Model of arterial tree and peripheral control for the study of physiological and assisted circulation

Bifurcation in Blood Oscillatory Rhythms for Patients with Ischemic Stroke: A Small Scale Clinical Trial using Laser Doppler Flowmetry and Computational Modeling of Vasomotion

We describe application of spectral analysis of laser Doppler flowmetry (LDF) signals to investigation of cerebrovascular haemodynamics in patients with post-acute ischemic stroke (AIS) and cerebrovascular insufficiency. LDF was performed from 3 to 7 days after the onset of AIS on forehead in the right and left supraorbital regions in patients. Analysis of LDF signals showed that perfusion in the microvasculature in AIS patients was lower than that in patients with cerebrovascular insufficiency. As a result of wavelet analysis of the LDF signals we obtained activation of the vasomotion in the frequency range of myogenic oscillation of 0.1 Hz and predominantly nutritive regime microcirculation after systemic thrombolytic therapy of the AIS patients. In case of significant stroke size, myogenic activity, and nutritive pattern microhaemodynamics were reduced, in some cases non-nutritive pattern and/or venular stasis was revealed. Wavelet analysis of the LDF signals also showed asymmetry in wavelet spectra of the LDF signals obtained in stroke-affected and unaffected hemispheres in the AIS patients. A mechanism underlying the observed asymmetry was analyzed by computational modeling of vasomotion developed in Arciero and Secomb (2012). We applied this model to describe relaxation oscillation of arteriole diameter which is forced by myogenic oscillation induced by synchronous calcium oscillation in vascular smooth muscle cells. Calculation showed that vasomotion frequency spectrum at the low-frequency range (0.01 Hz) is reciprocally modulated by myogenic oscillation (0.1 Hz) that correlates with experimental observation of inter-hemispheric variation in the LDF spectrum.

A Model of the Cardiorespiratory Response to Aerobic Exercise in Healthy and Heart Failure Conditions

The physiological response to physical exercise is now recognized as an important tool which can aid the diagnosis and treatment of cardiovascular diseases. This is due to the fact that several mechanisms are needed to accommodate a higher cardiac output and a higher oxygen delivery to tissues. The aim of the present work is to provide a fully closed loop cardiorespiratory simulator reproducing the main physiological mechanisms which arise during aerobic exercise. The simulator also provides a representation of the impairments of these mechanisms in heart failure condition and their effect on limiting exercise capacity. The simulator consists of a cardiovascular model including the left and right heart, pulmonary and systemic circulations. This latter is split into exercising and non-exercising regions and is controlled by the baroreflex and metabolic mechanisms. In addition, the simulator includes a respiratory model reproducing the gas exchange in lungs and tissues, the ventilation control and the effects of its mechanics on the cardiovascular system. The simulator was tested and compared to the data in the literature at three different workloads whilst cycling (25, 49 and 73 watts). The results show that the simulator is able to reproduce the response to exercise in terms of: heart rate (from 67 to 134 bpm), cardiac output (from 5.3 to 10.2 l/min), leg blood flow (from 0.7 to 3.0 l/min), peripheral resistance (from 0.9 to 0.5 mmHg/(cm³/s)), central arteriovenous oxygen difference (from 4.5 to 10.8 ml/dl) and ventilation (6.1–25.5 l/min). The simulator was further adapted to reproduce the main impairments observed in heart failure condition, such as reduced sensitivity of baroreflex and metabolic controls, lower perfusion to the exercising regions (from 0.6 to 1.4 l/min) and hyperventilation (from 9.2 to 40.2 l/min). The simulator we developed is a useful tool for the description of the basic physiological mechanisms operating during exercise. It can reproduce how these mechanisms interact and how their impairments could limit exercise performance in heart failure condition. The simulator can thus be used in the future as a test bench for different therapeutic strategies aimed at improving exercise performance in cardiopathic subjects.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Aortic valve dynamics using a fluid structure interaction model--The physiology of opening and closing

Comparative study among aortic valves requires the use of an unbiased and relevant boundary condition. Pressure and flow boundary conditions used in literature are not sufficient for an unbiased analysis. We need a different boundary condition to analyze the valves in an unbiased, relevant environment. The proposed boundary condition is a combination of the pressure and flow boundary condition methods, which is chosen considering the demerits of the pressure and flow boundary conditions. In order to study the valve in its natural environment and to give a comparative analysis between different boundary conditions, a fluid-structure interaction analysis is made using the pressure and the proposed boundary conditions for a normal aortic valve. Commercial software LS-DYNA is used in all our analysis. The proposed boundary condition ensures a full opening of the valve with reduced valve regurgitation. It is found that for a very marginal raise in the ventricular pressure caused by pumping a fixed stroke volume, the cardiac output is considerably raised. The mechanics of the valve is similar between these two boundary conditions, however we observe that the importance of the root to raise the cardiac output may be overstated, considering the importance of the fully open nodule of arantius. Our proposed boundary condition delivers all the insights offered by the pressure and flow boundary conditions, along with providing an unbiased framework for the analysis of different valves and hence, more suitable for comparative analysis.

A unified method for estimating pressure losses at vascular junctions

In reduced-order (0D/1D) blood or respiratory flow models, pressure losses at junctions are usually neglected. However, these may become important where velocities are high and significant flow redirection occurs. Current methods for estimating losses rely on relatively complex empirical equations that are only valid for specific junction geometries and flow regimes. In pulsatile multi-directional flows, switching between empirical equations upon reversing flow may introduce unrealistic discontinuities in simulated haemodynamic waveforms. Drawing from work by Bassett et al. (SAE Trans 112:565-583, 2003), we therefore developed a unified method (Unified0D) for estimating loss coefficients that can be applied to any junction (i.e. any number of branches at any angle) and any flow regime. Discontinuities in simulated waveforms were avoided by extending Bassett et al.'s control volume-based method to incorporate a 'pseudodatum' supplier branch, an imaginary effective vessel containing all inflow to the junction. Energy exchange between diverging flow streams was also accounted for empirically. The formulation was validated using high resolution computational fluid dynamics in a wide range flow conditions and junction configurations. In a pulsatile 1D simulation exhibiting transitions between four different flow regimes, the new formulation produced smooth transitions in calculated pressure losses.

Modeling Cerebral Blood Flow Velocity During Orthostatic Stress

Cerebral autoregulation refers to the physiological process that maintains stable cerebral blood flow (CBF) during changes in arterial blood pressure (ABP). In this study, we propose a simple, nonlinear quantitative model with only four parameters that can predict CBF velocity as a function of ABP. The model was motivated by the viscoelastic-like behavior observed in the data collected during postural change from sitting to standing. Qualitative testing of the model involved analysis of dynamic responses to step-changes in pressure both within and outside the autoregulatory range, while quantitative testing was used to show that the model can fit dynamics observed in data measured from a healthy young and a healthy elderly subject. The latter involved analysis of structural and practical identifiability, sensitivity analysis, and parameter estimation. Results showed that the model is able to reproduce observed overshoot and adaptation and predict the different responses in the healthy young and the healthy elderly subject. For the healthy young subject, the overshoot was significantly more pronounced than for the elderly subject, but the recovery time was longer for the young subject. These differences resulted in different parameter values estimated using the two datasets.

A clinically applicable stochastic approach for noninvasive estimation of aortic stiffness using computed tomography data

The degeneration of the vascular wall tissue induces a change of the arterial stiffness, i.e., the capability of the vessel to distend under the pulsatile hemodynamic load. In the literature, the aortic stiffness is usually computed following a simple deterministic approach, in which only the maximum and the minimum values of arterial diameter and blood pressure over the cardiac cycle are considered. In this paper, we propose a stochastic approach to assess the stiffness, and its spatial variation, of a given aortic region exploiting patient-specific geometrical data derived from computed tomography angiography (CTA). In particular, the arterial stiffness is computed linking the aortic kinematic information derived from CTA with pressure waveforms, generated using a lumped parameter model of the arterial circulation. The proposed method is able to include the uncertainty of the input variables as well as to use the entire diameter and blood pressure waveforms over the cardiac cycle rather than only their maximum and minimum values. Although the efficiency and accuracy of the proposed method are tested on a single patient-specific case, the proposed approach is powerful and already possesses the ability to evaluate regional changes of stiffness in human aorta using noninvasive data. The final objective of our paper is to support the adoption of techniques such as CTA as a standard tool for diagnosis and treatment planning of aortic diseases.

Inertance estimation in a lumped-parameter hydraulic simulator of human circulation

Pulsatile mock loop systems are largely used to investigate the cardiovascular system in vitro. They consist of a pump, which replicates the heart, coupled with a lumped-parameter hydraulic afterload, which simulates vasculature. An accurate dimensioning of components is required for a reliable mimicking of the physiopathological behavior of the system. However, it is not possible to create a component for the afterload inertance, and inertance contributions are present in the entire circuit. Hence, in the literature, inertance is neglected or qualitatively evaluated. In this paper, we propose two quantitative methods (Maximum-likelihood estimation (MLE) and Bayesian estimation) for estimating afterload inertance based on observed pressure and flow waveforms. These methods are also applied to a real mock loop system. Results show that the system has an inertance comparable with the literature reference value of the entire systemic circulation, and that the expected variations over inlet average flow and pulse frequency are in general confirmed. Comparing the methods, the Bayesian approach results in higher and more stable estimations than the classical MLE.

A dimensionally-heterogeneous closed-loop model for the cardiovascular system and its applications

In the present work a computational model of the entire cardiovascular system is developed using heterogeneous mathematical representations. This model integrates different levels of detail for the blood circulation. The arterial tree is described by a one dimensional model in order to simulate the wave propagation phenomena that take place at the larger arterial vessels. The inflow and outflow locations of this 1D model are coupled with lumped parameter descriptions of the remainder part of the circulatory system, closing the loop. The four cardiac valves are considered using a valve model which allows for stenoses and regurgitation phenomena. In addition, full 3D geometrical models of arterial districts are embedded in this closed-loop circuit to model the local blood flow in specific vessels. This kind of detailed closed-loop network for the cardiovascular system allows hemodynamics analyses of patient-specific arterial district, delivering naturally the appropriate boundary conditions for different cardiovascular scenarios. An example of application involving the effect of aortic insufficiency on the local hemodynamics of a cerebral aneurism is provided as a motivation to reproduce, through numerical simulation, the hemodynamic environment in patients suffering from infective endocarditis and mycotic aneurisms. The need for incorporating homeostatic control mechanisms is also discussed in view of the large sensitivity observed in the results, noting that this kind of integrative modeling allows such incorporation.

A lumped parameter model of cerebral blood flow control combining cerebral autoregulation and neurovascular coupling

Cerebral blood flow regulation is based on a variety of different mechanisms, of which the relative regulatory role remains largely unknown. The cerebral regulatory system expresses two regulatory properties: cerebral autoregulation and neurovascular coupling. Since partly the same mechanisms play a role in cerebral autoregulation and neurovascular coupling, this study aimed to develop a physiologically based mathematical model of cerebral blood flow regulation combining these properties. A lumped parameter model of the P2 segment of the posterior cerebral artery and its distal vessels was constructed. Blood flow regulation is exerted at the arteriolar level by vascular smooth muscle and implements myogenic, shear stress based, neurogenic, and metabolic mechanisms. In eight healthy subjects, cerebral autoregulation and neurovascular coupling were challenged by squat-stand maneuvers and visual stimulation using a checkerboard pattern, respectively. Cerebral blood flow velocity was measured using transcranial Doppler, whereas blood pressure was measured by finger volume clamping. In seven subjects, the model proposed fits autoregulation and neurovascular coupling measurement data well. Myogenic regulation is found to dominate the autoregulatory response. Neurogenic regulation, although only implemented as a first-order mechanism, describes neurovascular coupling responses to a great extent. It is concluded that our single, integrated model of cerebral blood flow control may be used to identify the main mechanisms affecting cerebral blood flow regulation in individual subjects.

On the integration of the baroreflex control mechanism in a heterogeneous model of the cardiovascular system

The aim of the present work is to describe the integration of a mathematical model for the baroreceptor reflex mechanism to provide regulatory action into a dimensionally heterogeneous (3D-1D-0D) closed-loop model of the cardiovascular system. Such heterogeneous model comprises a 1D description of the arterial tree, a 0D network for the venous, cardiac and pulmonary circulations and 3D patient-specific geometries for vascular districts of interest. Thus, the detailed topological description of the arterial network allows us to perform vasomotor control actions in a differentiated way, while gaining insight about the effects of the baroreflex regulation over hemodynamic quantities of interest throughout the entire network. Two examples of application are presented. Firstly, we simulate the hemorrhage in the abdominal aorta artery and analyze the action of the baroreflex over the system. Secondly, the self-regulated closed-loop model is applied to study the influence of the control action in the hemodynamic environment that determines the blood flow pattern in a cerebral aneurism in the presence of a regurgitating aortic valve.

Global sensitivity analysis of a wave propagation model for arm arteries

Wave propagation models of blood flow and blood pressure in arteries play an important role in cardiovascular research. For application of these models in patient-specific simulations a number of model parameters, that are inherently subject to uncertainties, are required. The goal of this study is to identify with a global sensitivity analysis the model parameters that influence the output the most. The improvement of the measurement accuracy of these parameters has largest consequences for the output statistics. A patient specific model is set up for the major arteries of the arm. In a Monte-Carlo study, 10 model parameters and the input blood volume flow (BVF) waveform are varied randomly within their uncertainty ranges over 3000 runs. The sensitivity in the output for each system parameter was evaluated with the linear Pearson and ranked Spearman correlation coefficients. The results show that model parameter and input BVF uncertainties induce large variations in output variables and that most output variables are significantly influenced by more than one system parameter. Overall, the Young's modulus appears to have the largest influence and arterial length the smallest. Only small differences were obtained between Spearman's and Pearson's tests, suggesting that a high monotonic association given by Spearman's test is associated with a high linear corelation between the inputs and output parameters given by Pearson's test.

Myogenic activity in autoregulation during low frequency oscillations

Lower body negative pressure (LBNP) was applied in eight human subjects to trigger low frequency oscillations in order to study the nature of functional coupling between the hemodynamic and autonomic nervous systems, with particular focus on how the myogenic response fits within this coupling. To this end muscle sympathetic nerve activity (MSNA), mean arterial pressure (MAP), heart rate (HR), cardiac output (CO), and total peripheral resistance (TPR) were measured at baseline and during LBNP and were then examined in both the time and frequency domains. At the height of low frequency oscillations (~0.1Hz) there was a strong coupling between all the five indices, marked by perfect alignment of their oscillatory frequencies. Results in the time domain show that a fall in MAP is followed by a fall in TPR at 1.58s SD 0.69), a rise in heart rate at 2.64s (SD 0.98), a rise in cardiac output at 3.72s (SD 0.60), a peak in MSNA at 5.71s (SD 1.27) and, finally, a rise in TPR at 7.13s (SD 1.02). A possible interpretation of the latter is that a drop in MAP first triggers a drop in TPR via a myogenic response before the expected rise in TPR via a rise in MSNA. In other words, following a drop in arterial pressure, myogenic response controls vessel diameter before this control is taken over by MSNA. These findings provide a possible resolution of a longstanding conceptual argument against attributing a significant role for the myogenic response in blood flow autoregulation.

Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way

To estimate arterial stiffness, different methods based either on distensibility, pulse wave velocity or a pressure-velocity loop, have been proposed. These methods can be employed to determine the arterial mechanical properties either locally or globally, e.g. averaged over an entire arterial segment. The aim of this study was to investigate the feasibility of a new method that estimates distributed arterial mechanical properties non-invasively. This new method is based on a wave propagation model and several independent ultrasound and pressure measurements. Model parameters (including arterial mechanical properties) are obtained from a reverse method in which differences between modeling results and measurements are minimized using a fitting procedure based on local sensitivity indices. This study evaluates the differences between in vivo measured and simulated blood pressure and volume flow waveforms at the brachial, radial and ulnar arteries of 6 volunteers. The estimated arterial Young's modulus range from 1.0 to 6.0MPa with an average of (3.8±1.7)MPa at the brachial artery and from 1.2 to 7.8MPa with an average of (4.8±2.2)MPa at the radial artery. A good match between measured and simulated waveforms and the realistic stiffness parameters indicate a good in vivo suitability.

Simulation study of autoregulation responses of peripheral circulation to systemic pulsatility

BACKGROUND

This simulation study investigated potential modulations of total peripheral resistance (TPR), due to distributed peripheral vascular activity, by means of a lumped model of the arterial tree and a non linear model of microcirculation, inclusive of local controls of blood flow and tissue-capillary fluid exchange.

RESULTS

Numerical simulations of circulation were carried out to compute TPR under different conditions of blood flow pulsatility, and to extract the pressure-flow characteristics of the cardiovascular system. Simulations showed that TPR seen by the large arteries was increased in absence of pulsatility, while it decreased with an augmented harmonic content. This is a typically non linear effect due to the contribution of active, non linear autoregulation of the peripheral microvascular beds, which also generated a nonlinear relationship between arterial blood pressure and cardiac output.

CONCLUSION

This simulation study, though focused on a simple effect attaining TPR modulation due to pulsatility, suggests that non-linear autoregulation mechanisms cannot be overlooked while studying the integrated behavior of the global cardiovascular system, including the arterial tree and the peripheral vascular bed.

Cerebral autoregulation: from models to clinical applications

Short-term regulation of cerebral blood flow (CBF) is controlled by myogenic, metabolic and neurogenic mechanisms, which maintain flow within narrow limits, despite large changes in arterial blood pressure (ABP). Static cerebral autoregulation (CA) represents the steady-state relationship between CBF and ABP, characterized by a plateau of nearly constant CBF for ABP changes in the interval 60-150 mmHg. The transient response of the CBF-ABP relationship is usually referred to as dynamic CA and can be observed during spontaneous fluctuations in ABP or from sudden changes in ABP induced by thigh cuff deflation, changes in posture and other manoeuvres. Modelling the dynamic ABP-CBFV relationship is an essential step to gain better insight into the physiology of CA and to obtain clinically relevant information from model parameters. This paper reviews the literature on the application of CA models to different clinical conditions. Although mathematical models have been proposed and should be pursued, most studies have adopted linear input-output ('black-box') models, despite the inherently non-linear nature of CA. The most common of these have been transfer function analysis (TFA) and a second-order differential equation model, which have been the main focus of the review. An index of CA (ARI), and frequency-domain parameters derived from TFA, have been shown to be sensitive to pathophysiological changes in patients with carotid artery disease, stroke, severe head injury, subarachnoid haemorrhage and other conditions. Non-linear dynamic models have also been proposed, but more work is required to establish their superiority and applicability in the clinical environment. Of particular importance is the development of multivariate models that can cope with time-varying parameters, and protocols to validate the reproducibility and ranges of normality of dynamic CA parameters extracted from these models.

Integrated model of endothelial NO regulation and systemic circulation for the comparison between pulsatile and continuous perfusion

Many experimental studies concerning nitric oxide (NO) release from endothelium and its vasodilative action are available in the literature, but no analytical description or modeling of these phenomena can be found. On the contrary, a large modeling literature is available concerning the other cardiovascular control mechanisms, such as the myogenic and metabolic control. In order to analytically describe these phenomena, a model of the endothelial control (defined in the Laplace domain and based on experimental data) was implemented and integrated with a lumped-parameter model of the systemic circulation, consisting of large artery segments and peripheral networks. The endothelial regulation model was based on the hypothesis proposed by Kuchan and Frangos, considering that NO release from the endothelium is generated by two parallel paths. The whole model was then applied to study the different vascular constriction or dilation under continuous or pulsatile perfusion, in order to better understand the clinical evidences of a poor organ perfusion in the presence of continuous with respect to pulsatile cardiopulmonary bypass. According to the experimental evidences, the main results obtained from the model revealed a widespread vascular constriction under continuous perfusion with respect to pulsatile. This result remains constant in the presence of different conditions of blood parameters and flow waveform.

Multivariate parametric model for the identification of diastolic pressure and pulse pressure components

Arterial pressure variability is a relatively unexplored topic among the various and detailed studies of cardiovascular variability. A deeper analysis of components and contributions carried by diastolic and pulse pressure may provide a unique insight on the potential systemic effects due to vasomotor activity and response at the level of microcirculation, whose dynamics are either driven by neural and vascular modulations. The aim of the present work is to develop a multivariate parametric model for the identification of the main components of diastolic and pulse pressure in order to investigate all the potential correlations between systemic arterial pressure variability and peripheral sources of oscillations and to analyze their interactions with the most known mechanisms of cardiovascular regulation.