We have
developed methods to address a number of bio-medical type processes along with
our development of general theories for transport phenomena in heterogeneous
media. The basic methodology allows us to treat multiple scale transport
processes ranging from the microscopic to the macroscopic. Some of the
phenomena we could model with a little enhancement of our present already
developed basic theories are:
Ø interaction between overall bulk blood perfusion in
brain matter and vascular morphology characteristics such as diameter of
vessels ( capillaries and arterioles), cerebral vascular tree morphometry and
vessel wall permeability.
Ø mathematical models for Cerebral Blood Flow (CBF)
could be developed and will constitute the significant improvements to those
used at present time and described, for example, in "Textbook of Head
Injury" (Muizelaar, J.P., pp. 221-240). The scaled VAT introduction to the
CBF would lead to a much more accurate calculation of CBF characteristics in
normal and posttraumatic intracranial medium.
Few projects we have some involvement in and could contribute to are:
"Cerebral Blood Flow Models for
Normal and with Acute Disorders Brain Intracranial Medium"
"Cerebral Blood Flow Extracranial
Thermal Diffusion Measurement Technique"
"Noninvasive Transcranial High
Resolution Doppler Ultrasonography Improvement"
"Optimization of Filter's
Morphology in Artificial Kidney Membranes"
To give a better idea how it might be procurable, the
contribution to following projects titled
A biomechanical model of the brain blood supply
system, beginning with the major blood input arteries and extending through a consequent
networks of arterioles, capillaries, venules and sinuses,could be developed.
The first step would be to create a mathematical model of the brain vessel
network morphology suitable for the scaled modeling and then map and develop a
data base for the brain vessel network morphology (BVNM). A detailed map of
BVNM and a database with morphometrical data would be used in subsequent steps
of the simulation, starting with the development of a theoretical, physical and
mathematical basis to simulate the flow of a non-Newtonian blood medium with
species exchange in at least three morphologically different brain blood
networks. A thorough morphometrical investigation of the BVNM would be
undertaken, accompanied by a numerical network simulation. A specific theoretical
biomechanical approach, database and software for the BVNM map would be the
result of this project. The database and BVNM map would have independent market
value and could be the basis for distinct improvement of medical service and
research.
had been made basically combining the respected brain
tissue engineering morphology and scaling consideration of the processes.
Another project comfortably came into an envelope as the
one naturally treatable with the VAT scaling methodology:
"Hierarchical
Multiphase Muscle Blood System Simulation"
This project would be aimed at
developing a physically based methodology for modeling and simulating transport
phenomena is a multiphase healthy blood medium within a muscle tissue blood
vessel network. Since no one model exists at the present time that can treat
the multiple scales that are present in actual blood vessel morphology, the
suggested development would treat the blood flow as a four scale heterogeneous
system where the four scales are:
1) dispersed
cell medium modeling of separate cells (red and white) including capillary and arteriole wall scale modeling,
2) single
blood vessel models that are based on from the first multiphase scale governing
equation statements,
3) single
muscle fiber capillary network scale modeling, and
4) three
phase blood transport modeling in a muscle fiber bundle capillary network.
To
create these kinds of models, the present nonlinear multiscale morphological
modeling approach will be used and significantly oriented toward the biomedical
improvements. The modeling procedures
will provide a more accurate physical model enabling considering the transport of blood constituents at each level of
the hierarchy. After being developed, these models would offer significant advantages
over existing one-phase-one-vessel models, due to their multilevel description
and the direct dependence on given specific muscle morphology.
This
later project had been formed even into the proposal to NIH in 1994 -