Multiscale modeling and data integration in the virtual physiological rat project

Abstract

It has become increasingly evident that the descriptions of many complex diseases are only possible by taking into account multiple influences at different physiological scales. To do this with computational models often requires the integration of several models that have overlapping scales (genes to molecules, molecules to cells, cells to tissues). The Virtual Physiological Rat (VPR) Project, a National Institute of General Medical Sciences (NIGMS) funded National Center of Systems Biology, is tasked with mechanistically describing several complex diseases and is therefore identifying methods to facilitate the process of model integration across physiological scales. In addition, the VPR has a considerable experimental component and the resultant data must be integrated into these composite multiscale models and made available to the research community. A perspective of the current state of the art in model integration and sharing along with archiving of experimental data will be presented here in the context of multiscale physiological models. It was found that current ontological, model and data repository resources and integrative software tools are sufficient to create composite models from separate existing models and the example composite model developed here exhibits emergent behavior not predicted by the separate models.

Figure 1

Integrated model of cardiovascular system dynamics. (a) Integrated model as a combination of the simple cardiovascular model of Smith et al. and the baroreflex model of Bugenhagen et al. The two ventricles of the heart are labeled “lv” and “rv,” for left and right ventricle. Two compliant compartments, labeled “ao” and “vc” for aorta and vena cava, represent the systemic circulation. Similarly, two compartments labeled “pa” and “pv” for pulmonary artery and pulmonary vein represent the pulmonary circulation. (b) Example output from the Smith et al. model, reproduced with permission. (c) Example fit of simulated to measured heart rate for the baroreflex model of Bugenhagen et al., reproduced with permission

Figure 2

Simulation of integrated cardiovascular mechanics model. The upper panel shows simulated left-ventricular and aortic pressure during baseline conditions, during a transient 20 mmHg increase in thoracic pressure (period labeled “Valsalva,” and during recovery. The lower panel shows predicted heart rate during the simulation

Figure 3

Integrative cellular based vessel model of the steady-state myogenic response. Vessel wall stress controls Ca²⁺ influx, which in turn determines level of VSM contraction and vessel diameter. Nine hypothetical stress-controlled ion channels were independently inserted into the model to show (upper panel of nine figures) six possibilities (boxed plots) to fit experimental data. However known trends of membrane potential, cytosolic Ca²⁺ and cytosolic Na⁺ are only matched by simulations (star) of the stress-controlled Na⁺ influx through non-selective cation (NSC) channel. Adapted from Carlson and Beard reproduced with permission

Figure 4

Integrated model of vascular blood flow regulation in a single vessel incorporating response to vessel wall stress induced by changes in intraluminal pressure and response to shear stress on VE cells due to changes in blood flow through the vessel. The VSM cell model incorporates a previous model by Kapela et al. with the addition of α₂-, β₁- and β₂-adrenoceptors and stress-controlled Ca²⁺ influx. The VE cell model utilizes an existing model by Silva et al. adding α- and β-adrenoceptors and O₂- and H₂O₂-dependent NO production. The vessel wall mechanics model is similar to a previous model by Carlson and Secomb with the addition of a viscous element

Figure 5

Description of workflow using JSim and SemGen used to develop the cardiovascular system dynamics model (a) and generic workflow necessary for the annotation and merging of computational models (b). In Example 1 CellML and MML were used as model instantiation languages while SemSim was the language used to capture both model instantiation and semantic annotation. JSim was used to facilitate the translation from CellML to MML and annotation, merging and translation of the composite model to MML were performed with SemGen. In (b) red arrows indicate model input, green arrows indicate model output and blue arrows indicate internal connections between Model 1 and Model 2 in the composite model