SCIENTIFIC PROGRAMS AND ACTIVITIES

March 28, 2024

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

July 7- August 1, 2014 Focus Program on
NEUROVASCULAR COUPLING AND RELATED PHENOMENA


Workshop on Cerebral Blood Flow (CBF) and Models of Neurovascular Coupling
July 14-18, 2014
at the Fields Institute
Organizer:
Tim David (Biomedical Engineering, Canterbury, NZ)

Abstracts and Brainstorm Ideas

Brainstorm Ideas

Tim David
The neurovascular coupling models have a large number of variables. We should look at the best way to analyse the sensitivity of these parameters. Uncertainty quantification analysis will help. What other methods can we utilise to investigate the complex mechanisms?

Marc Thiriet
1. Targeting BBB for selected mass transfer (nanopartcles) - Modeling
2. Influence of nervous impulse frequency on neuropeptide release.
3. Interaction between brain cell populations.

Pierre Gremaud
Brainstorming topics:We ought to talk about data analysis especially with a view towards patient specific simulation. We've done some work with a student of mine that shows scary patient dependent biases in standard measurement protocols.
Questions of interest:
-Can one detect, quantify or even predict these biases?
-Can methods from machine learning be helpful here? (I think they can).


Franck Plouraboue
three possible topics for discussions :
(i) Future issues and developments for in-vivo and ex-vivo brain microvascular network ?
(ii) How to model neuro-vascular couplings : from qualitative to quantitative ?
(iii) How high performance computing can be useful to model cerebral brain flow ?

James Kozloski
Possible topics:Multiscale modeling of neural tissue and vasculature and
Constitutive parameters estimation from tissue microstructure models


WORKSHOP ABSTRACTS

Brian Carlson
Models of acute blood flow regulation incorporating physiologically- and experimentally-based constraints.

A critical part of defining the practical complexity of a theoretical model of a physiological system is understanding what measurements can be made in an in vivo or in vitro setting and the limitations that the experimental preparation impose on the ability to define the theoretical model in addition to an understanding of the relevant physiology. So in order to represent a physiological system theoretically and identify the parameters of this model with experimental data the researcher must wear the three hats of an experimental, physiological and mathematical researcher simultaneously. In the field of acute blood flow regulation there is a wealth of existing experimental data and the methods of both in vivo and in vitro measurements are very well defined. This gives us an opportunity to capture our current understanding of the physiology of blood flow regulation in a manner that can be identified by a variety of experimental data sets.
This talk will present a couple examples of how our understanding of the physiology of blood flow regulation and experimental methods to quantify vascular responses can constrain the parameter space of the theoretical model. The first example focuses on the passive response of isolated vessels to pressure. Many models have been developed to characterize this response however it can be shown that many of these models cannot be uniquely identified by existing experimental data without imposing physiologically based constraints. In a second example the experimental method of measuring the response of an isolated vessel to pressure, phenylephrine and acetylcholine cannot uniquely define our existing models incorporating cellular smooth muscle and endothelial cell function. However combining these measurements with a secondary experiment aimed at determining the passive and active vessel response to pressure is sufficient to identify these cellular scale theoretical models of blood flow regulation.

Joshua Chang

The necessity of blood flow to the brain is obvious. The relationship between blood flow and brain pathologies however is much more subtle. In this talk I discuss a mathematical model for how blood flow changes influence a homeostatic phenomenon in the brain known as spreading depression. In spreading depression, a multiphase derangement of neurovascular coupling is known to occur.

In our model, the activity of neurons is coupled to the availability of oxygen delivered by blood vessels through modulation of ATPase pump activity. The major finding is that in some situations the metabolic needs of the brain can be elevated such that blood flow dynamics (to some extent) have a minimal effect on the recovery of the brain. After the recovery of ionic gradients in the brain, vascular dynamics are still perturbed. I will discuss a possible theory for this derangement which lasts on a long time scale and may be relevant to compromised brain states.

Tim David

A numerical model of neurovascular coupling (NVC) is presented based on neuronal activity coupled to vasodilation/contraction models via the astrocytic mediated perivascular \gls{K} and the smooth muscle cell \gls{Ca} pathway. Luminal agonists acting on P2Y receptors on the endothelial cell surface provide a flux of \gls{IP3} into the endothelial cytosol. This concentration of \gls{IP3} is transported via gap junctions between endothelial and smooth muscle cells providing a source of sacroplasmic derived \gls{Ca} in the smooth muscle cell. The model is able to relate a neuronal input signal to the corresponding vessel reaction. Results indicate the induced vasomotion by increased \gls{IP3} induced calcium from the SMC stores and the resulting CICR oscillation inhibits neurovascular coupling thereby relating blood flow to vessel contraction and dilation following neuronal activation. \gls{IP3} coupling between endothelial and smooth muscle cells seems to be important in the dynamics of the smooth muscle cell. The VOCC channels are, due to the hyperpolarisation from \gls{K} SMC efflux, almost entirely closed and do not seem to play a significant role during neuronal activity. The presented model shows that astrocytic \gls{Ca} is not necessary for neurovascular coupling to occur in contrast to a number of experiments outlining the importance of astrocytic \gls{Ca} in NVC whereas the current model makes clear that this pathway is not the only one mediating NVC. Agonists in flowing blood have a significant influence on the endothelial and smooth muscle cell dynamics.

We embed this complex model into an H-tree simulating the cerebro-vascular bed. A parallel environment is set up to solve the vascular tree where each leaf (perfusing vessel) of the tree is dynamically controlled by the solution of the NVU under neuronal activation. Our results show that the vascular bed properly dilates to accommodate increased flow to the neuronally activated tissue block. In addition the tree dynamics shows a "steal" phenomenon of blood from tissue blocks outside of the local activated tissue blocks.

Pierre Gremaud
Impedance boundary conditions for general transient hemodynamics (slides)

I will discuss the implementation and calibration of a new generalized structure tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. The performance of the method will be illustrated and validated on examples with in vivo data. I will also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. Joint work with Will Cousins (MIT).

James Kozloski
Generative Algorithms for Scaling Microstructural Models of Dendrites, Axons, and Synapses to Whole Tissues and Brain

We developed a novel neural tissue simulator to generate arbitrary neuronal morphologies, compose them into tissues, and solve for different compartment variables over shared topological constraints imposed by the tissue. Branched dendrites are generated using a simulation of diffusion subject to self referential path biases, and branched axons using a Poisson potential model for selecting longer fiber paths. With these capabilities, we demonstrate a simultaneous calculation of transmembrane voltage and calcium concentrations over a simulated Inferior Olive tissue. We introduce gap junctions at specific clusters of neuronal contacts selected based on structural criteria for olivary glomeruli. The glomeruli exchange both current and calcium among compartments across gap junctions, and we solve these without fixed point iteration beyond our two step predictor-corrector method. Robust synchronization across neurons in the tissue is achieved via these currents and calcium diffusion across coupled dendrites. We also present a novel tissue volume decomposition, and a hybrid branched cable equation solver for performing large-scale simulations of neural tissue (2011). The decomposition divides the simulation into regular tissue blocks and distributes them on a parallel multithreaded machine. The solver computes neurons that have been divided arbitrarily across blocks and can be considered a tunable hybrid of Hines' fully implicit method (1984), and the explicit predictor-corrector method of Rempe and Chopp (2006). We demonstrate thread, strong, and weak scaling of our approach on a machine of 4,096 nodes with 4 threads per node. Scaling synapses to physiological numbers had little effect on performance, since our decomposition approach generates synapses that are almost always computed locally.

Kozloski, J. and Wagner, J. (2011). Front. Neuroinform. 5:15.
Rempe, M. J., and Chopp, D. L. (2006). SIAM J. Sci. Comput. 28, 2139-2161.
Hines, M. (1984). Int. J. Biomed. Comput. 15, 69-76.

Fuyou Liang, SJTU-CU International Cooperative Research Center, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University,
Patient-specific multi-scale modeling of the cardiovascular system

Cardiovascular diseases are the world's largest killers, claiming 17.1 million lives a year (WHO). At present, the pathogenesis underlying many cardiovascular diseases remains to be fully understood. Hemodynamic factors have long been speculated to correlate closely with the onset and progression of cardiovascular diseases, which has accordingly motivated a large number of studies aimed to investigate the characteristics of hemodynamics in the context of certain cardiovascular diseases1. In these studies, model-based hemodynamic simulation has played an important role due to its ability to provide insight into the details of blood flows. The human cardiovascular system is highly complex in terms of both anatomic structure and hemodynamic behaviors. The extreme complexity of the system prevents a fully three-dimensional (3-D) modeling of the entire system. At this point, multi-scale modeling has emerged as a practical approach to obtaining detailed flow information in regions of interest while accounting for the global circulation at an affordable computational cost2. However, applying a general hemodynamic model in the clinical setting is challenging due to the presence of significant inter-patient differences in cardiovascular properties and pathological conditions3. This problem has raised the concept of patient-specific modeling, and numerous studies have contributed to this field in recent years. In this lecture, we will present several hemodynamic models that have been developed to describe various hemodynamic phenomena and introduce some methods for clinical data-based model personalization.
References
[1] Ku DN. Blood flow in arteries, Annu. Rev. Fluid Mech.1997; 29:399-434.
[2]Taelman L, Degroote J, Verdonck P, Vierendeels J, Segers P. Modeling hemodynamics in vascular networks using a geometrical multiscale approach: numerical aspects. Ann Biomed Eng. 2013; 41(7):1445-1458.
[3]Taylor CA, Figueroa CA. Patient-specific modeling of cardiovascular mechanics. Annu Rev Biomed Eng. 2009;11:109-134.

Greg Mader
Modeling cerebral blood flow velocity during orthostatic stress

Cerebral autoregulation (CA) is the brain's regulation mechanism by which cerebral blood flow (CBF) is maintained at its nominal level despite changes in the arterial blood pressure (ABP). Many previous models for CA use a lumped parameters approach or create statistical black-box models. In this work we propose a new simple quantitative model predicting CBFV from ABP on a patient-specific basis. The model is motivated by the viscoelastic-like trends observed in filtered patient pressure-flow data collected during a sit-to-stand experiment. After describing the nature of the experimental data and deriving the mechanical components of the model, the stability and identifiability of the model will be shown. Qualitative model behavior and parameter estimation will also be discussed. The model will be validated against time-series data from one normotensive young and one normotensive elderly subject.

Yoichiro Mori
Modeling Electrodiffusion and Osmosis in Physiological Systems

Electrolyte and cell volume regulation is essential in physiological systems. After a brief introduction to cell volume control and electrophysiology, I will discuss the classical pump-leak model of electrolyte and cell volume control. I will then generalize this to a PDE model that allows for the modeling of tissue-level electrodiffusive, convective and osmotic phenomena. This model will then be applied to the study of cortical spreading depression.

Franck Plouraboue (slides)

Albeit cerebral blood flow is a critical clinical parameter for brain function assessment, its intimate relationship to micro-vascular structure and hemodynamic is still under progress.
The first part of the presentation will be devoted to the topic's overview, either from the experimental and the modeling side. Recent In-vivo and ex-vivo imaging techniques and perspectives will be provided. Those advances in physiological imaging provides astonishing in vivo measurements to nourish and challenge modeling's predictions. Yet most valuable, local measurements are difficult to embrace in a more global picture, so that modeling is needed.
Modeling issues will also be exposed, either from the mechanical, the physiological and the mathematical view-point.
In a second part, we present recent results of cerebral blood flow from high-resolution micro-vascular images providing evidences that modeling offers new perspective to decipher brain's perfusion robustness, vascular territories, and input/output coupling between penetrating vessels.
Moreover, modeling also permit to challenge simple evidence such as cerebral blood flow (CBF) normalization, to be useful for the comparison of CBF estimated with different measurements or different clinical contexts.
Finally, the presentation will expose some recent advances in transfer modeling in very simple counter-current configurations, to motivate and challenge future modeling and approximations in more complex configurations.

Shu Tagaki
A Full Eulerian Method for Fluid-Membrane Interaction Problems and its Application to Blood Flows
Shu Takagi*1, Satoshi Ii2, Kazuyasu Sugiyama2, Seiji Shiozaki3 and Huaxiong Huang4
1 The University of Tokyo, 2 Osaka University, 3 Tokai University, 4York University

A novel full Eulerian fluid-elastic membrane coupling method on the fixed Cartesian coordinate mesh was proposed within the framework of the volume-of-fluid approach [1]. The present method is based on a full Eulerian fluid-(bulk) structure coupling solver [2]. In this talk, numerical results of flowing vesicles encapsulated by the hyperelastic membrane are presented. The membrane is described by volume-fraction information generally called VOF function. A smoothed phase indicator function is introduced as a phase indicator which results in a smoothed VOF function. This smoothed VOF function uses a smoothed delta function, and it enables a membrane singular force to be incorporated into a mixture momentum equation. In order to deal with a membrane deformation on the Eulerian fixed mesh, a deformation tensor is introduced and updated within a compactly supported region near the interface. Both the neo-Hookean and the Skalak models for red blood cells are employed in the numerical simulations. A smoothed (and less dissipative) interface capturing method is employed for the advection of the VOF function and the quantities defined on the membrane [3]. The stability restriction due to membrane stiffness is relaxed by using a quasi-implicit approach. The present method is validated by using the spherical membrane deformation problems, and is applied to a pressure-driven flow with red blood cells. The numerical results of flowing red blood cells and platelets are shown. The method was also extended to simulate platelet adhesion process which occurs at the initial stage of thrombosis. The platelet adhesion to the vessel wall is given by the large numbers of protein-protein bindings. This binding process of protein molecules are treated stochastically using the Monte Carlo method. More detail discussion will be given in the talk.

REFERENCES
[1] S. Ii, X. Gong, K. Sugiyama, J. Wu, H. Huang and S. Takagi, A Full Eulerian Fluid-Membrane Coupling Method. Commun. Comput. Phys, 12, pp. 544-576 (2012)
[2] K. Sugiyama, S. Ii, S. Takeuchi, S. Takagi and Y. Matsumoto, A full Eulerian finite difference approach for solving fluid-structure coupling problems. J. Comput. Physics. 230 , pp. 596-627 (2011)
[3] S. Ii, K. Sugiyama, S. Takeuchi, S. Takagi, Y. Matsumoto and F. Xiao, An interface capturing methodwith a continuous function: the THINCmethod withmulti-dimensional reconstruction. J. Comput. Phys., 231, 2328-2358 (2012)

Jingdong Tang
Inhibiting the superficial femoral artery sympathetic nervous to treat the Buerger diseases
Tang Jingdong, Gan Shujie, Zhang Ci, Li ke, Qian Shuixian
Corresponding Author: Tang Jingdong

Objective: To assess the inhibiting the superficial femoral artery sympathetic nervous to treat the Buerger diseases.Methods: The records of 30 cases of Buerger. All of the cases' treatment was the inhibiting the superficial femol artery sympathetic nervous by Radiofrequency ablation. Results: It was safe that all of the cases' treatment was the inhibiting the superficial femoral artery sympathetic nervous by Radiofrequency ablation. The checking results of the cases were ABI, CTA and DSA. Conclusions: It was not only preventing the human body from the complication of Lumbar sympathectomy, and also recovering Buerger's arteries. However, it was a few cases and follow up time, we should have a lot work to do.
Key Words: Radiofrequency ablation; Buerger; inhibiting the superficial femoral artery sympathetic nervous.

Tim Secomb
Oxygen transport in the brain and implications for neurovascular coupling

Oxygen transport to the brain may be regarded as the most critical function of the circulatory system. Because oxygen can diffuse only a short distance (of order 50 microns) into oxygen-consuming tissue, a dense network of microvessels carrying oxygenated blood is necessary to ensure that all tissue points are adequately supplied. Using a Green's function method, we simulated oxygen delivery by a three-dimensional network of microvessels in rat cerebral cortex, and predicted the distribution of partial pressure of oxygen (PO2) in tissue and its dependence on blood flow and oxygen consumption rates. In a typical control state with consumption 10 cm3O2/100cm3/min and perfusion 160 cm3/100cm3/min, the predicted minimum tissue PO2 was 7 mmHg. In comparison, a Krogh-type model with the same density of vessels, but with uniform spacing, predicted a minimum tissue PO2 of 23 mmHg. With a 40% reduction in perfusion, tissue hypoxia (PO2 < 1 mmHg) was predicted. These results suggest that the normal microcirculation operates with a relatively small 'safety' margin of excess supply relative to basal requirements. Although one might intuitively expect that hypoxia provides a feedback signal for the short-term regulation of blood flow to ensure tissue oxygenation, a substantial amount of evidence argues against this mechanism. Nonetheless, it appears that the structure of the brain microvasculature is finely tuned for oxygen delivery. As a resolution of this apparent paradox, we suggest that the structural control of the brain vasculature, through the processes of angiogenesis and vascular remodeling, is sensitive to the occurrence of tissue hypoxia, thus providing the necessary feedback control on a slow timescale. Supported by NIH grant HL070657.

Marc Thiriet
Signaling to the brain via nervous and endocrine inputs. Illustration by a biological and mathematical model of acupuncture (slides)

The brain is a complex processor that can sense chemical, physical, and mechanical signals, treat them, and transmit an output for bodily adaptation extremely quickly and more slowly using neural and vascular routes.
Surgical interventions can be carried out using either general anesthesia, that is, a medically induced coma, or acupuncture, that is, performing tasks in concious subjects naturally anesthetized. In the latter case, the brain that is capable of synthesizing opioids and antalgics is stimulated from acupoints that are known since 2~millenaries. In addition to a better confort for the patient who avoids coma, the cost for the health service is much lower. The lecture will emphasize signaling from a given acupoint to the brain and on the corresponding mathematical model.

1. Targeting BBB for selected mass transfer (nanopartcles) - Modeling
2. Influence of nervous impulse frequency on neuropeptide release.
Intercation between brain cell populations.

Qiming Wang
Modeling cardiovascular response to the umbilical cord occlusions in fetal sheep: the impact of hypoxia and asphyxia
Author:Qiming Wang, Martin G. Frasch, Huaxiong Huang, Steven Wang

One of the main issues during childbirth is the possibility of developing severe fetal acidemia caused by umbilical cord occlusions (UCO) due to repetitive uterine contractions. Despite of the extensive physiological insights provided by these studies, an important question remains open. From clinical point of view, developing an online detection of potential brain injuries is of vital importance. On the other hand, it is often difficult to measure fetal acidemia directly during childbirth. The question is: can we develop an indirect mean to detect fetal acidemia before it is too late so that clinical intervention can be applied? In current work, we carry out numerical simulations via a mathematical model to study the effects of the UCO on the fetal heart rate (FHR), arterial blood pressure, cerebral oxygen deficit as well as carbon dioxide accumulation in the fetus. For FHR control, our model incorporated known established mechanisms such as parasympathetic and sympathetic responses, with proper modifications motivated by experiments. Our model is capable of reproducing variability of FHR in response to the UCOs observed in experiments and addressing the role of different mechanisms on FHR when frequency and severity of UCO change.
In addition, our model also provides insights on the onset of asphyxia due to UCO. We show that the accumulation of carbon dioxide in the fetus can enhance the late deceleration and suppress the intermediate growth in FHR during UCOs, hence serve as a potential indicator in detecting severe asphyxia.

Alix Witthoft
Bidirectional neurovascular communication: modeling the vascular influence on astrocytic and neural function

The neurovascular unit is a relatively new concept, and many of the interaction pathways are still unclear. To help establish a complete picture, we have developed some of the first bidirectional models for communication at each interface (gliovascular, neuroglial, neurovascular) of the neurovascular unit.
Astrocytes are considered the critical link in inducing vasodilation during functional hyperemia. We present a bidirectional model wherein astrocytes trigger vasodilation by releasing potassium through inward rectifier (Kir) and BK channels, while vessel movements activate mechanosensitive TRPV4 calcium channels in the astrocyte endfoot.
At the neuroglial interface, neurons and astrocytes release and uptake neurotransmitters and other diffusibles at the synaptic space. Our model focuses on the astrocyte response to synaptic activity and its regulation of extracellular potassium, which alters neural excitability. The model demonstrates how astrocytic multidirectional potassium regulation is achieved through the balance of three transport mechanisms: Kir channels, sodium/potassium/chloride cotransport (NKCC), and sodium/potassium exchange (Na-K).
While astrocytes mediate communications between neurons and vasculature, there may also be direct pathways. Cortical interneurons are found in contact with microvessels, and express mechanosensitive pannexin (Px1) channels. To couple fluid dynamic blood flow simulations with neurovascular interactions, we are developing a discrete particle model of a flexible anisotropic microvessel. The multi-layer model comprises various collagen fibers attached to an elastin matrix, mimicking the structure of the vascular tissue. We use dissipative particle dynamics (DPD), a coarse-grained, mesoscopic simulation approach ideal for complex fluids.
We are simultaneously collaborating with experimental neuroscientists to develop a model for vessel-adjacent interneurons to explain observed network reactions to vascular movements. We use the model to formulate hypotheses about interneuron responses to changes in single-file red blood cell flow in tight capillaries.

Yuan-nan Young

Mechanical coupling between cell membrane and a transmembrane protein
The dynamics of red blood cells (RBCs) has been extensively studied experimentally, theoretically and numerically. When under shear stress, RBCs are known to release adenosine triphosphate (ATP) as a vasodilatory signaling in response to the increased shear stress inside arterial constriction. Although shear-induced ATP release from RBCs has been observed, the underlying mechanosensing mechanism inside RBCs is still controversial. In this work we couple a cell membrane under shear to a transmembrane protein, and examine the dynamical consequence of the protein configuration in a continuum model. A brief introduction to cell dynamics under flow will be presented, and results on modeling and simulating cell dynamics will be summarized.
A simple model for coupling the membrane dynamics to a transmembrane protein will be discussed, followed by some preliminary results. This work is a collaboration with On Shun Pak (Princeton University), Howard Stone (Princeton University), and Shravan Veerapaneni (University of Michigan). Support from NSF-DMS1222550 is gratefully acknowledged.

Bas-Jan Zandt
Modeling of metabolism, activity and ion concentrations in the neurovascular unit

Through feedback and feedforward mechanisms, functional hyperemia follows increased neuronal and synaptic activity. Indeed, the functioning of neural tissue is critically dependent on a sufficient supply of energy in the form of oxygen and glucose from the blood. Most energy in the brain is consumed by ion transporters and pumps, notably the Na/K-pump, responsible for homeostasis of the intra and extracellular ion concentrations. Their workload depends on activity of synapses and neuronal action potentials. In turn, neuronal activity depends on the ion concentrations. Many modeling work has been done on this in the context of spreading depression with single cell models, however, these neglect the important contribution of synaptic input and network dynamics.
I will present a model describing neuronal activity, ion concentration dynamics and metabolism. As part of this work, a method was developed to create a neural mass model of neuronal activity with a bottom-up approach, which naturally includes the effects of excitation and depolarization block by extracellular potassium.
This model may provide insight in the dynamics of the pathophysiological processes following ischemia (stroke, cardiac arrest).

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