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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