Abstract: Collagen extracellular matrix is one of the factors related to high passive stiffness of cardiac muscle. However, the architecture and the mechanical aspects of the cardiac collagen matrix are not completely known. In particular, endomysial collagen contribution to the passive mechanics of cardiac muscle as well as its micro anatomical arrangement is still a matter of debate. In order to investigate mechanical and structural properties of endomysial collagen, we consider two alternative computational models of some specific aspects of the cardiac muscle. These two models represent two different views of endomysial collagen distribution: (1) the traditional view and (2) a new view suggested by the data obtained from scanning electron microscopy (SEM) in NaOH macerated samples (a method for isolating collagen from the other tissue). We model the myocardial tissue as a net of spring elements representing the cardiomyocytes together with the endomysial collagen distribution. Each element is a viscous elastic spring, characterized by an elastic and a viscous constant. We connect these springs to imitate the interconnections between collagen fibers. Then we apply to the net of springs some external forces of suitable magnitude and direction, obtaining an extension of the net itself. In our setting, the ratio forces magnitude /net extension is intended to model the stress /strain ratio of a microscopical portion of the myocardial tissue. To solve the problem of the correct identification of the values of the different parameters involved, we use an artificial neural network approach. In particular, we use this technique to learn, given a distribution of external forces, the elastic constants of the springs needed to obtain a desired extension as an equilibrium position. Our experimental findings show that, in the model of collagen distribution structured according to the new view, a given stress /strain ratio (of the net of springs, in the sense specified above) is obtained with much smaller (w.r.t. the other model, corresponding to the traditional view) elasticity constants of the springs. This seems to indicate that by an appropriate structure, a given stiffness of the myocardial tissue can be obtained with endomysial collagen fibers of much smaller size.

Abstract: A Cyber-Physical System (CPS) comprises physical as well as software subsystems. Simulation-based approaches are typically used to support design and Verification and Validation (V&V) of CPSs in several domains such as: aerospace, defence, automotive, smart grid and healthcare. Accordingly, many simulation-based tools are available to support CPS design. This, on one side, enables designers to choose the toolchain that best suits their needs, on the other side poses huge interoperability challenges when one needs to simulate CPSs whose subsystems have been designed and modelled using different toolchains. To overcome such an interoperability problem, in 2010 the Functional Mock-up Interface (FMI) has been proposed as an open standard to support both Model Exchange (ME) and Co-Simulation (CS) of simulation models created with different toolchains. FMI has been adopted by several modelling and simulation environments. Models adhering to such a standard are called Functional Mock-up Units (FMUs). Indeed FMUs play an essential role in defining complex CPSs through, e.g., the System Structure and Parametrization (SSP) standard. Simulation-based V&V of CPSs typically requires exploring different simulation scenarios (i.e., exogenous input sequences to the CPS under design). Many such scenarios have a shared prefix. Accordingly, to avoid simulating many times such shared prefixes, the simulator state at the end of a shared prefix is saved and then restored and used as a start state for the simulation of the next scenario. In this context, an important FMI feature is the capability to save and restore the internal FMU state on demand. This is crucial to increase efficiency of simulation-based V&V. Unfortunately, the implementation of this feature is not mandatory and it is available only within some commercial software. As a result, the interoperability enabled by the FMI standard cannot be fully exploited for V&V when using open-source simulation environments. This motivates developing such a feature for open-source CPS simulation environments. Accordingly, in this paper, we focus on JModelica, an open-source modelling and simulation environment for CPSs based on an open standard modelling language, namely Modelica. We describe how we have endowed JModelica with our open-source implementation of the FMI 2.0 functions needed to save and restore internal states of FMUs for ME. Furthermore, we present experimental results evaluating, through 934 benchmark models, correctness and efficiency of our extended JModelica. Our experimental results show that simulation-based V&V is, on average, 22 times faster with our get/set functionality than without it.