A time-invariant visco-elastic windkessel model relating blood flow and blood volume

The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure-volume relationship of blood vessels is treated as a state variable dependent oil the rate of change of CBV, producing hysteresis in the pressure-volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and cardiovascular systems. (C) 2009 Elsevier Inc. All rights reserved

A Model for Transient Oxygen Delivery in Cerebral Cortex

Popular hemodynamic brain imaging methods, such as blood oxygen-level dependent functional magnetic resonance imaging (BOLD fMRI), would benefit from a detailed understanding of the mechanisms by which oxygen is delivered to the cortex in response to brief periods of neural activity. Tissue oxygen responses in visual cortex following brief visual stimulation exhibit rich dynamics, including an early decrease in oxygen concentration, a subsequent large increase in concentration, and substantial late-time oscillations (“ringing”). We introduce a model that explains the full time-course of these observations made by Thompson et al. (2003). The model treats oxygen transport with a set of differential equations that include a combination of flow and diffusion in a three-compartment (intravascular, extravascular, and intracellular) system. Blood flow in this system is modeled using the impulse response of a lumped linear system that includes an inertive element; this provides a simple biophysical mechanism for the ringing. The model system is solved numerically to produce excellent fits to measurements of tissue oxygen. The results give insight into the dynamics of cerebral oxygen transfer, and can serve as the starting point to understand BOLD fMRI measurements

Brain energetics plays a key role in the coordination of electrophysiology, metabolism and hemodynamics: evidence from an integrated computational model

The energetic needs of brain cells at rest and during elevated neuronal activation has been the topic of many investigations where mathematical models have played a significant role providing a context for the interpretation of experimental findings. A recently proposed mathematical model, comprising a double feedback between cellular metabolism and electrophysiology, sheds light on the interconnections between the electrophysiological details associated with changes in the frequency of neuronal firing and the corresponding metabolic activity. We propose a new extended mathematical model comprising a three-way feedback connecting metabolism, electrophysiology and hemodynamics. Upon specifying the time intervals of higher neuronal activation, the model generates a potassium based signal leading to the concomitant increase in cerebral blood flow with associated vasodilation and metabolic changes needed to sustain the increased energy demand. The predictions of the model are in good qualitative and quantitative agreement with experimental findings reported in the literature, even predicting a slow after-hyperpolarization of a duration of approximately 16 s matching experimental observations.The work of Daniela Calvetti was partly support by NSF grants DMS-1522334 and NIH grant 1U01 GM111251-01. The work of Erkki Somersalo was partly support by NSF grants DMS 1714617 and NIH grant 1U01GM111251-01

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

Optical Cerebral Blood Flow Monitoring of Mice to Men

This thesis describes cerebral hemodynamic monitoring with the optical techniques of diffuse optical spectroscopy (DOS) and diffuse correlation spectroscopy (DCS). DOS and DCS both employ near-infrared light to investigate tissue physiology millimeters to centimeters below the tissue surface. DOS is a static technique that analyzes multispectral tissue-scattered light intensity signals with a photon diffusion approach (Chapter 2) or a Modified Beer-Lambert law approach (Chapter 3) to derive tissue oxy- and deoxy-hemoglobin concentrations, which are in turn used to compute tissue oxygen saturation and blood volume (Section 2.13). DCS is a qualitatively different dynamic technique that analyzes rapid temporal fluctuations in tissue-scattered light with a correlation diffusion approach to derive tissue blood flow (Chapter 4). Further, in combination these measurements of blood flow and blood oxygenation provide access to tissue oxygen metabolism (Section 7.6). The new contributions of my thesis to the diffuse optics field are a novel analysis technique for the DCS signal (Chapter 5), and a novel approach for separating cerebral hemodynamic signals from extra-cerebral artifacts (Chapter 6). The DCS analysis technique extends the Modified Beer-Lambert approach for DOS to the DCS measurement. This new technique has some useful advantages compared to the correlation diffusion approach. It facilitates real-time flow monitoring in complex tissue geometries, provides a novel route for increasing DCS measurement speed, and can be used to probe tissues wherein light transport is non-diffusive (Chapter 5). It also can be used to filter signals from superficial tissues. For separation of cerebral hemodynamic signals from extra-cerebral artifacts, the Modified Beer-Lambert approach is employed in a pressure modulation scheme, which determines subject-specific contributions of extra-cerebral and cerebral tissues to the DCS/DOS signals by utilizing probe pressure modulation to induce variations in extra-cerebral hemodynamics while cerebral hemodynamics remain constant (Chapter 6). In another novel contribution, I used optical techniques to characterize neurovascular coupling at several levels of cerebral ischemia in a rat model (Chapter 7). Neurovascular coupling refers to the relationship between increased blood flow and oxygen metabolism and increased neuronal activity in the brain. In the rat, localized neuronal activity was increased from functional forepaw stimulation. Under normal flow levels, I (and others) observed that the increase in cerebral blood flow (surrogate for oxygen delivery) from forepaw stimulation exceeded the increase in cerebral oxygen metabolism by about a factor of 2. My measurements indicate that this mismatch between oxygen delivery and consumption are more balanced during ischemia (Chapter 7). In Chapters 2 and 3, I review the underlying theory for the photon diffusion model and the Modified Beer-Lambert law for DOS analysis. I also review the correlation diffusion approach for analyzing DCS signals in Chapter 4. My hope is that readers new to the field will find these background chapters helpful

Flight simulator for training gynaecologists:a mathematical model of the cardiotocogram for use in simulation training

Due to the high complexity and low incidences of emergencies during labor and delivery, gynaecologists often cannot rely on previous experiences during a crisis. Simulation training can provide both experience and skills in a safe environment, such that complications due to emergencies can be reduced as much as possible. Several simulators are available that support a safe learning environment for obstetric emergency training. However, none provides a realistic and physiology-based (simulation of) the cardiotocogram (CTG), which is a continuous and synchronous registration of uterine contractions and fetal heart rate. However, at the labor and delivery ward, the CTG is widely used as main indicator for fetal welfare. The CTG provides information on the fetal stress reaction to uterine contractions, based on oxygen levels in the fetal blood. Since the CTG is widely available and the only non-invasive method for fetal monitoring, medical decisions are often based on deviations in the CTG. The CTG is therefore an essential part of the clinical environment in medical simulation training. In a one-year clinical project as part of a qualified medical engineer training, a start is made with the development of a CTG simulator. The three main deviations in the CTG were studied: early, late and variable decelerations in fetal heart rate, caused by uterine contractions and complications in labor. The mechanism of these three deceleration types were studied, and each step was quantified for early and late decelerations. In this project, early decelerations were implemented in a mathematical model, based on the underlying physiological principles. In future, implementation of late and variable decelerations are planned within a PhD-project. A validation study was performed for the modeled CTG, where a comparison was made between real and computer-generated CTG tracings from our model, based on experts' opinion. The first results show no significant differences between real and computer-generated CTG tracings. However, the number of clinical experts was low, and a larger study has to be performed to confirm these results. Coupling of the modeled CTG to a simulator interface is planned in future. The model can be implemented in different types of simulators: in a screen-based simulator (individual in-depth training to improve insight into and interpretation of the CTG), as part of a full-body delivery simulator, and as part of a serious game (in these two cases the CTG is part of the clinical environment). Future plans include implementation in a screen-based simulator and a full-body delivery simulato

Resuscitation Endpoints in Trauma

Fluid and blood resuscitation is the mainstay of therapy for the treatment of hemorrhagic shock, whether due to trauma or other etiology. Cessation of hemorrhage with rapid hemostatic techniques is the first priority in the treatment of traumatic hemorrhagic shock, with concomitant fluid resuscitation with blood and crystalloids to maintain perfusion and organ function. “Hypotensive” or “low-volume” resuscitation has become increasingly accepted in the prehospital resuscitation phase of trauma, prior to definitive hemorrhage control, since aggressive fluid resuscitation may increase bleeding. Resuscitation after hemorrhage control is focused on restoration of tissue oxygenation. Efforts to optimize resuscitation have used “resuscitation endpoints” as markers of adequacy of resuscitation. The resuscitation endpoints that have been evaluated include both global (restoration of blood pressure, heart rate and urine output, lactate, base deficit, mixed venous oxygen saturation, ventricular end-diastolic volume) and regional (gastric tonometry, near-infrared spectroscopy for measurement of muscle tissue oxygen saturation) measures. This review critically evaluates the evidence regarding the use of resuscitation endpoints in trauma.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75386/1/j.1778-428X.2005.tb00127.x.pd