$$T\_a = T\_a^0 (1 + \alpha\_m (\frac{\upsilon\_a}{\mathbb{C}\_a})^{\beta\_m}) \tag{10}$$

$$\overline{T}\_d = \overline{T}\_a^0 (1 + a\_e(\frac{\overline{\upsilon}\_a}{\overline{\mathsf{C}}\_a})^{\beta\_e}) \tag{11}$$

where *va* = *w i* δ*w ia f w i* and *va* = *w i* δ*w ia f w i* represent vehicle flow and E-bike flow on link *a*, respectively, and α*m*(α*e*) and β*m*(β*e*) are constants defining how cost increases with traffic flow for vehicles (E-bikes). Note that, in reality, E-bikes have higher flexibility than vehicles and, despite lower maximum speed, E-bikes can maintain higher speeds than vehicles in congested areas. Hence, compared to the travel time of vehicles, the travel time of E-bikes is normally not significantly affected by traffic flow. That is, values of α*e* and β*e* can be smaller than those of α*m* and β*m*, respectively. Specifically, in reality, the vehicle link capacity can usually be calibrated due to designed travel speed, number of lanes, headway, etc., and the E-bike link capacity can be calibrated by real link travel data [5].

In some urban links, no independent bicycle lanes or bicycle lanes are separated from vehicle lanes by traffic markings, meaning vehicle lanes may be occupied by E-bikes and bicycle lanes may also be occupied by vehicles frequently. In this case, the link travel time functions related to links without physical separations between bicycle lanes and vehicle lanes are formulated as follows:

$$T\_a = T\_a^0 (1 + \alpha\_m (\frac{v\_a + \gamma\_m \overline{v}\_a}{\Theta\_m \mathbb{C}\_a})^{\beta\_m}) \tag{12}$$

$$\overline{T}\_a = \overline{T}\_a^0 (1 + \alpha\_e(\frac{\overline{\upsilon}\_a + \gamma\_e \upsilon\_a}{\partial\_e \overline{\mathsf{C}}\_a})^{\beta\_e}) \tag{13}$$

where γ*m*(γ*e*) is a constant characterizing the impact of traffic flow of E-bikes (vehicles) on travel cost of vehicles (E-bikes) and θ*m*(θ*e*) is a constant defining how the link capacity of vehicles (E-bikes) is influenced by the traffic flow of E-bikes (vehicles).

Despite no physical separation, vehicles and E-bikes are designed to run in separated lanes or spaces, and *Ca* and *Ca* represent the capacity of these designed lanes or spaces. However, due to no physical separation, one mode may occupy the designed lanes or spaces of other mode. Considering this phenomenon of occupation, parameters θ*m* and θ*e* are introduced to adjust the corresponding capacity, and γ*m* and γ*e* are considered to adjust the corresponding traffic flow. Since the volume of a vehicle is normally larger than that of a E-bike, γ*m* is assumed to be bigger than γ*e*. In fact, link time Functions (10) and (11) regarding cases of physical separation can be treated as special forms of link time Functions (12) and (13) for cases without physical separation, respectively. In this special form, γ*m* = γ*e* = 0 and θ*m* = θ*e* = 1.

#### **4. Uniqueness of Equilibrium Solution**

Note that link travel time Functions (10)–(13) are nonlinear and the proposed traffic assignment model is an NCP. According to the theory of VI/CP [40], since the feasible region of our problem is convex and route cost Function (9) is continuous, if the Jacobian matrix *J* of route cost Function (9) is definitely positive, the solution of the proposed NCP is unique.

The corresponding Jacobian matrix *J* is:

$$J = \begin{bmatrix} \frac{\partial \mathcal{C}\_i^w}{\partial f\_i^w} & \frac{\partial \mathcal{C}\_i^w}{\partial f\_i} \\ \frac{\partial \mathcal{C}\_i^w}{\partial \mathcal{C}\_i^w} & \frac{\partial \mathcal{C}\_i^w}{\partial f\_i^w} \end{bmatrix} = \begin{bmatrix} (1 + \lambda\_m) \sum\_a \delta\_a^i \dot{T}\_a & (1 + \lambda\_m) \sum\_a \delta\_a^i \ddot{T}\_a \\ (1 + \lambda\_\ell) \sum\_a \delta\_a^i \dot{\overline{T}}\_a & (1 + \lambda\_\ell) \sum\_a \delta\_a^i \ddot{\overline{T}}\_a \end{bmatrix} \tag{14}$$

where . *Ta* = ∂*Ta* ∂*va* , .. *Ta* = ∂*Ta* ∂*va* , . *Ta* = ∂*Ta* ∂*va* , and .. *Ta* = ∂*Ta* ∂*va* .

**Theorem 1.** *According to Equation (10) and Equation (11), the solution to the proposed NCP is unique in cases of physical separation.*

**Proof.** For cases of physical separation between vehicle lanes and bicycle lanes, .. *Ta* = . *Ta* = 0. Then, *J* becomes:

$$J = \begin{bmatrix} \left(1 + \lambda\_m\right) \sum\_a \delta\_a^i \dot{T}\_a & 0\\ 0 & \left(1 + \lambda\_e\right) \sum\_a \delta\_a^i \ddot{\overline{T}\_a} \end{bmatrix} \tag{15}$$

which is a standard diagonal matrix with positive diagonal elements. Obviously, in this case *J* is definitely positive. The uniqueness of the solution to the NCP under cases of physical separation is therefore proven. -

Next, we discuss the case of no physical separation between vehicle lanes and bicycle lanes on links of the transportation network.

**Theorem 2.** *Given link time Functions (12) and (13), if* 1 − γ*m*γ*e* > *0, the solution to the proposed NCP is unique for cases without physical separation.*

**Proof.** For cases of no physical separation between vehicle lanes and bicycle lanes, according to Equation (14), the first-order leading principal minor of *J* is (1 + λ*m*) *a* δ*i a* . *Ta*, which is positive. Then we discuss the second-order leading principal minor, i.e., *D*2:

$$\begin{aligned} D'\_2 &= \left| \begin{array}{cc} \left(1 + \lambda\_{\mathcal{U}}\right) \sum\_{a} \delta\_a^{\dot{i}} \dot{T}\_a & \left(1 + \lambda\_{\mathcal{W}}\right) \sum\_{a} \delta\_a^{\dot{i}} \ddot{T}\_a \\\ \left(1 + \lambda\_{\mathcal{C}}\right) \sum\_{a} \delta\_a^{\dot{i}} \dot{\overline{T}}\_a & \left(1 + \lambda\_{\mathcal{C}}\right) \sum\_{a} \delta\_a^{\dot{i}} \ddot{\overline{T}}\_a \\\ \end{array} \right| \\ &= \left(1 + \lambda\_{\mathcal{W}}\right) \left(1 + \lambda\_{\mathcal{C}}\right) \left(\sum\_{a} \delta\_a^{\dot{i}} \dot{T}\_a \sum\_{a} \delta\_a^{\dot{i}} \ddot{\overline{T}}\_a - \sum\_{a} \delta\_a^{\dot{i}} \ddot{\overline{T}}\_a \sum\_{a} \delta\_a^{\dot{i}} \ddot{\overline{T}}\_a\right). \end{aligned}$$

Thus, *D*2 > 0 if, and only if,

$$
\sum\_{a} \delta\_a^i \bar{T}\_a \sum\_{a} \delta\_a^i \bar{\overline{T}}\_a - \sum\_{a} \delta\_a^i \bar{T}\_a \sum\_{a} \delta\_a^i \bar{\overline{T}}\_a > 0 \tag{16}
$$

In Equation (16), . *Ta* = α*m*β*mT*0 *a* θ*mCa va*+γ*mva* θ*mCa* β*m*−1 , .. *Ta* = α*e*β*eT* 0 *a* θ*eCa va*+γ*eva* θ*eCa* β*e*−1 , .. *Ta* = α*m*β*m*γ*mT*0 *a* θ*mCa va*+γ*mva* θ*mCa* β*m*−1 , and . *Ta* = α*e*β*e*γ*eT* 0 *a* θ*eCa va*+γ*eva* θ*eCa* β*e*−1 . Denote *A*1 = α*m*β*mT*0 *a* θ*mCa va*+γ*mva* θ*mCa* β*m*−1 and *A*2 = α*e*β*eT* 0 *a* θ*eCa va*+γ*eva* θ*eCa* β*e*−1 , then:

$$\sum\_{a} \delta\_{a}^{i} \dot{T}\_{a} \sum\_{a} \delta\_{a}^{i} \ddot{\overline{T}}\_{a} - \sum\_{a} \delta\_{a}^{i} \ddot{T}\_{a} \sum\_{a} \delta\_{a}^{i} \dot{\overline{T}}\_{a} = (1 - \gamma\_{m} \gamma\_{c}) A^{1} A^{2} \tag{17}$$

Thus, if 1 − γ*m*γ*e* > 0, *D*2 > 0. -

In summary, if 1 − γ*m*γ*e* > 0, all order leading principal minors of *J* are positive, then the solution to the proposed NCP is unique for cases of no physical separation.

Note that values of γ*m* and γ*e* can impact the corresponding traffic flows of each mode due to interactions between flows of vehicles and E-bikes. In the most extreme case, vehicle lanes are occupied by all vehicles and E-bikes, and bicycle lanes are also occupied by all vehicles and E-bikes. In this case, γ*m* can be treated as the vehicle equivalent of an E-bike (denoted as VE) and γ*e* can be treated as the E-bike equivalent of a vehicle (denoted as EE). According to the conversion relationship, VE × EE = 1. In reality, despite no physical separation between vehicle lanes and bicycle lanes, some vehicles and E-bikes still run in the corresponding designed lanes, with not all vehicles (E-bikes) occupying the bicycle (vehicle) lane. Thus, γ*m* < VE and γ*e* < EE. Therefore, 1 − γ*m*γ*e* > 1 − VE ∗ EE = 0, that is, the condition 1 − γ*m*γ*e* > 0 in Theorem 2 is satisfied. In summary, the unique solution to the proposed NCP can be guaranteed in reality.

#### **5. Solution Algorithm**

Several algorithms were proposed in the literature to solve the traffic assignment problem formulated as an NCP. Among these algorithms, the nonsmooth and semismooth Newton methods were widely used, the basic idea being to convert the complementarity problem into an equal system of equations so as to solve them using the general Newton method.

First, we give the following definition.

**Definition 1.** *A function* φ : *R*2 → *R is called an NCP function if*

$$
\phi(a, b) \Leftrightarrow ab = 0, a \ge 0, b \ge 0 \tag{18}
$$

According to Definition 1, the NCP function related to NCP (5) can be defined as

$$\Phi(\mathbf{x}) = \begin{pmatrix} \phi(\mathbf{x}\_1, F\_1(\mathbf{x})) \\ \vdots \\ \phi(\mathbf{x}\_n, F\_n(\mathbf{x})) \end{pmatrix} \tag{19}$$

Then, the solution to NCP (5) can be obtained by solving φ(*x*) = **0**.

Note that the NCP function significantly impacts the effective solution algorithm. The following Fischer–Burmeister (FB) function [38] is frequently used as the NCP function.

$$
\phi\_{FB}(a,b) = a + b - \sqrt{a^2 + b^2} \tag{20}
$$

The FB Function (20) has many interesting properties, however, it is too flat in the positive orthant (the main region of interest for a complementarity problem) when dealing with a monotone complementarity problem. Chen et al. [37] introduced another NCP function, i.e.,

$$
\lambda \phi\_{\lambda}(a, b) = \lambda \phi \text{r} \mathbb{B}(a, b) + (1 - \lambda) a\_{+} b\_{+} \tag{21}
$$

where λ ∈ (0, 1] is an arbitrary parameter and *a*+*b*+ are penalties for violating the complementarity conditions, in which, for example, *z*+ is a nonnegative operator *z*+ = *max*(0, *z*) for ∀*z* ∈ *R*.

Based on the NCP Function (21), the equal system of equation related to NCP Function (5) is defined as

$$\Phi\_{\lambda}(\mathbf{x}) = \begin{pmatrix} \phi\_{\lambda}(\mathbf{x}\_{1}, F\_{1}(\mathbf{x})) \\ \vdots \\ \phi\_{\lambda}(\mathbf{x}\_{\mathsf{H}}, F\_{\mathsf{H}}(\mathbf{x})) \end{pmatrix} \tag{22}$$

Further, we define

$$
\varphi\_{\lambda}(a,b) = \frac{1}{2}\phi\_{\lambda}(a,b)^2\tag{23}
$$

Then, a natural merit function ψλ(*x*) of φλ(*x*) is given by

$$\Psi\_{\lambda}(\mathbf{x}) = \frac{1}{2} \|\Phi\_{\lambda}(\mathbf{x})\|^2 = \sum\_{i=1}^{n} \varphi\_{\lambda}(\mathbf{x}\_{i\cdot} F\_{i}(\mathbf{x})) \tag{24}$$

where · is the Euclidean norm.

The NCP Function (21) and the merit Function (24) were proven by Chen et al. [37] and Xu et al. [39] to possess all the positive features of the FB Function (20) and its corresponding merit function.

Thus, the Newton method introduced by Du Luca et al. [41] to solve the proposed NCP Function (5) with NCP Function (21) and merit Function (24) is given as follows.

#### **Algorithm 1**. Global algorithm.

**Step 1.1**. Initialize parameters μ ∈ (0, 1), ω ∈ 0, 1 2 , ρ > 0, *p* > 2, tolerance error ε > 0 to check convergence, iteration counter *k* = 0.

**Step 1.2.** Initialize solution vector *x***0** = ⎛ ⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

**Step 1.3.** If ∇ψλ *xk*  ≤ ε, then terminate. Otherwise, go to the next step.

*f* **0** *f* **0** π**0** ⎞ ⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ .

**Step 1.4.** Choose *Vk* from the C-subdifferential ∂*C*φλ *xk T* of φλ *xk* and let *dk* ∈ *R*2*n*1+*n*2 be a solution of the following linear system of equations:

$$\mathbf{V}\_{k}d = -\boldsymbol{\Phi}\_{\boldsymbol{\lambda}} \left(\mathbf{x}^{k}\right). \tag{25}$$

If solution *dk* cannot be found or if the descent test

$$\nabla \Psi \mu \left(\mathbf{x}^{k}\right)^{T} d\_{k} \le -\rho \|d\_{k}\|^{p} \tag{26}$$

does not satisfy, set *dk* = −∇ψλ *xk T* . **Step 1.5.** Linear search. Find the smallest nonnegative integer *l k* such that

$$
\omega \boldsymbol{\psi}\_{\boldsymbol{\lambda}} \left( \mathbf{x}^{k} + \boldsymbol{\mu}^{\boldsymbol{\mu}} \right) \leq \boldsymbol{\psi}\_{\boldsymbol{\lambda}} \left( \mathbf{x}^{k} \right) + \omega \boldsymbol{\mu}^{\boldsymbol{\mu}} \nabla \boldsymbol{\psi}\_{\boldsymbol{\lambda}} \left( \mathbf{x}^{k} \right)^{T} \boldsymbol{d}\_{k} \tag{27}
$$

**Step 1.6.** Set *xk*+1 = *xk* + μ*l k dk*, *k* = *k* + 1 and go to Step 1.3.

Step 1.2 is for the initialization of the solution vector *x***0**. Although we can set the arbitrary vector as the initial solution vector, to make the global algorithm more efficient in solving the proposed NCP Function (5), the following procedure (Algorithm 2) is used to initialize the solution vector.

**Algorithm 2**. Initialize the solution vector.

**Step 2.1**. Read in a predefined route set *Pw*. Choose any initial vehicle demand *qw v* and E-bike demand *qw e* , *qw v* + *qw e* = *qw*.

**Step 2.2**. Load demand *qw v* to route set *Pw* using the all-or-nothing method to obtain an initial vehicle route flow vector *f* **0**.

**Step 2.3**. Update the link time and route cost *Cw i* according to Equations (9)–(13).

**Step 2.4**. Load demand *qw e* to route set *Pw* using the all-or-nothing method to obtain an initial E-bike route flow vector *f* **0** .

**Step 2.5**. Update the route cost *Cw i* .

**Step 2.6**. Select the initial min-route cost π*w*,0 = *min Cw i* , *i* ∈ **R***w* and set π**0** = [... , π*w*,0, ...] *T* . **Step 2.7**. Set the initial solution vector *x***0** = ⎛ ⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝ *f* **0** *f* **0** π**0** ⎞ ⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ .

Further, in Step 1.4 of the global algorithm (Algorithm 1), we first need to choose *Vk* from the C-subdifferential ∂*C*φλ *xk T* (see [37,39] for definition). Similar to Chen et al. [37], we use the following Algorithm 3 to choose *Vk*.

**Algorithm 3**. Choose *Vk* ∈ ∂*C*φλ *xk T*

**Step 3.1**. Let *x* ∈ *R*2*n*1+*n*2 be given and *Vi* denote the *i*th row of a matrix *V* ∈ *R*(2*n*1+*n*2)×(2*n*1+*n*2) . **Step 3.2**. Set index set *S*1 = *i xi* = *Fi*(*x*) = 0 and *S*2 = *i*|*xi* >0, *Fi*(*x*) > 0 . **Step 3.3**. Set *z* ∈ *R*2*n*1+*n*2 such that *zi* = 0 for *i* - *S*1 and *zi* = 1 for *i* ∈ *S*1. **Step 3.4**. Set *Vi* as follows: If *i* ∈ *S*1, set *Vi* = λ ⎛ ⎜⎜⎜⎜⎜⎜⎝ 1 − *zi Tz* ⎞ ⎟⎟⎟⎟⎟⎟⎠ *e T i* + λ ⎛ ⎜⎜⎜⎜⎜⎜⎝ 1 − ∇*Fi*(*x*) *Tz Tz* ⎞ ⎟⎟⎟⎟⎟⎟⎠ ∇*Fi*(*x*) *T*. (28)

*zi*,∇*Fi*(*x*)

If *i* ∈ *S*2, set

$$V\_{l} = \left[\lambda\left(1 - \frac{\mathbf{x}\_{l}}{\|(\mathbf{x}\_{l}, F\_{l}(\mathbf{x}))\|\right) }\right] + (1 - \lambda)F\_{l}(\mathbf{x})\right]e\_{l}^{T} + \left[\lambda\left(1 - \frac{F\_{l}(\mathbf{x})}{\|(\mathbf{x}\_{l}, F\_{l}(\mathbf{x}))\|\right) }\right] + (1 - \lambda)\mathbf{x}\_{l}\right] \nabla F\_{l}(\mathbf{x})^{T} \tag{29}$$

If *i* -*S*1 ∪ *S*2, set

$$V\_{l} = \lambda \left(1 - \frac{\boldsymbol{\chi}\_{l}}{\|(\boldsymbol{\chi}\_{l}, F\_{l}(\mathbf{x}))\|\|}\right) \mathbf{e}\_{l}^{T} + \lambda \left(1 - \frac{F\_{l}(\mathbf{x})}{\|(\boldsymbol{\chi}\_{l}, F\_{l}(\mathbf{x}))\|\|}\right) \nabla F\_{l}(\mathbf{x})^{T} \tag{30}$$

*zi*,∇*Fi*(*x*)

#### **6. Numerical Examples**

In this section, we present numerical examples to verify the proposed model and analyze the users' mode (vehicle and E-bike) choice behavior.

#### *6.1. A Simple Example*

First, we apply the proposed NCP to a simple network as shown in Figure 1. The network has five nodes, five links, and two OD pairs (1-5 and 2-5). Link parameters are shown in Table 1. Demands of OD pairs 1-5 and 2-5 are set to be 300 and 200, respectively. Parameters in link time Functions (10)–(13) are set to be α*m* = 0.15, β*m* = 4,α*e* = 0.1, β*e* = 2, γ*m* = 0.3, and γ*e* = 3, for any link, and parameters in route cost Function (9) are set to be λ*m* = 0.1, ϕ*m* = 0.2, λ*e* = 0.2, ϕ*e* = 0.4, and θ*m* = θ*e* = 1.1 for any route.

**Figure 1.** A simple network.

**Table 1.** Link parameters of network in Figure 1.

Table 2 shows the results of link flows for two cases. The first case demonstrates no physical separation between the vehicle lane and the bicycle lane for any link in the network. The second case regards all links in the network having physical separations between vehicle lanes and bicycle lanes. As can be seen from Table 2, the link flow patterns are quite different for the two cases, indicating that physical separation between the vehicle lane and the bicycle lane has dramatic effects on the

equilibrium flow pattern. Table 3 shows the route flow and route cost of both vehicles and E-bikes, denoting that (a) the sum of route flows of vehicles and E-bikes for each OD pair is equal to the total demand of that OD pair, and (b) for any OD pair, the cost of each used route (including vehicles and E-bikes) is equal to its minimum travel cost (in bold) and the unused routes have higher costs than the minimum OD travel cost.

**Table 2.** Link flows of the nonlinear complementarity problem (NCP) for cases with and without physical separation.

**Table 3.** Route flows of the NCP for cases with and without physical separation.

Numbers in bold means the cost of each used route (including vehicles and E-bikes) is equal to its minimum travel cost.

Table 4 further compares some indicators of the flow patterns for cases with and without physical separation, including demand of vehicles, demand of E-bikes, and total travel time of the system. It can be seen from Table 4 that mode choice proportions are significantly influenced by physical separation between vehicle lanes and bicycle lanes. The total system travel time for cases with physical separation is much smaller than in cases without physical separation. This is because physical separation decreases the interference between vehicles and E-bikes, thereby reducing travel costs for both traffic modes.

**Table 4.** Indicators of the NCP for cases with and without physical separation.

#### *6.2. Sensitivity Analysis*

Figure 2 shows how mode choice proportions vary from the total demand. In this experiment, demands of OD pairs 1-5 and 2-5 are set to grow at the same rate. It can be seen from Figure 2 that proportion of vehicle demand decreases with increasing total demand, while the proportion of E-bike demand changes conversely. If the total demand is larger, the network tends to be more congested. As discussed before, E-bikes have higher flexibility than vehicles and can maintain higher speeds than vehicles in congested areas despite their lower maximum speeds. Hence, when the network is more congested, users of the network prefer to choose E-bikes rather than vehicles.

**Figure 2.** Mode choice proportions change with total demand for the example network.

Figure 3 shows how proportions of vehicle and E-bike demand vary by changes in values of out-of-pocket-related parameters ϕ*m*, λ*m*, ϕ*e*, and λ*e*. As shown in Equation (8), ϕ*m* and ϕ*e* denote the monetary cost per unit of distance traveled by vehicles and E-bikes, respectively, and λ*m* and λ*e* denote the monetary cost per unit of time for vehicles and E-bikes, respectively. Figure 3 shows that the proportion of vehicle (E-bikes) demand decreases with the growth of the corresponding parameters λ*m* and ϕ*m* (λ*e* and ϕ*e*). As mentioned before, out-of-pocket cost is impacted by fuel or electricity consumption, vehicle or E-bike depreciation, insurance, the environment, and so on. For example, when the price of fuel increases (values of ϕ*m* and λ*m* increase in this case), users tend to reduce vehicle use. Similarly, when the weather conditions are poor (such as raining) or the road safety conditions for nonmotor vehicles are low (values of ϕ*e* and λ*e* increase in these cases), out-of-pocket costs related to E-bikes increase, thus the choice proportion of E-bikes becomes smaller.

Table 5 shows the sensitivity analysis results of parameters related to interactions between vehicles and E-bikes (γ*m* and γ*e* in Equations (12) and (13)). In reality, the influence between flows of vehicles and E-bikes is mutual, that is, when the impact on vehicles from E-bikes becomes greater, the impact on E-bikes from vehicles also becomes greater simultaneously. Hence, in Table 5, the corresponding parameters γ*m* and γ*e* are shown to increase equidistantly. The results show that the total system total travel time increases with the degree of interaction between vehicles and E-bikes. The total travel time of each mode also tends to increase with the degree of interaction. Combined with results of Table 4, flow of vehicles and E-bikes should be physically separated as much as possible, and interference between vehicles and E-bikes should also be reduced as much as possible in links without physical separation between vehicle lanes and bicycle lanes, such as by regulating traffic.

**Figure 3.** Sensitivity analysis regarding parameters related to out-of-pocket cost.

**Table 5.** Sensitivity analysis regarding parameters related to interactions between vehicles and E-bikes.

#### *6.3. A Larger Network*

The proposed model is further tested using the well-known Nguyen–Dupuis network shown in Figure 4. It consists of 13 nodes, 38 bidirectional links, and 18 OD pairs (all possible combinations between the three left nodes {12, 1, 4} and the three right nodes {8, 2, 3}). Fifty routes considered by Zhu et al. [42] are used. The length of each link is set to be *LLa* = 10, and other link characteristic parameters are shown in Table 6. Parameters in link time Functions (12) and (13) are set to be γ*m* = 0.2 and γ*e* = 2 for any link, and other parameters in link time Functions (10)–(13) and route cost Function (9) are set to be the same as those of the simple example. The travel demands of 18 OD pairs are shown in Table 7.

**Figure 4.** The Nguyen–Dupuis network.

**Table 7.** Origin–Destination (OD) pairs and the corresponding demand.

As discussed before, cases of physical separation are special cases of those without physical separation, with the proposed model only tested for cases of no physical separation between vehicle lanes and bicycle lanes for any link in the network. Table 8 shows the resulting link flow pattern, where, for any link, the link flow of the E-bike is larger than that of vehicle. Hence, given the OD demand shown in Table 7, the proportion of E-bike demand is larger than that of vehicle demand. The simple example proves that the proportion of vehicle demand decreases with increasing total demand, while the proportion of E-bike demand increases with the total demand. Similarly, when we

reduce the total travel demand of the Nguyen–Dupuis network, vehicle choice proportion increases and E-bike choice proportion decreases.

**Table 8.** Link flows of the NCP for the Nguyen–Dupuis network.

To check the correctness of the solutions when applying the proposed NCP model to a larger network, Table 9 shows the resulting route flows and route costs. Without loss of generality, Table 9 only shows the results for OD pairs 1-3 and 4-2. First, the sum of route flows of vehicles and E-bikes for each OD pair should equal the total demand of that OD pair. In detail, for OD pair 1-3, the total vehicle route flow is 2.36 + 19.00 + 46.86 = 68.22 and the total E-bike route flow is 129.01 + 19.13 + 126.39 + 12.39 + 74.76 = 361.78. Hence, the total flow is 68.22 + 361.78 = 430, which equals the travel demand of OD pair 1-3. Thus, the sum of vehicle and E-bike route flows for each OD pair should equal to the total demand of the OD pair, which is satisfied for OD pair 1-3. Similarly, OD pair 4-2 is also verified. Second, for any OD pair, the cost of each used route (including vehicles and E-bikes) should equal its minimum travel cost, with the unused routes having higher costs than the minimum OD travel cost. Table 9 clearly shows that the resulting route flows and costs of vehicles and E-bikes satisfy the Wardrop UEprinciple.

**Table 9.** Route flows of the NCP for the Nguyen–Dupuis network.

#### **7. Conclusions**

To consider the mode choice behavior between vehicles and E-bikes, this paper presented a multimode traffic assignment model formulated as a CP. In this model, the route cost was assumed to consist of route travel time and out-of-pocket cost. Then, the BPR link travel time function was extended for cases with and without physical separation between vehicle lanes and bicycle lanes, respectively. Given the modified link travel time functions, the proposed multimode traffic assignment

model became an NCP. Further, the uniqueness of the equilibrium solution to the proposed NCP was proven and a solution algorithm based on the Newton method was developed.

Numerical examples were conducted on two different size networks, with the results showing that the solution to the proposed NCP was correct, that is, the solution satisfied the Wardrop UE principle and flow conservation law. Sensitivity analysis showed that since E-bikes are more flexible than vehicles, especially in congested areas, E-bike choice proportion increased with total travel demand and vehicle choice proportion decreased accordingly. Increased in out-of-pocket costs led to a reduction of the corresponding mode choice.

Through the comparison of cases with and without physical separations, it was found that reducing the inference between vehicles and E-bikes could significantly reduce total system travel time, indicating that traffic engineers and planners should try to physically separate the flow of vehicles and E-bikes as much as possible.

In reality, due to factors such as resource constraints, it is impossible for all links to be physically separated between vehicle lanes and bicycle lanes. Hence, in future research, it would be worthwhile to optimize which links should set up physical separations and extend the proposed CP model to the network design problem. Meanwhile, the application of the proposed model should be tested on real networks, and the modified link travel time function should be verified and calibrated by real link travel data. In addition, some travelers are accustomed to certain traffic modes and do not consider other modes in reality, and some travelers may have more alternatives besides vehicles and E-bikes, such as public transportation. Hence, extending the proposed CP model to consider more types of travelers in the future would be worthwhile.

**Author Contributions:** Conceptualization, S.Z. and J.M.; methodology, S.Z. and J.M.; validation, S.Z. and T.T.; formal analysis, Q.S.; investigation, T.T.; resources, Q.S.; writing—original draft preparation, S.Z. and J.M.; writing—review and editing, T.T., Q.S.; supervision, Q.S.; funding acquisition, S.Z. and Q.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Humanities and Social Science Foundation of the Ministry of Education in China, grant numbers 18YJCZH274, the Science and Technology Project of Jiangsu Province, China, grant numbers BK20190926, the National Natural Science Foundation of China, grant numbers 61771265, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China, grant numbers 19KJB580003, and the Science and Technology Project of Nantong City, grant numbers JC2019062.

**Acknowledgments:** The authors are grateful for comments made by anonymous referees.

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

#### **Appendix A Proof of the Equivalent Equations (3) and (4)**

**Proof.** Equations (3) and (4) are equivalent if π*w* has a strictly positive value. If π*w* is positive, the equality *i*∈*Pw f w i* + *f w i* = *qw* in Equation (3) must be satisfied. Therefore, to show the equivalence, it is sufficient to show that π*w* cannot equal 0.

Assume π*w* equals 0. Since π*w* represents the minimum travel cost of OD pair *w*, π*w* = 0 means the route flow of any route between OD pair *w* for both vehicles and E-bikes is 0. Thus, the demand *qw* of OD pair *w* is zero. Note *qw* > 0. Therefore π*w* cannot be 0, thereby proving that Equations (3) and (4) are equivalent. -

#### **References**

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

International Journal of *Environmental Research and Public Health*


**Seasonal Energy Flexibility Through Integration of Liquid Sorption Storage in Buildings**

#### **Luca Baldini \* and Benjamin Fumey**

Empa–Swiss Federal Laboratories for Materials Science and Technology, 8600 Dubendorf, Switzerland<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
Received: 30 April 2020; Accepted: 4 June 2020; Published: 8 June 2020

**Abstract:** The article estimates energy flexibility provided to the electricity grid by integration of long-term thermal energy storage in buildings. To this end, a liquid sorption storage combined with a compression heat pump is studied for a single-family home. This combination acts as a double-stage heat pump comprised of a thermal and an electrical stage. It lowers the temperature lift to be overcome by the electrical heat pump and thus increases its coefficient of performance. A simplified model is used to quantify seasonal energy flexibility by means of electric load shifting evaluated with a monthly resolution. Results are presented for unlimited and limited storage capacity leading to a total seasonal electric load shift of 631.8 kWh/a and 181.7 kWh/a, respectively. This shift, referred to as virtual battery effect, provided through long-term thermal energy storage is large compared to typical electric battery capacities installed in buildings. This highlights the significance of building-integrated long-term thermal energy storage for provision of energy flexibility to the electricity grid and hence for the integration of renewables in our energy system.

**Keywords:** long-term thermal energy storage; seasonal thermal energy storage; thermochemical energy storage; liquid sorption storage; power-to-heat; seasonal energy flexibility; seasonal load shifting; virtual battery effect


**Part 2**

**Malaria Vector Research**

36 Malaria Parasites

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**3**

V. Choumet *Institut Pasteur*

*France*

**Proteomics of** *Anopheles gambiae*

Mosquitoes are a family of around three and a half thousand species and belong to the order of Diptera. They are found throughout the world except in places permanently frozen. Three quarters of all mosquito species live in the humid tropics and subtropics, where the climate is warm and moist, well adapted to the development of all stages and allows adults survival. Mosquitoes are classified in three subfamilies (*Toxorhynchitinae*, *Anophelinae*, *Culicinae*). *Anopheles* mosquitoes are members of subfamily *Anophelinae*. Like all mosquitoes, its life cycle consists in four stages: egg, larva, pupa, and adult. Female mosquitoes lay 30- 150 eggs every 2-3 days in water. *Anopheles* favors as breeding places, quiet water, like permanent or temporary ponds, or quite cove of rivers. Each egg is protected by an eggshell. Mosquitoes can develop from egg to adult in as little as 5 days but usually take 10–14 days in tropical conditions. *Anopheles* can be distinguished from other mosquitoes by their palps, which are as long as the proboscis. Most *Anopheles* mosquitoes are not exclusively anthropophilic or zoophilic. *Anopheles* mosquitoes are more frequent in tropical and subtropical countries but are also found in temperate climates. They are not found at

*Anopheles* mosquitoes are vectors of several pathogens. They can transmit O'nyong-nyong virus as well as parasitic nematodes that cause lymphatic filariasis. Of the approximately 460 known species of *Anopheles*, less than 100 can transmit human malaria in nature. The primary malaria vectors in Africa, *A. gambiae* and *A. funestus*, are strongly anthropophilic

Malaria is a parasitic disease that affects 200 million people worldwide and causes 1.5 to 2.7 million deaths per year. Of the 300–500 million clinical cases annually, nearly 90% are in the sub-Saharan countries of Africa where the malaria parasite, *Plasmodium falciparum*, is primarily transmitted by the mosquito *Anopheles gambiae*. The increasing resistance of the parasite to inexpensive drugs and the resistance of mosquitoes to insecticides have created an urgent need for innovative methods that block parasite transmission during its development within the insect. Strategies for the development of malaria vaccine candidates target the stages found within humans e.g. the asexual erythrocytic stages. However vaccine candidates have also been developed against both the sexual stages of malaria in the mosquito (reviewed in [1] and against the mosquito vector itself (reviewed in [2]). The

and, consequently, are two of the most efficient malaria vectors in the world.

**1. Introduction**

altitudes above 2000-2500 m.

**1.1 Pathogens transmitted by** *Anopheles* **mosquitoes**


**1. Introduction**

Polyurethane (PU) is one of the most bio- and blood-compatible materials currently used for fabrication of various medical devices, e.g. blood bags, vascular/ureteral catheters and artificial heart. Originally, PU was conceived with other copolymers, aiming at similar goals, i.e. enough versatility to successfully meet biomedical devices constraints, such as biocompatibility, resistance to sterilization, physical features invariance over time and infection resistance during indwelling. PU in particular, has also other key properties particularly suited to biomedical industry, including strength, versatility and low cost. The surface of PU can be chemically functionalized with organic and biologically active molecules, resulting in improved durability, compliance, acceptance and tolerance in the human body during implantation. These features additionally strengthen PU as an appealing candidate for biomedical applications.

Normally, several polymers such as natural rubber, polyethylene, polyvinylchloride, fluoropolymers, hydrogels and silicon are used in biomedical applications. Despite the widespread use of these materials, PU still covers a relevant and dominant role, thanks to its high blood and tissue biocompatibility for improving the quality of patient's life. It conjugates a good stability over long implantation times, excellent physico-mechanical and surface tuning properties via anchoring of molecules. PU has simply a unique mix of features, highly required for almost any medical device.

PU is also widely used in cardiovascular applications, in particular for the preparation of venous and intravenous catheters and balloons for angioplasty and angiography. It has also been successfully used for tissue replacement and augmentation in breast implants, facial reconstruction and body joints. Artificial organs based on PU such as heart, kidneys and lungs have already been developed. Thanks to its above described unique features, PU has recently been proposed for new promising application fields, e.g. controlled drug delivery devices. A deep review on the use of PU in medicine and medical devices is also available (Zdrahala and Zdrahala 1999).

© 2012 Cauda and Cauda, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Cauda and Cauda, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Given its large use, in this chapter we will focus on the use of PU in urological applications, in particular as ureteral catheter, or stent, in endourology routines.

Polyurethane in Urological Practice 125

these encrustations can obstruct the device and impair the urinary flow, compromising with

Temporary prevention from encrustation includes stent replacement at regular intervals, modification of the type or size of catheters, washing the catheter and bladder with acidic, antiseptic or saline solutions (Arshad, Shah and Abbasi 2006). Antibiotics are still orally administered whenever stent is replaced or inserted for preventing infections (Reid 2001).

However all these approaches are mostly ineffective. For this reason stent surface modifications have been proposed to prevent bacterial and inorganic molecule adhesion. Various strategies have been conceived, using silver-coated surfaces (Leung *et al.* 1992; Multanen *et al.* 2000), surface modification towards hydrophobicity (Jansen *et al.* 1993) or functional groups creation with intrinsic antimicrobial activity. Heparin is a good candidate for solving these problems. In previous *in vitro* and *in vivo* studies, heparinization of medical devices showed a reduction of microbial colonization (Appelgren *et al.* 1996; Cauda *et al.* 2008; Ruggieri *et al.* 1987). Heparin is a highly sulfated, anionic polysaccharide known for its anti-coagulant and anti-thrombogenic properties (Piper 1946). It has a strong negative electrical charge able to prevent cells adhesion since bacterial' cell membrane surface is also negatively charged. Coating stents with heparin can be practical and low-cost. Over the last three decades several studies, especially in vascular medicine, were indeed reported, showing that this approach is effective (Appelgren, Ransjo, Bindslev et al. 1996; Hildebrandt

Another successful approach preventing biofilm formation comprises the use of Diamond-Like Carbon (DLC) coatings on the ureteral stent. DLC is a thermodynamically meta-stable state of carbon where diamond-like (sp3-hybridized) and graphite-like (sp2-hybridized) bonding coexist with a large fraction of sp3 bonds. Coatings can be prepared by miscellaneous deposition methods, e.g. ion deposition, sputtering, pulsed laser deposition and plasma-enhanced chemical vapor deposition, using accelerated hydrocarbon ions as film forming particles (Grill 1999). In general, they are characterized by high mechanical hardness and chemical inertness. Depending on the deposition conditions, the properties of DLC films can be adjusted depending on the applications, e.g. allowing enhancement of the wear and corrosion resistance of precision cutting and machining tools. These films are already used as protective coatings on magnetic hard disks and optical glasses. They showed excellent tribological and mechanical properties, corrosion resistance, biocompatibility, and hemocompatibility (Anne Thomson *et al.* 1991; Roy and Lee 2007; Voevodin and Donley 1996). Recent studies have been focused on their ability to decrease the formation of crystalline bacterial biofilm as well as stent related side effects and

The evaluation of the *in vivo* efficacy of both heparin and plasma deposited DLC-coated ureteral stent have been reported. Recent works show the superiority of both coated stents for preventing biofilm adhesion and encrustation compared to uncoated PU catheters

patient care and leading to kidney infections, sepsis and shock (Warren et al. 1994).

*et al.* 1999; Ruggieri, Hanno and Levin 1987).

discomfort (Laube *et al.* 2006; Laube *et al.* 2007).

(Cauda *et al.* 2009).

In urology, catheterization is defined as the insertion of tubes (stents), such as urinary catheters, into the patient's bladder through the urethra. A stent is usually a tube with ending coils at both sides (pig-tails), or with lateral holes to further improve urine drainage (JJ or double-J). Urethral stents are usually in latex, silicone or polyurethane, allowing patients' urine to drain freely from the bladder. Stents can also be used to inject liquids for treatment or bladder conditions diagnosis. A patient is typically catheterized in the case of acute or chronic urinary retention, orthopedic procedures that may limit movement, benign prostatic hyperplasia, incontinence, and effects of various surgical interventions involving bladder and prostrate.

In endourology, urine is drained by indwelling a catheter between the kidney and the patient's bladder, hence inserting the stent into the ureter. Nowadays, ureteral stenting has become a common procedure for safe urine drainage. It is effective for managing several diseases, such as ureteral obstruction by stones or clots, benign or malignant ureteral obstruction, or post-surgical treatments, i.e. ureteroscopy and ureteral surgery. Ureteral stents almost painlessly keep the ureteral lumen open, ensuring that urine flows while maintaining the correct renal function. Stents also promote ureteral healing and prevent strictures formation.

From a general urological viewpoint, these devices must be easily maneuverable, affordable, and radiopaque for a correct positioning under fluoroscopic guidance. Hence, ureteral stents are mainly fabricated in PU or silicone since some patients can be allergic or sensitive to latex after long-term use. Radiopacity is ensured by adding metallic salts, e.g. based on barium. According to a critical study on materials (Mardis et al. 1993), the use of strong materials, e.g. PU, permits the reduction of the stent wall thickness, enlarging the inner lumen and the size or number of lateral holes and increasing urine flow. Silicone stents are weaker than PU, and need to be fabricated with smaller inner diameters, compromising urine flow and increasing the lateral compressibility.

Despite the numerous advantages enabled by PU, some complications and challenges remain. Indeed, PU is not perfectly biocompatible, in the sense that it somehow affects the epithelial cells of the ureter (urothelium): urothelial ulceration and erosion may occur. Other complications are related to stent migration or fracture, erosion, development of ureteroarterial fistula, fever, infection, voiding symptoms including dysuria and hematuria (Arshad et al. 2006). Among these, the stent encrustation represents one of the most serious complications resulting from the use of PU double-J stents: a stent can be encrusted by inorganic salts flowing with urine, and bacterial colonies can grow on the surface. These infections are very common among the general population, sometimes leading to death. During infections, the bacteria grow in the internal lumen of the stent, forming the so-called "biofilm", normally an aggregation of bacteria with their extracellular products and several inorganic salts (Costerton 2007). This matrix covers the cells, leading to a reduced susceptibility to prophylactic antibiotics (Tenke et al. 2004). Moreover, the development of these encrustations can obstruct the device and impair the urinary flow, compromising with patient care and leading to kidney infections, sepsis and shock (Warren et al. 1994).

124 Polyurethane

bladder and prostrate.

strictures formation.

urine flow and increasing the lateral compressibility.

Given its large use, in this chapter we will focus on the use of PU in urological applications,

In urology, catheterization is defined as the insertion of tubes (stents), such as urinary catheters, into the patient's bladder through the urethra. A stent is usually a tube with ending coils at both sides (pig-tails), or with lateral holes to further improve urine drainage (JJ or double-J). Urethral stents are usually in latex, silicone or polyurethane, allowing patients' urine to drain freely from the bladder. Stents can also be used to inject liquids for treatment or bladder conditions diagnosis. A patient is typically catheterized in the case of acute or chronic urinary retention, orthopedic procedures that may limit movement, benign prostatic hyperplasia, incontinence, and effects of various surgical interventions involving

In endourology, urine is drained by indwelling a catheter between the kidney and the patient's bladder, hence inserting the stent into the ureter. Nowadays, ureteral stenting has become a common procedure for safe urine drainage. It is effective for managing several diseases, such as ureteral obstruction by stones or clots, benign or malignant ureteral obstruction, or post-surgical treatments, i.e. ureteroscopy and ureteral surgery. Ureteral stents almost painlessly keep the ureteral lumen open, ensuring that urine flows while maintaining the correct renal function. Stents also promote ureteral healing and prevent

From a general urological viewpoint, these devices must be easily maneuverable, affordable, and radiopaque for a correct positioning under fluoroscopic guidance. Hence, ureteral stents are mainly fabricated in PU or silicone since some patients can be allergic or sensitive to latex after long-term use. Radiopacity is ensured by adding metallic salts, e.g. based on barium. According to a critical study on materials (Mardis et al. 1993), the use of strong materials, e.g. PU, permits the reduction of the stent wall thickness, enlarging the inner lumen and the size or number of lateral holes and increasing urine flow. Silicone stents are weaker than PU, and need to be fabricated with smaller inner diameters, compromising

Despite the numerous advantages enabled by PU, some complications and challenges remain. Indeed, PU is not perfectly biocompatible, in the sense that it somehow affects the epithelial cells of the ureter (urothelium): urothelial ulceration and erosion may occur. Other complications are related to stent migration or fracture, erosion, development of ureteroarterial fistula, fever, infection, voiding symptoms including dysuria and hematuria (Arshad et al. 2006). Among these, the stent encrustation represents one of the most serious complications resulting from the use of PU double-J stents: a stent can be encrusted by inorganic salts flowing with urine, and bacterial colonies can grow on the surface. These infections are very common among the general population, sometimes leading to death. During infections, the bacteria grow in the internal lumen of the stent, forming the so-called "biofilm", normally an aggregation of bacteria with their extracellular products and several inorganic salts (Costerton 2007). This matrix covers the cells, leading to a reduced susceptibility to prophylactic antibiotics (Tenke et al. 2004). Moreover, the development of

in particular as ureteral catheter, or stent, in endourology routines.

Temporary prevention from encrustation includes stent replacement at regular intervals, modification of the type or size of catheters, washing the catheter and bladder with acidic, antiseptic or saline solutions (Arshad, Shah and Abbasi 2006). Antibiotics are still orally administered whenever stent is replaced or inserted for preventing infections (Reid 2001).

However all these approaches are mostly ineffective. For this reason stent surface modifications have been proposed to prevent bacterial and inorganic molecule adhesion. Various strategies have been conceived, using silver-coated surfaces (Leung *et al.* 1992; Multanen *et al.* 2000), surface modification towards hydrophobicity (Jansen *et al.* 1993) or functional groups creation with intrinsic antimicrobial activity. Heparin is a good candidate for solving these problems. In previous *in vitro* and *in vivo* studies, heparinization of medical devices showed a reduction of microbial colonization (Appelgren *et al.* 1996; Cauda *et al.* 2008; Ruggieri *et al.* 1987). Heparin is a highly sulfated, anionic polysaccharide known for its anti-coagulant and anti-thrombogenic properties (Piper 1946). It has a strong negative electrical charge able to prevent cells adhesion since bacterial' cell membrane surface is also negatively charged. Coating stents with heparin can be practical and low-cost. Over the last three decades several studies, especially in vascular medicine, were indeed reported, showing that this approach is effective (Appelgren, Ransjo, Bindslev et al. 1996; Hildebrandt *et al.* 1999; Ruggieri, Hanno and Levin 1987).

Another successful approach preventing biofilm formation comprises the use of Diamond-Like Carbon (DLC) coatings on the ureteral stent. DLC is a thermodynamically meta-stable state of carbon where diamond-like (sp3-hybridized) and graphite-like (sp2-hybridized) bonding coexist with a large fraction of sp3 bonds. Coatings can be prepared by miscellaneous deposition methods, e.g. ion deposition, sputtering, pulsed laser deposition and plasma-enhanced chemical vapor deposition, using accelerated hydrocarbon ions as film forming particles (Grill 1999). In general, they are characterized by high mechanical hardness and chemical inertness. Depending on the deposition conditions, the properties of DLC films can be adjusted depending on the applications, e.g. allowing enhancement of the wear and corrosion resistance of precision cutting and machining tools. These films are already used as protective coatings on magnetic hard disks and optical glasses. They showed excellent tribological and mechanical properties, corrosion resistance, biocompatibility, and hemocompatibility (Anne Thomson *et al.* 1991; Roy and Lee 2007; Voevodin and Donley 1996). Recent studies have been focused on their ability to decrease the formation of crystalline bacterial biofilm as well as stent related side effects and discomfort (Laube *et al.* 2006; Laube *et al.* 2007).

The evaluation of the *in vivo* efficacy of both heparin and plasma deposited DLC-coated ureteral stent have been reported. Recent works show the superiority of both coated stents for preventing biofilm adhesion and encrustation compared to uncoated PU catheters (Cauda *et al.* 2009).

Despite these recent advances, oral administration of antibiotics (e.g. ciproflaxin) cannot be avoided. Papers in this respect report that bacteria proliferation has been addressed with a local release of antibiotics or antiseptics (Cormio *et al.* 2001; John *et al.* 2007; Leung *et al.* 2001; Raad *et al.* 1997). Drug-Eluting Stent (DES) has the advantage of maximizing the local tissue levels of therapeutic agents while minimizing systemic toxicity. The problem has been faced with antibiotics incorporation (Gorman and Woolfson 2002) using novel biomimetic and bioactive silicones. For example, with a gentamicin-releasing urethral catheter, encrustation inhibition in a rabbit model has been shown in the short term (Cho *et al.* 2001). Other authors (Cadieux *et al.* 2006) reported on a triclosan-loaded ureteral stent implanted in rabbit bladders with bacterial infection. The study showed a significant decrease of urinary tract infection rate. However, a very high control on the delivery kinetics has been not achieved yet.

Polyurethane in Urological Practice 127

**indwelling**

like biofilm formation, inorganic encrustation extent, stiffness, brittleness or failure of the PU material depending on the indwelling time will be examined. The surface chemistry and morphology characterization of the indwelled stents will also be evaluated according to the surface coating and biofilm formation. The characterization techniques used in this work included Field Emission Scanning Electron Microscopy (FESEM), Energy Dispersive

We review here the results collected from 2006 to 2010, concerning the characterization studies on uncoated, heparin- and DLC-coated PU double-J ureteral stents (all provided by Cook Ireland LTD) after indwelling. We enrolled 59 patients (from 45 to 75 years old). 49 patients showed unilateral ureteral obstruction, thus requiring ureteral stenting in the affected ureter. The patients with unilateral obstruction received an heparin-coated, DLC-

10 patients suffered from bilateral obstruction, therefore the coated and uncoated PU stents were indwelled at the same time in both ureters, respectively. Each patient with bilateral obstruction received randomly both the coated stent (with heparin or with a diamond-like carbon coating) in one ureter, and the uncoated one, thus the pure PU stent, in the other ureter. Stents indwelling was also studied for different periods of time. The stent types and

**stents Coating Indwelling time Type of**

14 Heparin 1-3 months Unilateral 9 Heparin > 3 months Unilateral

19 Nonea 1-3 months Unilateral 3 None > 3 months Unilateral

4 DLC 1 month Unilateral

5b None 1 month Bilateral 5b Heparin 1 month Bilateral

5b None 1 month Bilateral 5b DLC 1 month Bilateral

b These stents were implanted bilaterally, thus inserting both the uncoated and the coated stents into both ureters

**Table 1.** Stents types and indwelling periods of the PU, heparin-coated and diamond-like carbon

**2.1. Experimental part: Patients, stents and characterization methods**

Spectroscopy (EDS), and Infrared (IR) spectroscopy.

coated or an uncoated PU stent in the ureter to be treated.

indwelling times are reported in Table 1.

a None indicates that the stent surface is of pure PU.

respectively of the same patient.

coated PU stents.

**Number of**

Another important problem with stents is that they require an additional cytoscopic procedure for their removal. Stents removal may be uncomfortable for the patient, in particular when these are encrusted, therefore requiring hospitalization and anaesthesia. Considering this big concern, the development of time bio-degradable stent materials has become a major keypoint. In principle, bio-adsorbable stents shall be designed to maintain their integrity for a given period of time, and undergo a dissolution process followed by spontaneous expulsion by the patient at the same time.

So far, the bio-degradable stents degrade very fast (typically 48h) or leave fragments removable by lithotripsy and ureteroscopy (Lingeman *et al.* 2003). Some tests on pigs with degradable poly-L-lactic-L-glycolic acid (PLGA) devices showed fragments embedded in the ureteral walls within cystic sacs, normally leading to fibrosis, inflammation and a large foreign body giant cell reaction (Olweny *et al.* 2002). These results show that further enhancement on their degradable characteristics is highly required. It is straightforward that the future of ureteral stents will head towards this direction, i.e. to chemically controlled biodegradation, combined to a concomitant release of biologically active molecules on target sites and with minimally invasive surgical procedures. Moreover, highly engineered stents can possibly work as a "scaffolds" for tissue regeneration via cell attachment and proliferation, finally controlling the local inflammation and healing (Zdrahala and Zdrahala 1999).

This chapter focuses in details on the use of PU catheters for endourological applications, providing new insights on the *in vivo* performances of PU stent. Given to our past expertise, we report on the influence of the PU surface treatments in preventing the encrustation and the formation of bacterial biofilm when implanted into the ureter.


*Article* **Analysis of the Viability of a Photovoltaic Greenhouse with Semi-Transparent Amorphous Silicon (a-Si) Glass**

**José-Ramón Aira 1 , Sara Gallardo-Saavedra 2 , Marcia Eugenio-Gozalbo 3 , Víctor Alonso-Gómez 4 , Miguel-Ángel Muñoz-García 5 and Luis Hernández-Callejo 2,\***

**Abstract:** For decades, society has been changing towards an energy mix that enhances the use of renewable sources and a more distributed generation of energy. The agricultural sector is included in this trend, which is why several studies are currently being carried out focused on the use of solar energy in greenhouses. This article aims to demonstrate the viability of a greenhouse that integrates, as a novelty, semi-transparent amorphous silicon photovoltaic (PV) glass (a-Si), covering the entire roof surface and the main sides of the greenhouse. The designed prototype is formed by a simple rectangular structure 12 m long and 2.5 m wide, with a monopitch roof, oriented to the southwest, and with a 35◦ inclination. The greenhouse is divided into two contiguous equal sections, each with an area of 15 m2 , and physically separated by an interior partition transparent wall. The surface enclosure of one of the sections is made of conventional glass, and the one of the other, of PV glass. How the presence of semitransparent PV glass influences the growth of horticultural crops has been studied, finding that it slightly reduces the production of vegetal mass and accelerates the apical growth mechanism of heliophilic plants. However, from a statistical point of view, this influence is negligible, so it is concluded that the studied technology is viable for horticultural production. The energy balance carried out indicates that the energy produced by the PV system is greater than the energy consumed by the greenhouse, which shows that the greenhouse is completely viable and self-sufficient for sites with the adequate solar resource.

**Keywords:** sustainable greenhouse; semi-transparent photovoltaic panels; amorphous silicon; building-integrated photovoltaics; distributed generation; microgrid