Mathematical modelling of cardiovascular response to the Valsalva manoeuvre

Postural orthostatic tachycardia syndrome explained using a baroreflex response model

Patients with postural orthostatic tachycardia syndrome (POTS) experience an excessive increase in heart rate (HR) and low-frequency (∼0.1 Hz) blood pressure (BP) and HR oscillations upon head-up tilt (HUT). These responses are attributed to increased baroreflex (BR) responses modulating sympathetic and parasympathetic signalling. This study uses a closed-loop cardiovascular compartment model controlled by the BR to predict BP and HR dynamics in response to HUT. The cardiovascular model predicts these quantities in the left ventricle, upper and lower body arteries and veins. HUT is simulated by letting gravity shift blood volume (BV) from the upper to the lower body compartments, and the BR control is modelled using set-point functions modulating peripheral vascular resistance, compliance, and cardiac contractility in response to changes in mean carotid BP. We demonstrate that modulation of parameters characterizing BR sensitivity allows us to predict the persistent increase in HR and the low-frequency BP and HR oscillations observed in POTS patients. Moreover, by increasing BR sensitivity, inhibiting BR control of the lower body vasculature, and decreasing central BV, we demonstrate that it is possible to simulate patients with neuropathic and hyperadrenergic POTS.

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.

Transcapillary transport of water, small solutes and proteins during hemodialysis

The semipermeable capillary walls not only enable the removal of excess body water and solutes during hemodialysis (HD) but also provide an essential mechanism for maintaining cardiovascular homeostasis. Here, we investigated transcapillary transport processes on the whole-body level using the three-pore model of the capillary endothelium with large, small and ultrasmall pores. The transcapillary transport and cardiovascular response to a 4-h hemodialysis (HD) with 2 L ultrafiltration were analyzed by simulations in a virtual patient using the three-pore model of the capillary wall integrated in the whole-body compartmental model of the cardiovascular system with baroreflex mechanisms. The three-pore model revealed substantial changes during HD in the magnitude and direction of transcapillary water flows through small and ultrasmall pores and associated changes in the transcapillary convective transport of proteins and small solutes. The fraction of total capillary hydraulic conductivity attributed to ultrasmall pores was found to play an important role in the transcapillary water transport during HD thus influencing the cardiovascular response to HD. The presented model provides a novel computational framework for a detailed analysis of microvascular exchange during HD and as such may contribute to a better understanding of dialysis-induced changes in blood volume and blood pressure.

Relative blood volume changes during haemodialysis estimated from haemoconcentration markers

Relative blood volume (RBV) monitoring is frequently used in haemodialysis patients to help guide fluid management and improve cardiovascular stability. RBV changes are typically estimated based on online measurements of certain haemoconcentration markers, such as haematocrit (HCT), haemoglobin (HGB) or total blood protein concentration (TBP). The beginning of a haemodialysis procedure, i.e. filling the extracorporeal circuit with the patient’s blood (with the priming saline being infused to the patient or discarded) may be associated with relatively dynamic changes in the circulation, and hence the observed RBV changes may depend on the exact moment of starting the measurements. The aim of this study was to use a mathematical model to assess this issue quantitatively. The model-based simulations indicate that when the priming saline is not discarded but infused to the patient, a few-minute difference in the moment of starting RBV tracking through measurements of HCT, HGB or TBP may substantially affect the RBV changes observed throughout the dialysis session, especially with large priming volumes. A possible overestimation of the actual RBV changes is the highest when the measurements are started within a couple of minutes after the infusion of priming saline is completed.

A model-based analysis of autonomic nervous function in response to the Valsalva maneuver

The Valsalva maneuver (VM) is a diagnostic protocol examining sympathetic and parasympathetic activity in patients with autonomic dysfunction (AD) impacting cardiovascular control. Because direct measurement of these signals is costly and invasive, AD is typically assessed indirectly by analyzing heart rate and blood pressure response patterns. This study introduces a mathematical model that can predict sympathetic and parasympathetic dynamics. Our model-based analysis includes two control mechanisms: respiratory sinus arrhythmia (RSA) and the baroreceptor reflex (baroreflex). The RSA submodel integrates an electrocardiogram-derived respiratory signal with intrathoracic pressure, and the baroreflex submodel differentiates aortic and carotid baroreceptor regions. Patient-specific afferent and efferent signals are determined for 34 control subjects and 5 AD patients, estimating parameters fitting the model output to heart rate data. Results show that inclusion of RSA and distinguishing aortic/carotid regions are necessary to model the heart rate response to the VM. Comparing control subjects to patients shows that RSA and baroreflex responses are significantly diminished. This study compares estimated parameter values from the model-based predictions to indices used in clinical practice. Three indices are computed to determine adrenergic function from the slope of the systolic blood pressure in phase II [α (a new index)], the baroreceptor sensitivity (β), and the Valsalva ratio (γ). Results show that these indices can distinguish between normal and abnormal states, but model-based analysis is needed to differentiate pathological signals. In summary, the model simulates various VM responses and, by combining indices and model predictions, we study the pathologies for 5 AD patients.NEW & NOTEWORTHY We introduce a patient-specific model analyzing heart rate and blood pressure during a Valsalva maneuver (VM). The model predicts autonomic function incorporating the baroreflex and respiratory sinus arrhythmia (RSA) control mechanisms. We introduce a novel index (α) characterizing sympathetic activity, which can distinguish control and abnormal patients. However, we assert that modeling and parameter estimation are necessary to explain pathologies. Finally, we show that aortic baroreceptors contribute significantly to the VM and RSA affects early VM.

Modeling Pathological Hemodynamic Responses to the Valsalva Maneuver

The Valsalva maneuver (VM) consisting in a forced expiration against closed airways is one of the most popular clinical tests of the autonomic nervous system function. When properly performed by a healthy subject, it features four characteristic phases of arterial blood pressure (BP) and heart rate (HR) variations, based on the magnitude of which the autonomic function may be assessed qualitatively and quantitatively. In patients with some disorders or in healthy patients subject to specific conditions, the pattern of BP and HR changes during the execution of the Valsalva maneuver may, however, differ from the typical sinusoidal-like pattern. Several types of such abnormal responses are well known and correspond to specific physiological conditions. In this paper, we use our earlier mathematical model of the cardiovascular response to the Valsalva maneuver to show that such pathological responses may be simulated by changing individual model parameters with a clear physiological meaning. The simulation results confirm the adaptability of our model and its usefulness for diagnostic or educational purposes.