Biomedical subjects

George H Weiss

Publications and source records attributed to George H Weiss.

12 recordsLinked to original sources

PubMed2006

Mean time-of-flight of photons in transillumination measurements of optically anisotropic tissue with an inclusion.

We study the effect of optical anisotropy on the mean time-of-flight of photons in a slab of turbid medium containing an inclusion whose optical properties differ from those of the bulk. For this analysis the difference in the mean time for a photon introduced into the slab to reach a specified target point with and without the inclusion is calculated. This difference is defined to be a measure of the contrast. The theoretical model is based on a continuous-time random walk on a lattice, which can be solved exactly and furnishes an exact expression for the contrast. Qualitative and quantitative characteristics of the contrast are analysed as functions of the geometric configuration of the system components (locations of the source, the inclusion and the detector), parameters that specify the optical anisotropy of the medium, and either the scattering properties of the inclusion or the lifetime of the small fluorophore in the case of the time-resolved fluorescence experimental configuration.

Algorithms↗

PubMed2006

Diffusion in multilayer media: transient behavior of the lateral diffusion coefficient.

A general formalism for treating lateral diffusion in a multilayer medium is developed. The formalism is based on the relation between the lateral diffusion and the distribution of the cumulative residence time, which the diffusing particle spends in different layers. We exploit this fact to derive general expressions which give the global and local time-dependent diffusion coefficients in terms of the average cumulative times spent by the particle in different layers and the probabilities of finding the particle in different layers, respectively. These expressions are used to generalize two recently obtained results: (a) A solution for the short-time behavior of the lateral diffusion coefficient in two layers separated by a permeable membrane obtained by a perturbation theory is extended to the entire range of time. (b) A solution for the time-dependent diffusion coefficient of a ligand, which repeatedly dissociates and rebinds to sites on a planar surface, obtained under the assumption that the medium above the surface is infinite, is generalized to allow for the medium layer of finite thickness. For the latter problem we derive an expression for the Fourier-Laplace transform of the propagator in terms of the double Laplace transform of the probability density of the cumulative residence time spent by the ligand in the medium layer.

Diffusion↗

PubMed2005

Time-dependent diffusion coefficients in periodic porous materials.

We derive an approximate solution for the Laplace transform of the time-dependent diffusion coefficient, D(t), of a molecule diffusing in a periodic porous material. In our model, the material is represented by a simple cubic lattice of identical cubic cavities filled with a solvent and connected by small circular apertures in otherwise reflecting cavity walls, the thickness of which can be neglected. The solution describes the decrease of D(t) from its initial value, D(0) = D, where D is the diffusion constant in the free solvent, to its asymptotic value, D(infinity) = D(eff), which is much smaller than D. A simple heuristic formula for the mean-squared displacement of the diffusing molecule is suggested. The theoretically predicted results are in good agreement with the data obtained from Brownian dynamics simulations.

Diffusion↗

PubMed2005

Monte Carlo simulations of increased/decreased scattering inclusions inside a turbid slab.

We analyse the effect on scattered photons of anomalous optical inclusions in a turbid slab with otherwise uniform properties. Our motivation for doing so is that inclusions affect scattering contrast used to quantify optical properties found from transmitted light intensity measured in transillumination experiments. The analysis is based on a lattice random walk formalism which takes into account effects of both positive and negative deviations of the scattering coefficient from that of the bulk. Our simulations indicate the existence of a qualitative difference between the effects of these two types of perturbations. In the case of positive perturbations the time delay is found to be proportional to the square of the size of the inclusion while for negative perturbations the time delay is a linear function of its volume.

Algorithms↗

PubMed2005

Estimation of anisotropic optical parameters of tissue in a slab geometry.

The scattering and absorption coefficients of many homogeneous biological tissues such as muscle, skin, white matter in the brain, and dentin are often anisotropically oriented with respect to their bounding interface. In consequence the curves of equal intensity of re-emitted light on the surface of the slab will no longer be circular. We here consider the problem of determining the parameters allowing one to estimate the angles defining anisotropy, directional bias of diffusive spreading, and scattering and absorbing coefficients from data obtained from time-gated measurements of light intensity transmitted through a slab of the tissue. Our model can be solved exactly and leads to accurate approximations in which measured values of the surface intensity are shown to be elliptical. The parameters of the ellipses suffice to estimate the anisotropy of the tissue interior. A summary of the parameter estimates with the observables from which they are found is given in a table. Our analysis is based on a diffusion model.

Algorithms↗

PubMed2004

Diffusion in the presence of periodically spaced permeable membranes.

The diffusion of molecules in biological tissues and some other microheterogeneous systems is affected by the presence of permeable barriers. This leads to the slowdown of diffusion at long times as compared to barrier-free diffusion. At short times the effect of barriers is weak. In consequence, the diffusion coefficient D(t) decreases as a function of time. We derive an exact solution for the Laplace transform of D(t) for diffusion in a space separated into layers by equally spaced, parallel identical planes of arbitrary permeability. Additionally, we give an approximation to D(t) which is reasonably accurate over the whole range of the partition permeability from zero (the case of isolated layers) to infinity (the case of no barriers).

Journal Article↗

PubMed2004

Photon migration in turbid media with anisotropic optical properties.

We analyse properties of photon migration in reflectance measurements made on a semi-infinite medium bounded by a plane, in which optical parameters may vary in directions neither parallel to, nor perpendicular to the bounding plane. Our aim in doing this is to develop the formulae necessary to deduce parameters of directionality from both time-gated and continuous wave measurements. The mathematical development is based on a diffusion picture, in which the bounding plane is regarded as being totally absorbing so that all photons reaching the surface contribute to the reflectance.

Algorithms↗

PubMed2004

Rate constant for diffusion-influenced ligand binding to receptors of arbitrary shape on a cell surface.

The theory of ligand binding to receptors on a cell surface suggested by Berg and Purcell and generalized by Zwanzig and Szabo uses the assumption that receptors are circular absorbing disks on an otherwise reflecting sphere. One of the key ingredients of this theory is a solution for the rate constant for ligand binding to a single circular receptor on a reflecting plane. We give an exact solution for the rate constant for binding to a single elliptic receptor and an approximate solution for binding to a single receptor of more general shape. The latter was tested by Brownian dynamics simulations. We found that the approximate formula predicted the rate constant with better than 10% accuracy for all studied receptor shapes. Using our solutions one can find the rate constant for ligand binding to a cell covered by N noncircular receptors by means of the Zwanzig-Szabo formula.

Cell Membrane↗

PubMed2004

Kinetics of ligand equilibration between tubular and vesicular parts of the endosome.

The kinetics of ligand equilibration between the tubular and vesicular parts of the endosome are studied for ligands diffusing in the vesicle and in a narrow cylindrical tubule attached to it. The key quantity in our analysis is the fraction of ligands in the vesicle at time t, P(ves)(t). We derive an expression for the Laplace transform of P(ves)(t) as a function of the vesicle volume and the length and radius of the tubule as well as the ligand diffusion coefficients in the vesicle and in the tubule. This transform is used to find the average equilibration time as a function of the system parameters.

Biological Transport, Active↗

PubMed2003

Effects of anisotropic optical properties on photon migration in structured tissues.

It is often adequate to model photon migration in human tissue in terms of isotropic diffusion or random walk models. A nearly universal assumption in earlier analyses is that anisotropic tissue optical properties are satisfactorily modelled by using a transport-corrected scattering coefficient which then allows one to use isotropic diffusion-like models. In the present paper we introduce a formalism, based on the continuous-time random walk, which explicitly allows the diffusion coefficients to differ along the three axes. The corrections necessitated by this form of anisotropy are analysed in the case of continuous-wave and time-resolved measurements and for both reflectance and transmission modes. An alternate model can be developed in terms of a continuous-time random walk in which the times between successive jumps differ along the three axes, but is not included here.

Anisotropy↗

PubMed2003

Continuous-time random-walk model for financial distributions.

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollar-deutsche mark future exchange, finding good agreement between theory and the observed data.

Journal Article↗

PubMed2002

Number of distinct sites visited by a random walker trapped by an absorbing boundary.

The number of distinct sites visited by a lattice random walker is a subject of continuing interest in both mathematics and physics. All previous investigations have used the assumption that the lattice is unbounded. An assessment of the amount of tissue interrogated by a photon in reflectance measurements for diagnostic purposes suggests analyzing properties of the average number of distinct sites visited by a random walker trapped by an absorbing plane at time t. We show that for sufficiently large t this number is the same as the average number of distinct sites visited for this time when the surface is not present. A more complete analysis is possible for a random walk on a line terminated by an absorbing point.

Absorption↗