Norman Davids

General Computer Method of Analysis of Conduction and Diffusion in Biological Systems with Distributive Sources

A method of analysis by use of the computer has been developed which permits the physical laws governing conduction, or diffusion, to be expressed in first‐order finite form. Solutions are obtained in the one‐dimensional case for rectangular, cylindrical, and spherical geometries without the use of transcendental functions or other conventional mathematical iterative methods. The case of the cylindrical calorimeter with concentric insulating and conducting layers of varying chemical properties and with distributive heat sources arising from biochemical reactions at the center is treated in the transient and steady‐state case.

A computer analysis method for thermal diffusion in biochemical systems

In the thermal detection of rapid biochemical reactions it is necessary to correct the temperature data for transient heat conduction losses in a cylindrical calorimeter. To handle the complexities arising from varying thermal-relaxation times of concentric insulating layers, a computer program was developed which gives the temperature distribution of the system as a function of radius and time. This distribution is corrected at each step by a subroutine which calculates the instantaneous chemical state of the reaction, as well as the heat produced by this reaction. The program is based on a direct statement of Fouriers law of heat conduction and the chemical rate equation to provide a “bookkeeping law” to follow the reactants and the flow of heat packets, in such a way that the computer continually stores the heat distribution. A computer analysis method is here regarded as one in which the physical laws of a process are used explicitly in the program. Usually this results in bypassing much of the mathematical procedures conventionally used.

Dynamical finite element analysis for elastic waves in beams and plates

Abstract A special method of analysis, hereafter referred to as “Direct Analysis”, is described and applied to the solution of the problem of traveling flexural waves in beams and plates, for which shear correction and rotatory inertia are considered. Finite beams and plates are considered so that the influence of reflected waves is included. The proper boundary conditions for these problems, several input stress pulses, as well as the effect of the length of the bounded medium (beam or plate) on the magnitude of the stress are considered. Implications to design of structures are discussed. The characteristic features of the Direct Analysis are then presented.

Penetration experiments with fiberglass-reinforced plastics

The penetration resistance of fiberglass-reinforced plastics against small-caliber projectiles is determined by firing experiments. Relations, found to be linear, between energy loss, stopping power and thickness of plate are given. The effect of distance of separation, for two plates, on stopping power is determined. The weight efficiency of the fiberglass cloth is found to be greater than steel.

Differential Microcalorimeter for Biochemical Reaction Studies

A differential solution microcalorimeter with a mixing system is described. Up to 1 ml of reagent A may be mixed with up to 3 ml of reagent B in less than 1 sec with a heating artifact of less than 0.5 mcal. A temperature range of 0 to 40°C has been utilized with a 2 h temperature equilibration time. The time course of biochemical reactions has been followed for up to 1 h. Computer simulation of the calorimeter permits data correction for heat conduction losses. For reaction heats greater than 25 mcal, ΔH and the rate constant of the reaction may be determined to ±2%. Detectivity is ±20 μcal. A digital computer simulation technique based on a finite‐element analysis of heat conduction, which is of general applicability, was developed to correct the output data for heat conduction losses.

Computer simulation for deconvolution of a heat conduction batch microcalorimeter by the D-B finite element technique

The method described here is a general numerical analysis procedure which has been applied to a heat conduction Batch calorimeter for the deconvolution of its thermograms, and is based on a computer simulation of the heat conduction behavior of the instrument with time. We show by means of test signals that the method can deconvolute the signal with a resolving time that is about two orders of magnitude smaller than the time constant of the calorimeter itself. The method can be applied to time signals generally, provided that the instrument producing them can be simulated.

A viscous model for plug formation in plates

Abstract This paper presents the analysis of a viscous model for the study of the impact of plates by projectiles under conditions which would lead to failure of the plate by the formation of a plug. The impact is represented by a velocity uniformly distributed over a circular area on the plate surface. Only the vertical shearing stress is considered and it is assumed to depend only on the radial coordinate. The stress, velocity and displacement profiles are calculated for the viscous model. The calculated displacement profiles are compared with experimental profiles determined from photographs of an actual plugging experiment.

An automated differential thermal and potentiometric titration apparatus for binding studies

A differential pH-thermal titration apparatus is described which can detect pH differences with a sensitivity of +/- 0.0001 pH units and a thermal sensitivity of +/- 0.00002 degree C at a time constant of 0.1 s. With a reaction which yields 1 kcal mol-1, the current system can detect concentrations as low as 4 X 10(-6) M or, in a 2 ml volume, a total amount of 40 nmol. With a time constant of 0.1 s, the sensitivity is 20 +/- 4 micro degrees C. The experimental protocol is specified by a microprocessor and three modes of operation are possible: titration at constant rate of reagent addition, titration at variable rates of addition so that the contents of both cells are at either constant pH or at a constant temperature and variable rate when a rate of change is specified. Experimental data are collected in files, corrected for heat loss, initial baseline drift, and changes in volume. The final corrected data from the standardized run of 0.01338 M HCl in 0.2 M KCl at 25 degrees C calibrate the pH scale and yield the calorimetric conversion constants and pKw which are calculated and stored for subsequent corrections for the titration of an unknown acid or the measurement of binding constants and heats.

Finite element methods of studying mechanical factors in blood flow.

This paper reviews some biomechanical analyses of blood flow in large arteries based on a general computer modeling using the finite element method. We study the following question: What is the role played by the interrelated factors of mechanical stress, flow irregularities, and diffusion through the endothelium on the etiology of atherosclerosis or the aggravation of vascular injury. It presents the computational features of the method and stresses the physiological significance of the results, such as the effect of geometric complexities, material nonlinearities, and non-Newtonian rheology of the blood. The specific mechanical and fluid dynamic factors analyzed are wall shear stress, flow profiles, and pressure variations. After simulating tubes of circular cross section, we apply the analysis to a number of physiological situations of significance, including blood flow in the entrance region, at bifurcations, in the annular region between an inserted catheter of varying diameter and the vessel. A model study of pulsatile flow in a 60 degree bifurcated channel of velocity profiles provided corroborative measurements of these processes with special emphasis on reversed or distributed flow conditions. The corresponding analysis was extended to the situation in which flow separates and reverses in the neighborhood of stagnation points. This required developing the nonlinear expression for the convective velocity change in the medium. A computer algorithm was developed to handle simultaneous effects of pressure and viscous forces on velocity change across the element and applied to the canine prebranch arterial segment. For mean physiological flow conditions, low shear stresses (0-10 dynes/cm2) are predicted near the wall in the diverging plane, higher values (50 dynes/cm2) along the converging sides of the wall. Backflow is predicted along the outer wall, pressure recovery prior to and into the branches, and a peak shear at the divider lip.

SIMULATION OF HEMOGLOBIN KINETICS USING FINITE ELEMENT NUMERICAL METHODS

Publisher Summary This chapter discusses one elementary method of analyzing biochemical kinetic problems to show what some of the issues are–including how such methods appear to a user, in terms of ease of use. The general solution of a complex reaction— in this case hemoglobin (Hb) binding to carbon monoxide (CO)— including a global fit using a curve fitter is discussed in the chapter . The finite element (FE) method has the advantage that its steps are formulated easily, as they deal directly with the physics or chemistry of the problem. It simulates the problem in the sense that if the computation is stopped for any reason at an earlier time, it shows the state of the system at that time. It can easily deal with an additional boundary condition or the presence of additional effects, such as electric or magnetic fields, without invalidating the work up to that point. On the other hand, instabilities are difficult to deal with, just as with other numerical methods.