A computational model for emergent dynamics in the kidney

Modeling the Steady-State Effects of Mean Arterial Pressure on the Kidneys

Goal: We describe the relationship between mean arterial pressure (MAP) and glomerular filtration rate (GFR) since therapies affecting MAP can have large effects on kidney function. Methods: We developed a closed-loop, steady-state mechanistic model of the human kidney with a reduced parameter set estimated from measurements. Results: The model was first validated against literature models. Further, GFR was validated against intensive care patient data (root mean squared error (RMSE) 13.5 mL/min) and against hypertensive patients receiving sodium nitroprusside (SNP) (RMSE less than 5 mL/min). A sensitivity analysis of the model reinforced the fact that vascular resistance is inversely related to GFR and showed that changes to either vascular resistance or renal autoregulation cause a significant change in sodium concentration in the descending limb of Henle. Conclusions: This model can be used to determine the impact of MAP on GFR and overall kidney health. The modeling framework lends itself to personalization of the model to a specific human.

Intraglomerular crosstalk elaborately regulates podocyte injury and repair in diabetic patients: insights from a 3D multiscale modeling study

Podocytes are mainly involved in the regulation of glomerular filtration rate (GFR) under physiological condition. Podocyte depletion is a crucial pathological alteration in diabetic nephropathy (DN) and results in a broad spectrum of clinical syndromes such as protein urine and renal insufficiency. Recent studies indicate that depleted podocytes can be regenerated via differentiation of the parietal epithelial cells (PECs), which serve as the local progenitors of podocytes. However, the podocyte regeneration process is regulated by a complicated mechanism of cell-cell interactions and cytokine stimulations, which has been studied in a piecemeal manner rather than systematically. To address this gap, we developed a high-resolution multi-scale multi-agent mathematical model in 3D, mimicking the in situ glomerulus anatomical structure and micro-environment, to simulate the podocyte regeneration process under various cytokine perturbations in healthy and diabetic conditions. Our model showed that, treatment with pigment epithelium derived factor (PEDF) or insulin-like growth factor-1 (IGF-1) alone merely ameliorated the glomerulus injury, while co-treatment with both cytokines replenished the damaged podocyte population gradually. In addition, our model suggested that continuous administration of PEDF instead of a bolus injection sustained the regeneration process of podocytes. Part of the results has been validated by our in vivo experiments. These results indicated that amelioration of the glomerular stress by PEDF and promotion of PEC differentiation by IGF-1 are equivalently critical for podocyte regeneration. Our 3D multi-scale model represents a powerful tool for understanding the signaling regulation and guiding the design of cytokine therapies in promoting podocyte regeneration.

Implementation of a model of bodily fluids regulation

The classic model of blood pressure regulation by Guyton et al. (Annu Rev Physiol 34:13–46, 1972a; Ann Biomed Eng 1:254–281, 1972b) set a new standard for quantitative exploration of physiological function and led to important new insights, some of which still remain the focus of debate, such as whether the kidney plays the primary role in the genesis of hypertension (Montani et al. in Exp Physiol 24:41–54, 2009a; Exp Physiol 94:382–388, 2009b; Osborn et al. in Exp Physiol 94:389–396, 2009a; Exp Physiol 94:388–389, 2009b). Key to the success of this model was the fact that the authors made the computer code (in FORTRAN) freely available and eventually provided a convivial user interface for exploration of model behavior on early microcomputers (Montani et al. in Int J Bio-med Comput 24:41–54, 1989). Ikeda et al. (Ann Biomed Eng 7:135–166, 1979) developed an offshoot of the Guyton model targeting especially the regulation of body fluids and acid–base balance; their model provides extended renal and respiratory functions and would be a good basis for further extensions. In the interest of providing a simple, useable version of Ikeda et al.’s model and to facilitate further such extensions, we present a practical implementation of the model of Ikeda et al. (Ann Biomed Eng 7:135–166, 1979), using the ODE solver Berkeley Madonna.

Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis

We present a lumped-nephron model that explicitly represents the main features of the underlying physiology, incorporating the major hormonal regulatory effects on both tubular and vascular function, and that accurately simulates hormonal regulation of renal salt and water excretion. This is the first model to explicitly couple glomerulovascular and medullary dynamics, and it is much more detailed in structure than existing whole organ models and renal portions of multiorgan models. In contrast to previous medullary models, which have only considered the antidiuretic state, our model is able to regulate water and sodium excretion over a variety of experimental conditions in good agreement with data from experimental studies of the rat. Since the properties of the vasculature and epithelia are explicitly represented, they can be altered to simulate pathophysiological conditions and pharmacological interventions. The model serves as an appropriate starting point for simulations of physiological, pathophysiological, and pharmacological renal conditions and for exploring the relationship between the extrarenal environment and renal excretory function in physiological and pathophysiological contexts.

The Virtual Kidney: an eScience interface and Grid portal

The Virtual Kidney uses a web interface and distributed computing to provide experimental scientists and analysts with access to computational simulations and knowledge databases hosted in geographically separated laboratories. Users can explore a variety of complex models without requiring the specific programming environment in which applications have been developed. This initiative exploits high-bandwidth communication networks for collaborative research and for shared access to knowledge resources. The Virtual Kidney has been developed within a specialist community of renal scientists but is transferable to other areas of research requiring interaction between published literature and databases, theoretical models and simulations and the formulation of effective experimental designs. A web-based three-dimensional interface provides access to experimental data, a parameter database and mathematical models. A multi-scale kidney reconstruction includes blood vessels and serially sectioned nephrons. Selection of structures provides links to the database, returning parameter values and extracts from the literature. Models are run locally or remotely with a Grid resource broker managing scheduling, monitoring and visualization of simulation results and application, credential and resource allocation. Simulation results are viewed graphically or as scaled colour gradients on the Virtual Kidney structures, allowing visual and quantitative appreciation of the effects of simulated parameter changes.