MRI
of capillary system
The Magnetic Resonance Imaging (MRI) has become a most efficient
technique of noninvasive diagnostics with applications in various
areas of medicine. Compared to two other widely used imaging
techniques – Computed Tomography (CT) and Positron Emission
Tomography (PET), the MRI scanning procedure is considered the
safest one. It uses the radio frequency (RF) waves and generates
low intensity “non-harming” electric and magnetic fields while CT
is based on the X-Rays and PET requires injection of the
radioactive tracer. The Nuclear Magnetic Resonance (NMR) effect
serves as a basis of the MRI scanning technology.
Most NMR models are considering only stationary magnetic field of
the main magnet and gradient coils and ignore the time-dependent
magnetic and electric fields created by the RF coils when the
scanner is turned on. Such an ignorance leads to inconsistency
between the mathematical models of MR image formation and the
actual images.
My approach to MR image formation is based on the solution of full
system of time-dependent Maxwell’s equations with nonlinear
constitutive relations describing wave propagation in anisotropic
media. To model the NMR effect the magnetization field is updated
in time as a solution to the Bloch-Torrey equation.
Publications:
E. Kashdan, Dynamic modeling of capillary system MRI,
Mathematical Methods in
Systems Biology workshop, Tel Aviv, Israel, 2010
DIC Microscope
The main goal of this project is to build a reliable numerical
model of Differential Interference Contrast (DIC) microscope image
formation for human embryo studies.
The DIC microscope is commonly used for the visualization of live
biological specimens. As a non-invasive modality, it enables to
observe transparent specimens while preserving their viability.
However, large size and thickness of the human embryo cell relative
to other specimen makes existing mathematical and computational
methods used in DIC microscope image formation studies ineffective
and often non-valid.
The mathematical “building blocks” of the microscope image
formation model include the interaction of light with the
biological matter and its propagation through the microscope
components. We divide it on 3 stages, each of them requires
separate numerical modeling: Object-Objective
→
Objective →Objective-Detector
Plane. As the result of our high-order accurate numerical
simulations the model of the image observed on the detector plane
has the same characteristics as it is expected from the principles
of DIC microscopy and object parameters (thickness and geometry)
could be accurately estimated.
Publications:
S. Trattner, E. Kashdan, H. Greenspan and N. Sochen, Modeling
DIC Microscope Image Formation of Thick Biological Specimen,
Mathematical Methods in
Systems Biology workshop, Tel Aviv, Israel, 2010
S. Trattner, E. Kashdan, H. Greenspan and N. Sochen, “Human
Embryo under the DIC microscope – vectorial approach to the
electromagnetic scattering simulation”, 8th International
Conference on Spectral and High-Order Accurate Methods (ICOSAHOM),
Trondheim, Norway, 2009
S. Trattner, E. Kashdan, M. Feigin, H. Greenspan, C.-F. Westin and
N. Sochen, "DIC microscopic imaging of living cell and Error
analysis of Born approximation", 3rd Workshop on Microscopic
Image Analysis with Applications in Biology, pp. 103 — 110, New
York City, 2008.
