A Computer Model of Oxygen Dynamics in the Cortex of the Rat Kidney at the Cell-Tissue Level.

The renal cortex drives renal function. Hypoxia/reoxygenation are primary factors in ischemia-reperfusion (IR) injuries, but renal oxygenation per se is complex and awaits full elucidation. Few mathematical models address this issue: none captures cortical tissue heterogeneity. Using agent-based modeling, we develop the first model of cortical oxygenation at the cell-tissue level (RCM), based on first principles and careful bibliographical analysis. Entirely parameterized with Rat data, RCM is a morphometrically equivalent 2D-slice of cortical tissue, featuring peritubular capillaries (PTC), tubules and interstitium. It implements hemoglobin/O2 binding-release, oxygen diffusion, and consumption, as well as capillary and tubular flows. Inputs are renal blood flow RBF and PO2 feeds; output is average tissue PO2 (tPO2). After verification and sensitivity analysis, RCM was validated at steady-state (tPO2 37.7 ± 2.2 vs. 36.9 ± 6 mmHg) and under transients (ischemic oxygen half-time: 4.5 ± 2.5 vs. 2.3 ± 0.5 s in situ). Simulations confirm that PO2 is largely independent of RBF, except at low values. They suggest that, at least in the proximal tubule, the luminal flow dominantly contributes to oxygen delivery, while the contribution of capillaries increases under partial ischemia. Before addressing IR-induced injuries, upcoming developments include ATP production, adaptation to minutes-hours scale, and segmental and regional specification.

Integration of detailed modules in a core model of body fluid homeostasis and blood pressure regulation.

This paper presents a contribution to the definition of the interfaces required to perform heterogeneous model integration in the context of integrative physiology. A formalization of the model integration problem is proposed and a coupling method is presented. The extension of the classic Guyton model, a multi-organ, integrated systems model of blood pressure regulation, is used as an example of the application of the proposed method. To this end, the Guyton model has been restructured, extensive sensitivity analyses have been performed, and appropriate transformations have been applied to replace a subset of its constituting modules by integrating a pulsatile heart and an updated representation of the renin-angiotensin system. Simulation results of the extended integrated model are presented and the impacts of their integration within the original model are evaluated.

A computational model of the circulating renin-angiotensin system and blood pressure regulation.

UNLABELLED: The renin-angiotensin system (RAS) is critical in sodium and blood pressure (BP) regulation, and in cardiovascular-renal (CVR) diseases and therapeutics. As a contribution to SAPHIR project, we present a realistic computer model of renin production and circulating RAS, integrated into Guyton's circulatory model (GCM). Juxtaglomerular apparatus, JGA, and Plasma modules were implemented in C ++/M2SL (Multi-formalism Multi-resolution Simulation Library) for fusion with GCM. Matlab optimization toolboxes were used for parameter identification. In JGA, renin production and granular cells recruitment (GCR) are controlled by perfusion pressure (PP), macula densa (MD), angiotensin II (Ang II), and renal sympathetic activity (RSNA). In Plasma, renin and ACE (angiotensin-converting enzyme) activities are integrated to yield Ang I and II. Model vs. data deviation is given as normalized root mean squared error (nRMSE; n points). IDENTIFICATION: JGA and Plasma parameters were identified against selected experimental data. After fusion with GCM: (1) GCR parameters were identified against Laragh's PRA-natriuresis nomogram; (2) Renin production parameters were identified against two sets of data ([renin] transients vs. ACE or renin inhibition). Finally, GCR parameters were re-identified vs. Laragh's nomogram (nRMSE 8%, n = 9). VALIDATION: (1) model BP, PRA and [Ang II] are within reported ranges, and respond physiologically to sodium intake; (2) short-term Ang II infusion induces reported rise in BP and PRA. The modeled circulating RAS, in interaction with an integrated CVR, exhibits a realistic response to BP control maneuvers. This construction will allow for modelling hypertensive and CVR patients, including salt-sensitivity, polymorphisms, and pharmacotherapeutics.

SAPHIR: a physiome core model of body fluid homeostasis and blood pressure regulation.

We present the current state of the development of the SAPHIR project (a Systems Approach for PHysiological Integration of Renal, cardiac and respiratory function). The aim is to provide an open-source multi-resolution modelling environment that will permit, at a practical level, a plug-and-play construction of integrated systems models using lumped-parameter components at the organ/tissue level while also allowing focus on cellular- or molecular-level detailed sub-models embedded in the larger core model. Thus, an in silico exploration of gene-to-organ-to-organism scenarios will be possible, while keeping computation time manageable. As a first prototype implementation in this environment, we describe a core model of human physiology targeting the short- and long-term regulation of blood pressure, body fluids and homeostasis of the major solutes. In tandem with the development of the core models, the project involves database implementation and ontology development.

Dynamic simulation of mitochondrial respiration and oxidative phosphorylation: comparison with experimental results.

Hypoxia hampers ATP production and threatens cell survival. Since cellular energetics tightly controls cell responses and fate, ATP levels and dynamics are of utmost importance. An integrated mathematical model of ATP synthesis by the mitochondrial oxidative phosphorylation/electron transfer chain system has been recently published (Beard, PLoS Comput Biol 1(4):e36, 2005). This model was validated under static conditions. To evaluate its performance under dynamical situations, we implemented and simulated it (Simulink), The Mathworks). Inner membrane potential (DeltaPsi) and [NADH] (feeding the electron transfer chain) were used as indicators of mitochondrial function. Root mean squared error (rmse) was used to compare simulations and experiments (isolated cardiac mitochondria, Bose et al. J Biol Chem 278(40):39155-39165, 2003). Steady-state experimental data were reproduced within 2-6%. Model dynamics were evaluated under: (i) baseline, (ii) activation of NADH production, (iii) addition of ADP, (iv) addition of inorganic phosphate, (v) oxygen exhaustion. In all phases, except the last one, DeltaPsi and [NADH] as well as oxygen consumption, were reproduced (within 10, 7 and 12%, respectively). Under anoxia, simulated DeltaPsi markedly depolarized (no change in experiments). In conclusion, the model reproduces dynamic data as long as oxygen is present. Anticipated improvement by the inclusion of ATP consumption and explicit Krebs cycle are under evaluation.

SAPHIR - a multi-scale, multi-resolution modeling environment targeting blood pressure regulation and fluid homeostasis.

We present progress on a comprehensive, modular, interactive modeling environment centered on overall regulation of blood pressure and body fluid homeostasis. We call the project SAPHIR, for "a Systems Approach for PHysiological Integration of Renal, cardiac, and respiratory functions". The project uses state-of-the-art multi-scale simulation methods. The basic core model will give succinct input-output (reduced-dimension) descriptions of all relevant organ systems and regulatory processes, and it will be modular, multi-resolution, and extensible, in the sense that detailed submodules of any process(es) can be "plugged-in" to the basic model in order to explore, eg. system-level implications of local perturbations. The goal is to keep the basic core model compact enough to insure fast execution time (in view of eventual use in the clinic) and yet to allow elaborate detailed modules of target tissues or organs in order to focus on the problem area while maintaining the system-level regulatory compensations.