Mathematical methods for modeling the microcirculation

The microcirculation plays a major role in maintaining homeostasis in the body. Alterations or dysfunctions of the microcirculation can lead to several types of serious diseases. It is not surprising, then, that the microcirculation has been an object of intense theoretical and experimental study over the past few decades. Mathematical approaches offer a valuable method for quantifying the relationships between various mechanical, hemodynamic, and regulatory factors of the microcirculation and the pathophysiology of numerous diseases. This work provides an overview of several mathematical models that describe and investigate the many different aspects of the microcirculation, including geometry of the vascular bed, blood flow in the vascular networks, solute transport and delivery to the surrounding tissue, and vessel wall mechanics under passive and active stimuli. Representing relevant phenomena across multiple spatial scales remains a major challenge in modeling the microcirculation. Nevertheless, the depth and breadth of mathematical modeling with applications in the microcirculation is demonstrated in this work. A special emphasis is placed on models of the retinal circulation, including models that predict the influence of ocular hemodynamic alterations with the progression of ocular diseases such as glaucoma

Doctor of Philosophy

dissertationThe cerebrovasculature is vital in maintaining health in the brain, but can be damaged by traumatic brain injury (TBI). Even in cases without hemorrhage, vessels are deformed with the surrounding tissue. Subfailure deformation could result in altered mechanical properties and dysfunction of these vessels. This dissertation aims to provide a better understanding of the biaxial mechanical properties of cerebral arteries, as well as determine mechanical stretch thresholds which produce ultimate failure and subfailure alteration of mechanical properties or vessel function. Three in vitro studies were undertaken. Passive biaxial mechanical properties under physiological loading, as well as failure properties of rat middle cerebral arteries (MCAs), were measured and compared to those of human pial arteries. Best fit parameters for a Fung type strain energy function are provided for the biaxial mechanical properties. Rat MCAs are stiffer in the axial direction than the circumferential, but less stiff in both directions than human arteries. Rat MCAs also exhibit a lower ultimate failure stress but higher failure stretch. The effect of subfailure axial overstretch on the contractile behavior of smooth muscle cells (SMCs) in rat MCAs was investigated. Potassium dose response tests were conducted before and after a single axial overstretch, with varying magnitude and strain rate. Overstretches beyond a threshold of both magnitude and strain rate significantly reduced SMC contraction relative to time-matched controls, mirrored by an increase in potassium concentration required to evoke the half maximal contraction. The effect of subfailure axial overstretch on passive mechanical properties in sheep MCAs was investigated. Axial response was measured before and after a single quasi-static overstretch of various magnitudes. Post-overstretch, samples showed persistent softening (lower stress values at a given level of stretch). Softening was only observed above an overstretch threshold, and then increased with overstretch severity until a second threshold was reached, above which softening did not increase until failure. This dissertation provides improved understanding of cerebrovascular mechanics and relationships between such data acquired from animals and humans. It also provides insight into the potential role of subfailure cerebrovascular damage in disease states associated with TBI, such as second impact syndrome and strok

Piezo1: Proteins for mechanotransduction and integration of endothelial shear stress & intravascular pressure

Piezo proteins are transmembrane ion channels, specialized in detecting mechanosensitive stimuli and transduce mechanical forces into biochemical signals. Piezo proteins research has helped understand physiological mechanisms, but the integrative role that Piezo1 plays in the regulation of the microvasculature has remained unstudied. Our main objective was to characterize ex vivo microvascular responses to the blockade of Piezo1 mechanotransduction in male (n=29) and female (n=24) Sprague-Dawley (SD) rats. Gracilis arterioles (GA) and middle cerebral arterioles (MCA) were harvested for ex-vivo vessel preparations. After vessel viability confirmation, every vessel was submitted to myogenic and flow challenges under control conditions and after Grammostola Mechanotoxin 4 (GsMTx4) incubation to blocking Piezo1 channels, to quantify the homeostatic response of arterioles before and after Piezo1 antagonism. We are able to report Piezo1 as indispensable component in vascular smooth muscle cells (VSMC) and Endothelial cells (EC) to sense and change vessel diameter based on intravascular pressure and shear stress, correspondingly. Also, we report for the first time a heterogeneous response in males and females after Piezo1 antagonism in representative resistance arterioles from the skeletal muscle and cerebral circulation

Age-associated Arterial Remodelling and Cardiovascular Diseases

Arterial remodelling is a major risk factor for a variety of age-related diseases and represents a potential target for therapeutic development. During ageing, the structural, mechanical and functional changes of arteries predispose individuals to the development of diseases related to vascular abnormalities in vital organs such as the brain, heart, eye and kidney. For example, aortic stiffness increases nonlinearly with advancing age – a few percent prior to 50 years of age but over 70% after 70 years of age. The elevated stiffness in large elastic arteries leads to increased transmission of high pressure to downstream smaller blood vessels, in turn affecting the microcirculation and end-organ functions. Meanwhile, the augmented remodelling of small arteries accelerates central arterial stiffening. This chapter is to provide an overview of age-associated changes in the arterial wall and their contributions to both central and peripheral vascular abnormalities associated with ageing. Therapeutics that specially target the different aspects of arterial remodelling are expected to be more effective than the traditional medications, particularly for the treatment and management of vascular ageing-related diseases.published_or_final_versio

TRPM4 in cerebral artery smooth muscle cells

2012 Fall.Includes bibliographical references.Cerebral arterial tone is dependent on the depolarizing and hyperpolarizing currents regulating membrane potential and governing the influx of Ca2+ needed for smooth muscle contraction. Several ion channels have been proposed to contribute to membrane depolarization, but the underlying molecular mechanisms are not fully understood. In this review, we will discuss the historical and physiological significance of the Ca2+-activated cation channel, TRPM4, in regulating membrane potential of cerebral artery smooth muscle cells. As a member of the recently described transient receptor potential super family of ion channels, TRPM4 possesses the biophysical properties and upstream cellular signaling and regulatory pathways that establish it as a major physiological player in smooth muscle membrane depolarization

Towards clinical assessment of cerebral blood flow regulation using ultrasonography : model applicability in clinical studies

For preservation of its vital functions, the brain is largely dependent of a sufficient delivery of oxygen and nutrients. Blood flow to the brain is essentially regulated by 2 control mechanisms i.e. neurovascular coupling and cerebral autoregulation. Cerebral autoregulation aims for constant adequate blood supply by compensating for blood pressure variations by dilatation or narrowing of the cerebral microvasculature. Neurovascular coupling adjusts blood supply to the local metabolic need. Cerebral perfusion and blood flow regulation are compromised in several pathological conditions. Clinical examination of cerebral blood flow and its regulation may therefore provide helpful diagnostic, predictive and therapeutic information. The work in this thesis was aimed at putting a step forward towards development of reliable and clinically usable parameters for cerebral blood flow regulation assessment using ultrasonography. Regarding early diagnostics, screening and monitoring of cerebral blood flow and its regulation, ultrasonography has major advantages over other imaging tools because of its noninvasiveness, cost-effectiveness, easy usability and its good time resolution. It allows examination of blood flow velocities at multiple locations throughout the extra- and intracranial circulation and evaluation of both control mechanisms by transfer function analysis. For evaluation of cerebral autoregulation, transcranial Doppler blood flow velocities in the large middle cerebral arteries have been recorded simultaneously with plethysmographic (finger) blood pressure. Gain and phase of the pressure-flow transfer function have been determined to obtain quantitative measures for cerebral autoregulation. Neurovascular coupling has been assessed by presenting a visual block stimulus to a subject and simultaneous measurement of the blood flow velocity in the artery exclusively supplying the visual cortex. The obtained visually-evoked blood flow response (VEFR) has been considered as the step response of a linear second order control system model providing patient-specific parameters such as gain and damping as quantitative measures for neurovascular coupling . In chapter 2, a clinical study has been described in which extra- and intracranial blood flow velocities (BFVs), measured at multiple sites in the circulation, have been compared between Alzheimer patients (AD), patients with mild cognitive impairment (MCI) and healthy aging controls (HC). BFVs of AD were significantly lowered at proximal sites but preserved at distal sites for the internal carotid artery and middle and posterior cerebral arteries as compared to those of MCI or HC. This specific pattern can presumably be ascribed to reduced distal diameters resulting from AD pathology. MCI BFV were similar to HC BFV in the extracranial and intracranial posterior circulation, whereas they were intermediate between AD and HC in the intracranial anterior circulation. This suggests that intracranial anterior vessels are most suitable for early detection of pathological alterations resulting from AD. The study findings further indicate that extensive ultrasonographic screening of intra- and extracranial arteries is useful for monitoring BFV decline in the MCI stage. Future follow-up of MCI patients may reveal the predictive value of location-specific BFV for conversion to AD. In the same study cohort, dynamic cerebral autoregulation has been studied as discussed in chapter 3. Cerebral autoregulatory gain and phase values were similar for AD, MCI and HC which implies that the cerebral autoregulatory mechanism is preserved in AD. However, the cerebrovascular resistance index i.e. the ratio between absolute time-averaged blood pressure and flow velocity, was significantly higher in AD as compared to MCI and HC indicating that vessel stiffness is increased in AD. Indeed, it appeared to be a potential biomarker for AD development of MCI. The cerebrovascular resistance increase in AD was furthermore confirmed by windkessel model findings of a significantly elevated peripheral resistance in AD. Arterial resistance and peripheral compliance were equal for all groups. From chapter 4, the focus was shifted to assessment of local blood flow regulation. Visuallyevoked blood flow responses (VEFRs) of formerly (pre-)eclamptic patients and healthy controls have been examined to evaluate neurovascular coupling first in a relative young study population. The aim of the study was to investigate whether possible local (pre)eclampsia-induced endothelial damage was reversible or not. The measured VEFRs have been fitted with the step response of a 2nd order control system model. Although inter-group differences in model parameters were not found, a trend was observed that critical damping (z>1) occurred more frequently in former patients than in controls. Critical damping reflects an atypical VEFR, which is either uncompensated (sluggish, z>1; Tv <20) or compensated by a rise in rate time (intermediate, z>1; Tv > 20). Since these abnormal VEFRs were mainly found in former patients (but not exclusively), these response types were hypothesized to result from pathological disturbances. A revised VEFR analysis procedure to account for reliability and blood pressure dynamics has been proposed in chapter 5. This revised procedure consists of the introduction of a reliability measure for model parameters and of a model extension to consider possible blood pressure contribution to the measured VEFR. The effects of these adjustments on study outcomes have been evaluated by applying both the standard VEFR analysis procedure (applied in chapter 4) and the revised procedure to the AD study cohort. Reliability consideration resulted in about 40% VEFR exclusion, mainly due to the models’ inability to fit critically damped responses. Reliability consideration reduced parameter variability substantially. Regarding the influence of blood pressure variation, a significantly increased damping was found in AD for the standard but not for the revised model. This reversed the study conclusion from altered to normal neurovascular coupling in AD. Considering their influence on obtained parameters, both aspects i.e. reliability and blood pressure variation should be included in VEFR-analysis. Regarding clinical study outcomes, neurovascular coupling seems to be unaffected in AD since the finding of an increased damping may be ascribed to ignorance of blood pressure contribution to VEFR. Study conclusions of earlier chapters (4 and 5) emphasize the need for a model incorporating physiological features. In chapter 6, preliminary results have been reported of the application of a newly developed lumped parameter model of the visual cortex vasculature to the 3 different VEFR types. In the new model, regulatory processes i.e. neurogenic, metabolic, myogenic and shear stress mechanisms, act on smooth muscle tone which inherently leads to adjustment of microcirculatory resistance and compliance. This allows the study of effects of pathological changes on the VEFR. It may be concluded that the model provides an improved link between VEFR and physiology. Preliminary results show that the physiology-based model can describe VEFR type representatives reasonably well obtaining physiologically plausible parameter values. Thus, from a clinical perspective it may be concluded that (Duplex) ultrasonography has great potential as a standard screening tool for MCI patients. It seems worthwhile to examine all future MCI patients on extra- and intracranial blood flow velocity and to determine their cerebrovascular resistance index by simultaneous blood pressure recording. Follow-up of MCI patients will reveal the predictive value of these parameters for future AD development. Furthermore, from a methodological perspective, it can be concluded that the current standard of control system analysis to assess local cerebral blood flow regulation has limitations regarding parameter reliability and VEFR interpretation. Both reliability and interpretation may be improved by optimization and control of data acquisition quality and by use of physiology-based models. Physiological mechanisms influencing VEFR establishment should be incorporated in such a model to possibly explain part of its variance. Efforts should be directed to development and validation of physiology-based models aimed at reliable description of VEFRs by physiologically meaningful parameters

Pericytes Wrap Vessels Tight and Keep Blood Flowing Right: An Updated View of the Structure and Function of Cerebral Pericytes

The cerebrovasculature modulates its resistance to flow in order to match blood supply with the high metabolic demand of the brain. While it is accepted that vascular smooth muscle cells are capable of modulating blood flow resistance through arterioles, whether pericytes can similarly regulate blood flow through capillaries has been a topic of debate for over 100 years. First we used new transgenic mice to characterize the structural spectrum of pericytes in the brain, and found a wide range of pericyte shapes that could be grouped into two main pericyte types. We then mapped where these “ensheathing pericytes” and “capillary pericytes” live along the cerebrovascular tree, and stimulated one or two of them at a time in vivo using two photon optogenetics through a cranial window. We found that both types of pericytes can constrict their underlying blood vessel in a way that decreases local blood flow. Importantly, vascular smooth muscle cells exhibited much more dramatic constriction upon stimulation, indicating that pericytes modulate blood flow in a slower and subtler way than do vascular smooth muscle cells. To investigate if pericytes use this ability to modulate blood flow under physiological conditions, we ablated one or two capillary pericytes in the living brain. We were surprised to find that 3 days after ablation we observed a dilation of capillaries left uncovered by the pericyte ablation, which corresponded with a doubling in the number of red blood cells flowing through that capillary. Critically, we did not observe any hemodynamic changes in control animals that either did not express optogenetic proteins, or did not have any pericytes ablated. The results therefore suggest that pericytes play a role in shaping capillary blood flow through the brain. This will inform the longstanding debate, and could lead to new ways of correcting blood flow abnormalities that plague numerous neurological diseases like traumatic brain injury, epilepsy, and stroke

Regulation of Coronary Blood Flow

The heart is uniquely responsible for providing its own blood supply through the coronary circulation. Regulation of coronary blood flow is quite complex and, after over 100 years of dedicated research, is understood to be dictated through multiple mechanisms that include extravascular compressive forces (tissue pressure), coronary perfusion pressure, myogenic, local metabolic, endothelial as well as neural and hormonal influences. While each of these determinants can have profound influence over myocardial perfusion, largely through effects on end-effector ion channels, these mechanisms collectively modulate coronary vascular resistance and act to ensure that the myocardial requirements for oxygen and substrates are adequately provided by the coronary circulation. The purpose of this series of Comprehensive Physiology is to highlight current knowledge regarding the physiologic regulation of coronary blood flow, with emphasis on functional anatomy and the interplay between the physical and biological determinants of myocardial oxygen delivery. © 2017 American Physiological Society. Compr Physiol 7:321-382, 2017