A mathematical model of long-term renal sympathetic nerve activity inhibition during an increase in sodium intake

Modeling essential hypertension with a closed-loop mathematical model for the entire human circulation

Arterial hypertension, defined as an increase in systemic arterial pressure, is a major risk factor for the development of diseases affecting the cardiovascular system. Every year, 9.4 million deaths worldwide are caused by complications arising from hypertension. Despite well-established approaches to diagnosis and treatment, fewer than half of all hypertensive patients have adequately controlled blood pressure. In this scenario, computational models of hypertension can be a practical approach for better quantifying the role played by different components of the cardiovascular system in the determination of this condition. In the present work we adopt a global closed-loop multi-scale mathematical model for the entire human circulation to reproduce a hypertensive scenario. In particular, we modify the model to reproduce alterations in the cardiovascular system that are cause and/or consequence of the hypertensive state. The adaptation does not only affect large systemic arteries and the heart but also the microcirculation, the pulmonary circulation and the venous system. Model outputs for the hypertensive scenario are validated through assessment of computational results against current knowledge on the impact of hypertension on the cardiovascular system.

Mathematical modeling of antihypertensive therapy

Hypertension is a multifactorial disease arising from complex pathophysiological pathways. Individual characteristics of patients result in different responses to various classes of antihypertensive medications. Therefore, evaluating the efficacy of therapy based on in silico predictions is an important task. This study is a continuation of research on the modular agent-based model of the cardiovascular and renal systems (presented in the previously published article). In the current work, we included in the model equations simulating the response to antihypertensive therapies with different mechanisms of action. For this, we used the pharmacodynamic effects of the angiotensin II receptor blocker losartan, the calcium channel blocker amlodipine, the angiotensin-converting enzyme inhibitor enalapril, the direct renin inhibitor aliskiren, the thiazide diuretic hydrochlorothiazide, and the β-blocker bisoprolol. We fitted therapy parameters based on known clinical trials for all considered medications, and then tested the model's ability to show reasonable dynamics (expected by clinical observations) after treatment with individual drugs and their dual combinations in a group of virtual patients with hypertension. The extended model paves the way for the next step in personalized medicine that is adapting the model parameters to a real patient and predicting his response to antihypertensive therapy. The model is implemented in the BioUML software and is available at https://gitlab.sirius-web.org/virtual-patient/antihypertensive-treatment-modeling.

Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Here we present a modular agent-based mathematical model of the human cardiovascular and renal systems. It integrates the previous models primarily developed by A. C. Guyton, F. Karaaslan, K. M. Hallow, and Y. V. Solodyannikov. We performed the model calibration to find an equilibrium state within the normal vital sign ranges for a healthy adult. We verified the model's abilities to reproduce equilibrium states with abnormal physiological values related to different combinations of cardiovascular diseases (such as systemic hypertension, chronic heart failure, pulmonary hypertension, etc.). For the model creation and validation, we involved over 200 scientific studies covering known models of the human cardiovascular and renal functions, biosimulation platforms, and clinical measurements of physiological quantities in normal and pathological conditions. We compiled detailed documentation describing all equations, parameters and variables of the model with justification of all formulas and values. The model is implemented in BioUML and available in the web-version of the software.

The sympathies of the body: functional organization and neuronal differentiation in the peripheral sympathetic nervous system

During the last 30 years, our understanding of the development and diversification of postganglionic sympathetic neurons has dramatically increased. In parallel, the list of target structures has been critically extended from the cardiovascular system and selected glandular structures to metabolically relevant tissues such as white and brown adipose tissue, lymphoid tissues, bone, and bone marrow. A critical question now emerges for the integration of the diverse sympathetic neuron classes into neural circuits specific for these different target tissues to achieve the homeostatic regulation of the physiological ends affected.

Sir George Johnson FRCP (1818-96), high blood pressure and the continuing altercation about its origins

NEW FINDINGS

What is the topic of this review? The review takes a historical approach to examining where in the body it might be possible to identify the most common cause, or causes, of long-term hypertension. It gathers evidence from histology, human and animal physiology, and computational modelling. The burden of decades of controversy is noted. What advances does it highlight? The review highlights the distinctive pathology of the afferent renal circulation and what its consequences are for the widespread view that essential hypertension is caused by elevated peripheral vascular resistance.

ABSTRACT

The widely promulgated notion that long-term elevation in mean arterial blood pressure (MAP) can be caused by raised peripheral vascular resistance remains a subject of vigorous debate. According to the 1967 mathematical model of Guyton and Coleman, such a causal relationship is impossible, kidney function being the determining factor. We explore this altercation starting with Sir George Johnson's 19th-century renal vascular histological observations in patients with Bright's disease. We note the striking physiological measurements in hypertensives by Gómez and Bolomey in the 1950s, moving on to the mathematical modelling of the circulation from the 1960s up to the ∼100-parameter computer models of the present day. Confusion has been generated by the fact that peripheral resistance is raised in hypertension in close proportion to MAP whilst cardiac output often stays normal, an apparent autoregulation, the mechanism of which is poorly understood. All models allowing for the circulation to be an open system show that isolated changes in peripheral resistance cannot lead to long-term hypertension, but models fail so frequently to account for results from experiments such as salt loading that their credibility with regard to this key finding is compromised. Laboratory animal models of adrenergic renal actions resonate with a contemporary emphasis on the sympathetic nerve supply to the kidney as contributing to the characteristically markedly elevated renal afferent resistance that appears to be the most common cause of hypertension. Remarkably, there remains no account of the way in which the fixed structural changes in vessels observed by Johnson relate to this sympathetic overactivity, which can itself be modified by drugs in the medium term. In this account, we seek to locate the crime scene and identify a smoking gun.

Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis

Congestive heart failure is characterized by suppressed cardiac output and arterial filling pressure, leading to renal retention of salt and water, contributing to further volume overload. Mathematical modeling provides a means to investigate the integrated function and dysfunction of heart and kidney in heart failure. This study updates our previously reported integrated model of cardiac and renal functions to account for the fluid exchange between the blood and interstitium across the capillary membrane, allowing the simulation of edema. A state of heart failure with reduced ejection fraction (HF-rEF) was then produced by altering cardiac parameters reflecting cardiac injury and cardiovascular disease, including heart contractility, myocyte hypertrophy, arterial stiffness, and systemic resistance. After matching baseline characteristics of the SOLVD clinical study, parameters governing rates of cardiac remodeling were calibrated to describe the progression of cardiac hemodynamic variables observed over one year in the placebo arm of the SOLVD clinical study. The model was then validated by reproducing improvements in cardiac function in the enalapril arm of SOLVD. The model was then applied to prospectively predict the response to the sodium-glucose co-transporter 2 (SGLT2) inhibitor dapagliflozin, which has been shown to reduce heart failure events in HF-rEF patients in the recent DAPAHF clinical trial by incompletely understood mechanisms. The simulations predict that dapagliflozin slows cardiac remodeling by reducing preload on the heart, and relieves congestion by clearing interstitial fluid without excessively reducing blood volume. This provides a quantitative mechanistic explanation for the observed benefits of SGLT2i in HF-rEF. The model also provides a tool for further investigation of heart failure drug therapies.

Sex-specific computational models for blood pressure regulation in the rat

In the past decades, substantial effort has been devoted to the development of computational models of the cardiovascular system. Some of these models simulate blood pressure regulation in humans and include components of the circulatory, renal, and neurohormonal systems. Although such human models are intended to have clinical value in that they can be used to assess the effects and reveal mechanisms of hypertensive therapeutic treatments, rodent models would be more useful in assisting the interpretation of animal experiments. Also, despite well-known sexual dimorphism in blood pressure regulation, almost all published models are gender neutral. Given these observations, the goal of this project is to develop the first computational models of blood pressure regulation for male and female rats. The resulting sex-specific models represent the interplay among cardiovascular function, renal hemodynamics, and kidney function in the rat; they also include the actions of the renal sympathetic nerve activity and the renin-angiotensin-aldosterone system as well as physiological sex differences. We explore mechanisms responsible for blood pressure and renal autoregulation and notable sexual dimorphism. Model simulations suggest that fluid and sodium handling in the kidney of female rats, which differs significantly from males, may contribute to their observed lower salt sensitivity as compared with males. Additionally, model simulations highlight sodium handling in the kidney and renal sympathetic nerve activity sensitivity as key players in the increased resistance of females to angiotensin II-induced hypertension as compared with males.

Mathematical models for kidney function focusing on clinical interest

We give an overview of mathematical models of renal physiology and anatomy with the clinician in mind. Beyond the past focus on issues of local transport mechanisms along the nephron and the urine concentrating mechanism, recent models have brought insight into difficult problems such as renal ischemia (oxygen and CO₂ diffusion in the medulla) or calcium and potassium homeostasis. They have also provided revealing 3D reconstructions of the full trajectories of families of nephrons and collecting ducts through cortex and medulla. The recent appearance of sophisticated whole-kidney models representing nephrons and their associated renal vasculature promises more realistic simulation of renal pathologies and pharmacological treatments in the foreseeable future.

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.