Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models

Unraveling autonomic cardiovascular control complexity during orthostatic stress: Insights from a mathematical model

Understanding cardiovascular control mediated by the autonomic system remains challenging due to its inherent complexity. Consequently, syndromes such as orthostatic intolerance continue to evoke debates regarding the underlying pathophysiological mechanisms. This study develops a comprehensive mathematical model simulating the control of the sympathetic branch of the cardiovascular system in individuals with normal and abnormal responses to the head-up-tilt test. We recruited four young women: one control, one with vasovagal syncope, one with orthostatic hypertension, and one with orthostatic hypotension, exposing them to an orthostatic head-up tilt test (HUTT) employing non-invasive methods to measure electrocardiography and continuous blood pressure. Our work encompasses a compartmental model formulated using a system of ordinary differential equations. Using heart rate as input, we predict blood pressure, flow, and volume in compartments representing the veins, arteries, heart, and the sympathetic branch of the baroreflex control system. The latter is modulated by high- and low-pressure baroreceptor afferents activated by changes in blood pressure induced by the HUTT. Sensitivity analysis, parameter subset selection, and optimization are employed to estimate patient-specific parameters associated with autonomic performance. The model has seven sensitive and identifiable parameters with significant physiological relevance that can serve as biomarkers for patient classification. Results show that the model can reproduce a spectrum of blood pressure responses successfully, fitting the trajectory displayed by the experimental data. The controller exhibits behavior that emulates the operation of the sympathetic system. These encouraging findings underscore the potential of computational methods in evaluating pathologies associated with autonomic nervous system control, warranting further exploration and novel approaches.

Nonlinear Closed-Loop Predictive Control of Heart Rate and Blood Pressure Using Vagus Nerve Stimulation: An In Silico Study

We propose a nonlinear model-based control technique for regulating the heart rate and blood pressure using vagus nerve neuromodulation. The closed-loop framework is based on an in silico model of the rat cardiovascular system for the simulation of the hemodynamic response to multi-location vagal nerve stimulation. The in silico model is derived by compartmentalizing the various physiological components involved in the closed-loop cardiovascular system with intrinsic baroreflex regulation to virtually generate nominal and hypertension-related heart dynamics of rats in rest and exercise states. The controller, using a reduced cycle-averaged model, monitors the outputs from the in silico model, estimates the current state of the reduced model, and computes the optimum stimulation locations and the corresponding parameters using a nonlinear model predictive control algorithm. The results demonstrate that the proposed control strategy is robust with respect to its ability to handle setpoint tracking and disturbance rejection in different simulation scenarios.

Parameter inference in a computational model of haemodynamics in pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.

Seven Mathematical Models of Hemorrhagic Shock

Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject's responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.

Patient-specific parameter estimation: Coupling a heart model and experimental data

This study develops a hemodynamic model involving the atrium, ventricle, veins, and arteries that can be calibrated to experimental results. It is a Windkessel model that incorporates an unsteady Bernoulli effect in the blood flow to the atrium. The model is represented by ordinary differential equations in terms of blood volumes in the compartments as state variables and it demonstrates the use of conductance instead of resistance to capture the effect of a non-leaking heart valve. The experimental results are blood volume data from 20 young (half of which are women) and 20 elderly (half of which are women) subjects during rest, inotropic stress (dobutamine), and chronotropic stress (glycopyrrolate). The model is calibrated to conform with data and physiological findings in 4 different levels. First, an optimization routine is devised to find model parameter values that give good fit between the model volume curves and blood volume data in the atrium and ventricle. Patient-specific information are used to get initial parameter values as a starting point of the optimization. Also, model pressure curves must show realistic behavior. Second, parametric bootstrapping is performed to establish the reliability of the optimal parameters. Third, statistical tests comparing mean optimal parameter values from young vs elderly subjects and women vs men are examined to support and present age and sex related differences in heart functions. Lastly, statistical tests comparing mean optimal parameter values from resting condition vs pharmacological stress are studied to verify and quantify the effects of dobutamine and glycopyrrolate to the cardiovascular system.

A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during an endotoxin challenge

KEY POINTS

Inflammation in response to bacterial endotoxin challenge impacts physiological functions, including cardiovascular, thermal and pain dynamics, although the mechanisms are poorly understood. We develop an innovative mathematical model incorporating interaction pathways between inflammation and physiological processes observed in response to an endotoxin challenge. We calibrate the model to individual data from 20 subjects in an experimental study of the human inflammatory and physiological responses to endotoxin, and we validate the model against human data from an independent study. Using the model to simulate patient responses to different treatment modalities reveals that a multimodal treatment combining several therapeutic strategies gives the best recovery outcome.

ABSTRACT

Uncontrolled, excessive production of pro-inflammatory mediators from immune cells and traumatized tissues can cause systemic inflammatory conditions such as sepsis, one of the ten leading causes of death in the USA, and one of the three leading causes of death in the intensive care unit. Understanding how inflammation affects physiological processes, including cardiovascular, thermal and pain dynamics, can improve a patient's chance of recovery after an inflammatory event caused by surgery or a severe infection. Although the effects of the autonomic response on the inflammatory system are well-known, knowledge about the reverse interaction is lacking. The present study develops a mathematical model analyzing the inflammatory system's interactions with thermal, pain and cardiovascular dynamics in response to a bacterial endotoxin challenge. We calibrate the model with individual data from an experimental study of the inflammatory and physiological responses to a one-time administration of endotoxin in 20 healthy young men and validate it against data from an independent endotoxin study. We use simulation to explore how various treatments help patients exposed to a sustained pathological input. The treatments explored include bacterial endotoxin adsorption, antipyretics and vasopressors, as well as combinations of these. Our findings suggest that the most favourable recovery outcome is achieved by a multimodal strategy, combining all three interventions to simultaneously remove endotoxin from the body and alleviate symptoms caused by the immune system as it fights the infection.