Ralph Nossal

Model for laser Doppler measurements of blood flow in tissue.

A theory is developed which relates quasi-elastic light scattering measurements to blood flow in tissue micro-vasculature. We assume that the tissue matrix surrounding the blood cells is a strong diffuser of light and that moving erythrocytes, therefore, are illuminated by a spatially distributed source. Because the surrounding tissue is considered to be stationary, Doppler shifts in the frequency of the scattered light arise only from photon interactions with the moving blood cells. The theory implies that the time decay of the photon autocorrelation function scales proportionally with cell size and inversely with mean translational speed. Analysis of multiple interactions of photons with moving cells indicates the manner in which spectral measurements additionally are sensitive to changes in blood volume. Predictions are verified by measurements of particle flow in model tissues.

Model for photon migration in turbid biological media

Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability gamma(n, rho)d2 rho that a photon will be emitted in the infinitesimal area d2 rho centered at surface point rho = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.

Principles of Laser-Doppler Flowmetry

Light scattering has long been used to probe properties of bulk matter. In transparent media such as air or clear water, measurements can be analyzed easily and remote sensing can be done over great distances. The basic principles relating the intensity of scattered light to underlying molecular structure were established by Lord Rayleigh in his classic 1871 paper explaining why the sky appears to be blue.

Theory of Threshold Fluctuations in Nerves: I. Relationships between Electrical Noise and Fluctuations in Axon Firing

Relations describing threshold fluctuation phenomena in nerves are derived by calculating the approximate response of the Hodgkin-Huxley (HH) axon to electrical noise. We use FitzHughs reduced phase space approximation and describe the dynamics of a noisy nerve by a two-dimensional brownian motion. The theory predicts the functional form and parametric dependence of the relation between probability of firing and stimulus strength. Expressions are also obtained for the firing probability as a function of stimulus duration and for the distribution of latency times as a function of stimulus strength.

Resolution limits for optical transillumination of abnormalities deeply embedded in tissues

Random walk theory is used to calculate the line spread function (LSF) of photons as they cross the midplane of a slab of finite thickness. The relationship between the LSF and the photon transit time in transillumination time-resolved experiments is investigated. It is found that the LSF is approximately Gaussian distributed, with a standard deviation, sigma, which can be used as a criterion of the spatial resolution of the imaging system. Results are substantiated by comparison with actual data in the literature. Any given resolution can be improved by reducing the excess transit time delta t, but heterogeneity of the scattering medium and low levels of detected light enormously complicate the achievement of subcentimeter spatial resolution. The latter point is discussed by using optical parameters of breast tissues for visible and near-infrared radiation (NIR) light.

Statistics of Penetration Depth of Photons Re-emitted from Irradiated Tissue

Abstract We derive some statistical properties of photons emitted from bulk tissue that has been irradiated by a continuous beam of laser light. The properties include the distribution and moments of the depth reached by a photon, conditional on its having reached the surface at a (dimensionless) distance, ϱ, from the point of entry of the beam into the tissue. Theoretical predictions are made on the basis of a lattice random-walk model and are checked by simulations of the light penetration problem for a more realistic continuum model.

Fabrication of hydrogels with steep stiffness gradients for studying cell mechanical response.

Many fundamental cell processes, such as angiogenesis, neurogenesis and cancer metastasis, are thought to be modulated by extracellular matrix stiffness. Thus, the availability of matrix substrates having well-defined stiffness profiles can be of great importance in biophysical studies of cell-substrate interaction. Here, we present a method to fabricate biocompatible hydrogels with a well defined and linear stiffness gradient. This method, involving the photopolymerization of films by progressively uncovering an acrylamide/bis-acrylamide solution initially covered with an opaque mask, can be easily implemented with common lab equipment. It produces linear stiffness gradients of at least 115 kPa/mm, extending from ∼1 kPa to 240 kPa (in units of Youngs modulus). Hydrogels with less steep gradients and narrower stiffness ranges can easily be produced. The hydrogels can be covalently functionalized with uniform coatings of proteins that promote cell adhesion. Cell spreading on these hydrogels linearly correlates with hydrogel stiffness, indicating that this technique effectively modifies the mechanical environment of living cells. This technique provides a simple approach that produces steeper gradients, wider rigidity ranges, and more accurate profiles than current methods.

Photon migration in layered media

Surface emission profiles and related functions are computed for particles (photons) migrating within a semiinfinite medium containing a surface layer whose absorbance differs from that of the underlying layer. Photons are assumed to be inserted at a single point on the surface. In certain cases distinct features appear in the emission profiles which enable determination of the thickness of the top layer and of the absorption coefficients of both layers. Computations are performed to provide estimates of parameter ranges for which the presence of one layer distorts photon emission profiles from the other. Several ancillary functions are calculated, including the absorbance profile as a function of depth, the expected path length of photons that are reemitted at a distance rho from the point of insertion, and the average depth probed by those reemitted photons.

Energetics of Clathrin Basket Assembly

A minimal thermodynamic model is used to study the in vitro equilibrium assembly of reconstituted clathrin baskets. The model contains parameters accounting for i) the combined bending and flexing rigidities of triskelion legs and hubs, ii) the intrinsic curvature of an isolated triskelion, and iii) the free energy changes associated with interactions between legs of neighboring triskelions. Analytical expressions for basket size distributions are derived, and published size distribution data (Zaremba S, Keen JH. J Cell Biol 1983;97: 1339–1347) are then used to provide estimates for net total basket assembly energies. Results suggest that energies involved in adding triskelions to partially formed clathrin lattices are small (of the order of kBT), in accord with the notion that lattice remodeling during basket formation occurs as a result of thermodynamic fluctuations. In addition, analysis of data showing the effects of assembly proteins (APs) on basket size indicates that the binding of APs increases the intrinsic curvature of an elemental triskelial subunit, the stabilizing energy of leg interactions, and the effective leg/hub rigidity. Values of effective triskelial rigidity determined in this investigation are similar to those estimated by previous analysis of shape fluctuations of isolated triskelia.

Theory of Threshold Fluctuations in Nerves: II. Analysis of Various Sources of Membrane Noise

Threshold fluctuations in axon firing can arise as a result of electrical noise in the excitable membrane. A general theoretical expression for the fluctuations is applied to the analysis of three sources of membrane noise: Johnson noise, excess 1/f noise, and sodium conductance fluctuations. Analytical expressions for the width of the firing probability curve are derived for each of these noise sources. Specific calculations are performed for the node of Ranvier of the frog, and attention is given to the manner in which threshold fluctuations are affected by variations of temperature, ion concentrations, and the application of various drugs. Comparison with existing data suggests that threshold fluctuations can best be explained by sodium conductance fluctuations. Additional experiments directed at distinguishing among the various noise sources are proposed.