ALBERT

Notes: Abstract The chromosomal theory of inbreeding based on a gametic interaction system lead us to define a depression coefficientD. Comparison of random, sib and half-sib matings (with inbreeding coefficientF=0, 1/4 and 1/8) shows thatD depends on the structure of the starting population and on values of the model parameters. This result accounts for responses of lines whose depression does not depend directly on the inbreeding coefficient and which theories of inbreeding based on increasing homozygosity fail to explain.

Notes: Abstract An idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur. It is also shown that this model, under reinterpretation, corresponds to a cellular automaton in which growth occurs by differentiation only (i.e., the state into which any cell is born is thereadfter fixed). Hence this latter model of growth is also computationally universal.

Notes: Abstract Kinetics of biological light emission processes do not mean what they seem to mean, because measured light intensity is not proportional to reactant concentration but to reaction rate. Therefore, the differential equation for light decay is usually different from that of concentration decay, so that mass action interpretations cannot be applied directly to light intensity decay. An observed second order light decay for Chlorella at 6.5°C, implies Elovich solid state reaction kinetics, which agrees with other evidence for solid state processes in photosynthesis. An observed 1.5 order light decay for Cholorella at 28°C implies second order liquid or solid state reaction kinetics. First ordere light decay implies first order reaction kinetics.

Notes: Abstract Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ R θ(x 1,x 2,t) dx 1 dx 2 of a biological species with an area-density distribution function θ=θ(x 1,x 2,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇2θ +fθ −gθ n+1 whereD (〉0),n (〉0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(x 1,x 2, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn〉1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ R θ(x 1,x 2, 0)2 dx 1 dx 2 sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.

Notes: Abstract The equilibrium probability distribution of the process level is studied for a general class of reversible stochastic reactions. A calculationally convenient approximation for equilibrium probabilities is derived and its accuracy is investigated over a range of values of the equilibrium constant. A method of approximating the equilibrium means and variance is developed and illustrated forQ th-order processes.

Notes: Abstract Beside the concept of material inputs and outputs of components of the representation of biological systems given to us by Rosen, the concept of energy is incorporated. The interaction of material and energy is represented by a cartesian product; and separate material and energetical mappings are considered as the new representation of components. These developments generate aMα category, and it is shown thatMα is isomorphic to theM category of previous developments.

Notes: Abstract This paper discusses the solution of a generaln-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversiblen-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.

Notes: Abstract The relations (inflow) = (dose)/(area under indicator curve), and (volume of distribution) = (throughflow) × (mean transit time) are derived by a matrix method for a system of interconnected subsystems, within which spatial indicator activity gradients may exist, and for compartments, within which the indicator activity is spatially uniform. The inflow theorem, is different from the outflow theorem. Equivalent labeling of multi-input systems reduces them formally to single input systems. Foreign indicator flow-volume kinetics are more general than, and include as a special case, tracer flux-mass (metabolic) kinetics. Volume of distribution in the indicator steady state may be different from the equilibrium volume of distribution.

Notes: Abstract Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.

Notes: Abstract Signal Detection Theory can be used to provide a mathematical model describing the choice of a predator trying to distinguish between a model and a Batesian mimic. The mathematical model yields a number of a deductions, in particular that it may or may not assist the mimic population if mimics more closely resemble their models. The assumptions underlying the analysis are discussed in some detail.

Notes: Abstract A new type of physical transition, denotedS→S *, has been detected in irradiated organic molecules (λ=546 nm) through their interaction with specific biological macromolecules. In a specific enzyme-substrate interaction, a clear enhancement of the reaction rate is observed, when the substrate is irradiated with sharply well defined times. These “efficient irradiation times” are always of the 5k sec type (k=1, 2, 3, …). They have been consistently revealed in a great number of specific biological interactions. The present note demonstrates an important property, i.e. that forevery irradiation time aS→S * transition is induced in organic molecules. It is shown that for any irradiation times different from the 5k sec type (k=1, 2, 3, …) states of theS * type may occur, but the biological macromolecules may “detect” only theS * states induced by irradiations of the 5k sec type.

Notes: Abstract A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using pressure drop, flow rate and hematocrit reduction data. It has been found from the available data in the literature that for a given sample of blood the extent of plug flow increases with decreasing tube diameter. Also for a flow through a given tube it increases with hematocrit. The wall layer thickness is found to decrease with increase in blood hematocrit. A comparison between the results of rigid particulate suspensions and blood reveals that the thicker wall layer and smaller plug flow radius in the case of blood may be attributed to the deformability of the erythrocytes.

Notes: Abstract Three dimensional laminar, viscid flow is developed for Newtonian fluids which provides absolute values for axial, radial and tangential velocity fields everywhere if the dimensions of the vessel are known and two simultaneous axial velocities e.g. on and off the central axis in the same plane, and the central axis axial velocity gradient are measured. In addition, normal and shear stresses are determinable. The equation set satisfies geometric and other known flow limiting conditions such as no slip at surfaces etc. and are amenable for inclusion in general, dynamic flow expressions. Alternatively they may be used alone for certain problems involving gradients and secondary flows. A range of illustrations are shown for a distorting vessel with elliptic cross-section and small axial taper (analogous to the pulmonary trunk during ejection).

Notes: Abstract A regulated left ventricular dynamics model is presented which involves interaction of the dynamics of the left ventricular and circulatory systems and their regulation by the central nervous system. On-line human parametric simulation (parameter estimation) and consequential prognostic implications (based on parametric values) are demonstrated. Model responses to simulated physiologic stresses help delineate tolerances of subjects. In order to have an estimate of the reliability of the model, the sensitivity of the model's responses to changes in the values of its intrinsic parameters is assessed. Also determined is the extent to which errors in measuring the pressure affect the calculated values of the model's simulation parameters and subsequently influence the values of other diagnostically useful variables (such as contractility, oxygen consumption rate, heart rate), when the model is used to determine the limiting physiological stress sustainable by the subject. A comparison of the model's composition with those of other similar cardio-circulatory models is included.

Notes: Abstract Then-stage harvesting strategy of Elizarov and Svirezhev is examined. As a result, some important new features appear. A discussion is presented on whether or not one should harvest a species at one time stage or wait until a later time. The paper is concerned with contributions which are primarily mathematical formulations and results for continuous, as well as discrete time, logistic growth of a single species being harvested. Age class structure is ignored.

Notes: Abstract In order to evaluate the effect of anatomic asymmetries on the gas concentration distribution in the pulmonary airways, a Monte Carlo simulation of combined bulk flow and molecular diffusion was carried out in a realistic distal airway model (Parkeret al., 1971). This airway model, composed of branches distal to the 0.5-ram diameter airways, contained an upper symmetric segment consisting of four generations of conducting airways and a lower asymmetric segment of alveolar ducts and sacs arranged in five transport paths of varying lengths. In accounting for the volume increases of these ducts and sacs occurring during normal respiration, uniform alveolar filling rates and a fixed length-to-diameter ratio of all airways were assumed. For a pulse injection of inert tracer gas, the simulation was employed to determine the longitudinal concentration profiles in the conducting airways. In the alveolated airways, not only were the longitudinal profiles determined along each path, but radial transport from the core to the periphery of the airways was considered. The results of the simulations indicate that geometric asymmetries alone contribute substantially to regional concentration variations in the distal airways. For example, when a gas bolus is injected at mid*inspiration, there are concentration differences as great as 40% between two points along different transport paths located equi-distant from the proximal end of the model. As viewed from the terminal end of the model (acinus), average concentration differences as large as 6-to-1 exist between the longest and shortest transport paths respectively for gas boli introduced near the end of inspiration. The results further indicate because of large radial diffusion rates, no significant concentration differences exist between the periphery a-ld the central core of alveolated airways. Simulation of the expired concentration profiles indicate that boll injected very late during inspiration exhibit a sloping tail, unlike the earlier injected boll whose tails are virtually horizontal. Through the use of superposition teehniqnes, it was found that these sloping tails correspond to an alveolar slope of 1.5 vol% between 750 and 1250 ml expired for a continuous washing of tracer. This result is in disagreement with other transport analyses which did not directly account for the effect of geometric asymmetries.

Notes: Abstract Assuming a spherical geometry for the left ventricle, passive elastic stiffness-stress relations have been obtained on the basis of linear elasticity theory and large deformation theory. Employing pressure-volume aata taken from rat hearts of various age groups, it is shown that young rat heart muscle (1 month) is stiffer than either adult (7 months) or old rat heart muscle (17 months). Although the qualitative results are similar for both elasticity theories, the large deformation theory gave results in closer agreement with those obtained from papillary muscle studies. These results imply that stiffness of muscleper se can be assessed from left ventricular pressure-volume data.

Notes: Abstract Deliberate evaluation of the quantum theory of nerve excitation is made by comparing it with Hill's theory in fitting the experimental data on threshold-frequency relation, optimum frequency (v0) for nerve excitation and strength-duration relation. Decrease of v0 and increase of all the time constants (Hill's λ andk, Wei'sT 2 and spike durationw) with decreasing temperature are interpreted on the basis of the dipole relaxation timeT 2 but inexplicable from Hill's theory or any other existing theory. The closeness ofk,T 2 andw values is explained. A variety of experimental results obtained by others is discussed. Finally, a comparison is made between the Hodgkin-Huxley equations and the quantum theory. Most of the facts (electrical and non-electrical) tend to support the thesis that nerve excitation is a macroscopic expression of quantum transitions of dipoles between energy states.

Notes: Abstract In the periodic Leslie model the asymptotic period of total population is a divisor of the asymptotic period of the population vector. Under reasonable circumstances these periods are identical.

Notes: Abstract A number of biological branching systems, such as the bronchial and pulmonary arterial trees, are being investigated in an ongoing study in order to define their physiological properties. The technique involves the description of branching trees by the use of hierarchical systems of ordering, especially those described by Horsfield and by Strahler. During this work some mathematical properties of branching trees were demonstrated and these are described in this paper.

Notes: Abstract Luteinizing hormone (LH) is secreted continuously from the anterior pituitary gland. The concentration in the blood of this gonadotropic hormone plays a regulatory role in the development of puberty in both sexes, in the induction of ovulation in females, and in the production of testosterone in males. The secretion of LH is in turn controlled by luteinizing hormone releasing hormone (LHRH) secreted by the hypothalamus. LH and LHRH are removed from the blood by degradation and excretion. This hormonal system is modelled by a system of ordinary differential equations based upon specific physiological and biochemical assumptions current among experimentalists in this field. The one exception is the assumption that LHRH may bind reversibly to a serum protein; an analysis of the data shows that this or a similar mechanism is a crucial specification. Data on the serum levels of LH and LHRH in two human subjects were fitted using the model. The data consist of the transients and subsequent decays created by a bolus intravenous injection of LHRH.

Notes: Abstract A thick-wall incompressible, elastic sphere was used as a model for the diastolic rat left ventricle. A model for myocardial nonhomogeneity was derived assuming that fiber (circumferential) stress was independent of position in the ventricular wall. The theoretical implications of the resulting constitutive relations together with the spherical model were analyzed in the context of large deformation elasticity theory. It was found that muscle stiffness at a given level of uniaxial stress increased monotonically from the endocardium to the epicardium. In addition, fiber stress was found to be essentially a linear function of transmural pressure above a pressure of 6 g/cm2. It was also shown theoretically that neglecting the nonhomogeneity of the myocardium resulted in a state of stress which differed significantly from that predicted by the nonhomogeneous model. For example, at a transmural pressure of 14 g/cm2, fiber stress in the nonhomogenous model was equal to 17 g/cm2 while fiber stress in the homogeneous model varied between 100 g/cm2 at the endocardial surface and 2 g/cm2 at the epicardial surface. The change in muscle stiffness with position which characterized the nonhomogeneous model also tended to linearize the highly curvilinear radial stress distribution predicted by the homogeneous model at a given transmural pressure.

Notes: Abstract The phenomenon of axonal transport has been well documented (Ochs, 971; Lasek, 1970; and Grafstein, 1967). In a previous paper, we showed how diffusion alone could not account for this process. In this report we show that convection or convection with diffusion can account for the observed build-up of material. By including a first-order catabolic sequestration term, we are able to offer an understanding of the several apparent rates of transport with the same underlying velocity and variable sequestration.

Notes: Abstract It is known that the Lotka-Volterra coupled nonlinear differential equations for a two-species prey-predator ecosystem possess a periodic solution, although its exact form is not yet obtained analytically. The conventional linearization approximation for solving these nonlinear equations leads to a harmonic oscillator whose frequency depends only on the intraspecific coefficients. We propose here a prescription for obtaining nonlinear correction to the linear frequency by using the Hamilton-Jacobi canonical formalism of classical mechanics. It is found that the first-order correction, which also involves interspecific parameters, exhibits the basic qualitative features of the nonlinearity.

Notes: Abstract Environmental safety testing typically requires procedures for extrapolating from the relatively high experimental to the very low use doses of potentially harmful substances. In the present paper, a stochastic mammillary compartmental model for environmental safety testing is proposed and extrapolation procedures based on its dose-response relationship are developed. The proposed model is a direct generalization of one of the basic safety models, the one-hit model, in that a harmful reaction is assumed to occur if at any time any of the peripheral compartments attains a specified threshold of particles. Consideration of a closed model yields an upper bound on the probability of attaining a certain threshold level, thus providing a conservative procedure for extrapolating to a low dose, while a lower bound obtained from a related open model provides a useful monitoring device as to the sharpness of the upper, bound. The extrapolation procedure is illustrated with simulated data and approximations for initial values are developed.

Notes: Abstract By using chromosome images as a framework, algorithms for finding most dissimilar images are presented and illustrated by examples. In terms of angles, a chromosome image consists of two exterior biangles and two interior biangles. Biangles are defined and classified into 180° biangles, 〉180° biangles and 〈180° biangles. The dissimilarity of biangles and its geometric interpretation together with various properties of biangles are also presented. The results may have useful applications in pattern recognition, scene analysis, information storage and retrieval, artificial intelligence and fuzzy set theory.

Notes: Abstract The Volterra equations which represent competitions between two species are utilized to examine the phenomenon of boundary formation between two species of plants. The set of stable stationary points for these equations is determined and is illustrated in a product space of parameters and dynamical variables. The stages of boundary appearance and succession are visualized by considering slow changes of the parameters as functions of time and space.

Notes: Abstract The study of systems exhibiting a band-pass function is completed for systems whose parameters are time-dependent. In the case of periodic parametric excitations, it is demonstrated that some systems can get into “resonance” for a particular frequency. By studying this problem, a new and probably fruitful approach of some rhythmic behaviours can be made.

Notes: Abstract Analytical techniques are developed which permit objective control of asiist device driving systems. In addition to being objective, the techniques described in this paper are optimal in the sense of minimizing a performance index which consists of a term involving left ventricular power and a term involving deviations of aorta hemodynamic parameters from normal values. Comparisons are included of off-line computations and measurements on dogs with experimentally induced myocardial infarctions undergoing intraaortic balloon pumping.

Notes: Abstract A mathematical model simulating a cell growing in a culture medium is obtained. Using this model, various behavioral patterns of the cell are obtained under different types of disturbances, in particular when (i) a Mg2+ deficiency experiment and, (ii) a split-dose ionizing radiation experiment are carried out, (iii) when disturbances on the rate constants of the biochemical reactions taking place in the nucleus of the cell are applied, and (iv) when the cell's interior components are perturbed. The cell model results obtained agree well with experimental results for the Mg2+ and split dose experiments, and explain the mechanism of the split dose radiation experiment without the need to introduce additional axioms (e.g. healing processes) into the dynamics of the cell. Conditions are obtained which cause the cell to behave in a rapidly growing ‘tumor-like’ mode; it is shown that once the cell moves into this ‘tumor-like’ mode, its behavior is irreversible, i.e. if a disturbance of opposite type is then applied to the ‘tumor’ cell, the cell will not revert back to its original normal behavior.

Notes: Abstract Solution of the equation that describes simulatenous liquid flow and diffusion in a spherical model of the vitreous body of the eye shows that a small dissolved specie can move both anteriorly and posteriorly from a source behind the lens even though there is a slow liquid movement almost entirely in the posterior direction. This results explains why tracer studies using large particles (dyes or colloids) show only a posterior flow, whereas studies using sodium ion show anterior movement as well.

Notes: Abstract The equations relating hybridized RNA to free RNA, in the case of simple hybridization, or to ratio of labelled and unlabelled RNA in competitive hybridization, are derived. Analysis of the equations shows how hybridization data may be used to infer properties of the distribution of components in an RNA mixture, or the relation between two distributions in competitive hybridization. A critical examination of the assumptions underlying the equations indicates that some of then may be violated in certain cases, or have no current support, evidential or theoretical. The consequences of such qualifications for the interpretation of hybridization data are indicated.

Notes: Abstract A method, based on symmetry, is suggested for determining the information content of systems. A comparison has been made between the information for symmetry, topology, and chemical composition. The new information measure increases when the asymmetry of the molecules and the number of atoms in the latter increases. It can distinguish between different molecular conformations, and give a linear correlation with the absolute entropy for homologous series of chemical compounds.

Notes: Abstract The micromorphic theory of Eringen is applied to study the tube flow of blood. The blood is considered to be a deformable suspension, with constitutive relations of the form of those of simple microfluids. By means of energy consideration, a relation is established between the local concentration parameter and the measure of rotationality involving both macro-and micromotions. The tube flow problem is then solved with some analyses on viscosity coefficients and boundary conditions. The results obtained indicate an integrated explanation of various important physical phenomena associated with blood flow, such as the tube size dependence of the apparent viscosity and the non-uniform concentration distribution over a tube cross section.

Notes: Abstract By observing that the n-tuple of rate functionsQ(c) is orthogonal to the c-space gradients of each of the (n - 1) constants of the motion Φ v (c), a generic canonical expression for the rate functions is given in terms of the exterior product of the gradients of the (n - 1) Φ v 's. For models withQ so prescribed from the outset, an analytical general solution is obtainable directly for the system of autonomous ordinary differential equations dc/dt =Q(c). Thus, the generic canonical expression for the rate functions can be utilized to construct analytically solvable models for interacting biological species, as ilIus~rated by examples here.

Notes: Abstract The steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network. A detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions. The characteristics of the dissipative structures are discussed and it is shown that the observed behavior depends strongly on both the boundary and initial conditions. The theoretical expressions are limited to the neighborhood of the marginal stability point. Computer simulations allow not only the verification of their predictions but also the investigation of the behavior of the system for larger deviations from the instability point. It is shown that new features such as multiplicity of solutions and secondary bifurcations can appear in this region.

Notes: Abstract A model for the extraocular plant of the human visual eye tracking mechanisms is discussed. Its sensitivity to variation of controller signal nervous activity is studied in order to determine the type of activity that yields realistic simulations characteristic of typical saccadic eye movements.

Notes: Abstract Mathematical models of predator-prey systems in which the prey species has a three-stage life cycle are studied. Certain stages of the prey life history are allowed to use younger stages as food. It is shown that sufficiently restricted cannibalism can result in an increase in the numbers of adult prey on a sustained basis when cannibalism decreases the vulnerability of a stage subject to predation or increases overall productivity.

Notes: Abstract A general analysis is presented for the thermal behavior of a biological tissue. Energy transport by the circulatory system is assumed to be represented by a modified Fick's law. General boundary conditions are assumed for the two-dimensional model and solutions are obtained for rectangular, cylindrical, and spherical geometries. The effects of blood perfusion rate, metabolic rate, arterial temperature and heat exchange with the environment are considered. Results indicate a region of almost constant temperature in the deeper layers of the tissue and reaffirm the important role which blood flow plays in maintaining homeostasis.

Notes: Abstract The oscillatory aspect in a system having two steady states is studied theoretically using a model of excitable nerve membrane. The condition for the occurrence of oscillatory instability is discussed on the basis of the kinetic picture of nerve excitation in consideration of the non-Markoffian effect caused by ion transport in the system. Small oscillations around a steady state as well as a giant fluctuation between two states are obtained. Results are compared with experiments carried out with squid giant axons perfused intracellularly.

Notes: Abstract An expression for the variance in birth volumes during balanced growth of a cell population is derived. The requirement of this expression being positive and finite allows a discussion of some of the requirements imposed on the mechanisms of growth and division.

Notes: Abstract The phenomenon of axonal transport of material has been well documented (Ochs, 1971; Lasek, 1970; and Grafstein, 1967). This report seeks to establish the role of diffusion—if any—in such a transport process. We report that diffusion cannot account for the observed build-up of material as reported in the literature.

Notes: Abstract The question of how to fit a general cubic model of a multicomponent, interactive growth system to observed data is addressed. A multidimensional-polynomial type of regression analysis is used, with a least-squares criterion. By testing the scheme on a problem with known solution, the way in which the accuracy of the results varies with the number of datum points used is investigated in an heuristic manner.

Notes: Abstract The describing function method is used as a guide to the behaviour of the solutions of the equations of Danziger and Elmergreen, proposed as a model of periodic catatonia. The method suggests that whenever the equilibrium point is unstable it is surrounded by a stable closed periodic orbit. This is confirmed in specific cases by computation.

Notes: Abstract A theory of ambiguous pattern perception is formulated. This theory proposes a feature selector (field of attention) based on the time-sequential discrete property of the attention, a short-term memory for storage of the selected features, and a displayer (perception) to display the consecutively stored features. Since the selected features continuously enter, and since the features can only be stored in the short-term memory for a short period, the features which can be displayed in the displayer vary with time. When all the essential features belonging to one pattern happen to be in the displayer, the picture is perceived to be that pattern; when all the essential features belonging to another pattern happen to be in the displayer, then the picture is perceived to be the other pattern. Thus the picture appears to vary with time and alternate between two patterns. A numerical calculation is presented.

Notes: Abstract The thermodynamics of irreversible processes is derived from the principles of dynamical field theory independently of all elements of thermostatics, in particular the assumption of local equilibrium. Field thermodynamics proceeds from the premise that all driving forces experienced by the molecules in a continuum are conservative and arise from scalar potential functions. Dynamically the temperature potentialT is no different from the pressure potentialp. A field is converted to a force upon multiplication by a scale factor. A potential is converted to potential energy by the same scale factor. To scale the field −∇p to the force per mole of molecular speciesk, the partial molar, volume $$\bar V_k $$ is the scale factor. Similarly the partial molar entropy, $$\bar S_k $$ , scales the temperature field. The transition from the scale factors (which are physical parameters) to the systemic variables, for example $$\bar S_k \to s\left( {x,y,z;t} \right)$$ , is not trivial. From the dynamics and the structure of the derived potential energy function are inducted the conjugate variables such as (p, V I) and (T, s). The meta-mechanical properties of the thermal variables (T, s) are discovered via the local First Law of Thermodynamics, which relates internal energy, thermal flux, and work, and from the local Second Law, which prescribes, the possible partitions of internal energy between kinetic, potential, and thermal energies. From the form of the potential energy come Maxwell's relationships. From the energy partition comes the equation of continuity for entropy, with its important source term. In contrast to earlier theories of irreversible thermodynamics, the dissipation function does not include the stress tensor, a constitutive parameter.

Notes: Abstract The transfer of solute through a membrane separating two aqueous solutions is studied with the time-dependent diffusion equation for composite media. By introducing new independent and dependent variables it is shown that the differential equations and boundary conditions can be transformed into a dimensionless form which does not explicitly depend on the diffusivities of the media. Laplace transforms are used to derive explicit solutions for the solute concentration as a function of position and time. It is shown that at large time the concentration approaches the equilibrium distribution exponentially. Explicit results are given for the decay time as a function of the parameters of the system. In addition, an accurate and simplified expression is derived for the decay time for the case of small membrane permeability. The accuracy of the analytic solutions for the concentration profiles is tested by comparing them with numerical results obtained by solving the diffusion equations by the method of finite differences. Excellent agreement is found.

Notes: Abstract Physiological systems are often modelled by a set of compartments. Alternatively they can be described by the diffusion-convection-reaction equations governing distributed systems. The problem considered here is that of identifying a continuously changing input of some metabolite )tracee), endogenous to the system and hence inaccessible, when a nonlinear or time-varying component is also introduced into the loss parameter, as for example through feedback mechanisms. A tracer is used to determine the steady-state impulse response under time-invariant, linear conditions. A known input of tracer is also administered when the system is driven out of steady state. The integral equations developed utilize the predetermined impulse response, the measured concentrations of both tracer and tracee (output) in some region of the system to estimate the changing loss parameter and the unknown input in a continuous fashion.

Notes: Abstract The equilibrium distribution for a generalQth-order multivariate reaction system is studied. The state transition intensity matrix is developed and examples are given for small numbers of reaction components. A closed-form expression for the equilibrium distribution for systems which are symmetric with respect to the order of component reactions is presented. Numerical examples for three component systems are discussed.

Notes: Abstract The model recently proposed by Dreitlein and Smoes for oscillatory kinetic systems is studied. Diffusion of the oscillating species is taken into account, and bounds on the total number of individuals of each species are determined for both two- and three-dimensional finite regions with various boundary conditons applied. It is found that in general the effect of diffusion on the system behavior is to reduce the maximum possible radius of limit cycles. In particular, in some cases global limit cycle behavior is precluded.

Notes: Abstract The Kedem-Katchalsky equations for fluid flux across membranes may not be adequate for large solvent flows. In particular, for an example of two membranes in series, it is argued that they would predict physically unreasonable behavior. An alternate equation for solute flow is proposed for a simple sieving membrane. For the same example, this equation predicts more physically reasonable results.

Notes: Abstract Krylov-Bogoliubov-Mitropolsky perturbation method was used to study the effect of nonlinearity in the Volterra-gause-Witt (VGW) model for a two species prey-predator system. The first order corrections to both the frequency of oscillation and the amplitude of the linearized system were computed. It was found that the basic qualitative features of the nonlinearity are exhibited by the first order result. We have also discussed the Lotka-Volterra problem which is a special case of VGW model.

Notes: Abstract This paper presents a mathematical analysis of a tumor model first proposed by Skipper and Zubrod. The tumor model is comprised of three compartments, a proliferative compartment, a nonproliferative but viable compartment, and a dead compartment. By the suitable selection of functions describing loss of cells from the proliferative and nonproliferative compartments, the model is capable of describing tumor behavior during periods of growth and drug treatment. The loss functions during treatment are related to pharmacokinetic functions and may be chosen according to known drug properties. Tumor properties may be simulated by the appropriate choice of cell cycle parameters. It therefore seems feasible to simulate tumor behavior for scheduled treatment with chemotherapeutic agents. Another important result of this analysis is the derivation of a fraction labelled mitosis function which incorporates the nonproliferative compartments.

Notes: Abstract Techniques of modelling and simulation are discussed as they relate to bioengineering systems. The advantages and disadvantages of different analytical engineering methods utilized to gather information concerning the behavior of complex physiological and neuromuscular control mechanisms are explained. An Inners Criterion is developed to determine if the roots of a model lie within a certain “biologically realistic region” ΓB, in the complex plane which contains the roots of linearized models for a large variety of neuromuscular systems. Several algorithmic methods based on the Jury Inners Test are described which specify whether the model roots lie within the desired region, thereby providing an indication as to the validity of the proposed model. This technique can help to eliminate tedious simulation on an unrealistic model with roots lying far outside this region. An exemplary model for control of vergence eye movements is presented and shown to satisfy the ΓB criterion; several counter-examples are also discussed. The Inners approach can be adapted to other classes of bioengineering systems by specifying the region based on models that are contained in the class of interest.

Notes: Abstract In this paper I consider how information is required to specify various systems. It is shown that the transitive information of any physical system, is distributed among three distinct components. One of these, the selective component, is required to specify the elemental parts of the system. Another, the connective component, is required to specify the macrostructure of the system; that is the way the parts are put together. And a third, the conformative component, is required to specify the intrinsic complexion or microstructure of the system. An interesting method for analyzing branched systems which takes account of connective ambiguity is described in some detail. The relationship between information and entropy, known as the Clausius-Shannon Identity, is then discussed with reference to selected thermodynamic models: and that aspect of information which is often overlooked, namely the distinction, between transitive and intransitive information is highlighted. The applications (or perhaps more correctly, the limitations of applying this treatment) to problems of biological interest are also indicated.

Notes: Abstract This paper discusses two compartment models with interaction allowed between the compartments. The total number of particles in the system at any time is discussed along with the number to the found in each separate compartment. An interesting result is that the number of particles in each of the two compartments areindependent random variables. Some asymptotic results are also given. The paper is a continuation of some earlier work by the author.

Notes: Abstract General criteria which either preclude time-periodic dissipative structure solutions or imply asymptotically steady solutions are derived for generic systems of reaction-diffusion equations ∂c i /∂t =D i ∇2 c i +Q i (c) subject to boundary conditions of practical interest, where the enumerator indexi runsl ton, c i =c i (x,t) denotes the concentration or density of theith participating molecular or biological species,D i is the diffusivity constant for theith species, andQ i (c), an algebraic function of then-tuplec=(c 1,...,c n ), expresses the local rate of production of theith species due to chemical reactions or biological interactions. It is demonstrated that certain functionals ofc which decrease monotonically with time can often be found, as exemplified here for Volterra and Verhulst-Volterran-species model systems, and thus time-periodic dissipative structure solutions are precluded for such systems of reaction-diffusion equations. It is shown that all solutions to a generic system of reaction-diffusion equations evolve dynamically to a unique steady state, $$\mathop {\lim }\limits_{t \to \infty } c_i (x, t) = \hat c_i (x)$$ , if the diffusivity constants are all sufficiently large in magnitude. A necessary condition for the existence of a periodic solution (either spatially uniform or non-uniform) is formulated in terms of the curl ofQ(c) inc-space. Finally, necessary and sufficient conditions are derived for the existence of time-periodic dissipative structure solutions in cases of “weak diffusion” with the reaction rate terms dominant in the governing equations.

Notes: Abstract A model nonlinear network involving chemical reactions and diffusion is studied. The time evolution and bounds on the steady state solutions are analyzed. Spatially ordered solutions of the equations of the dissipative structure type are found by bifurcation theory. These solutions are calculated analytically and their qualitative properties are discussed.

Notes: Abstract Models based on molecular mechanisms are presented for pattern formation in developing organisms. It is assumed that there exists a diffusion governed gradient in the morphogenetic field. It is shown that cellular differentiation and the subsequent pattern formation result from the interaction of the diffusing morphogen with the genetic regulatory mechanism of cells. In a second stage it is shown that starting from a homogeneous distribution of morphogen, polarity can be generated spontaneously in the morphogenetic field giving rise to the establishment of a gradient. The stability of these gradients is demonstrated. The onset of a morphogenetic gradient and pattern formation are combined in a single coherent model. Size invariance and its biological implications are discussed.

Notes: Abstract The paper introduces a basic mathematical form, which is characteristic of a number of linear one-dimensional diffusion equations with coefficients being represented as simple polynomials in the spatial coordinate. A number of particular diffusion equations are introduced and their corresponding exact mathematical solutions are obtained.

Notes: Abstract In this paper we examine a set of nonlinear rate equations (devised by M. Eigen (1971)) which describe the process of selection in a collection of self-reproducing, macromolecular information carriers. We construct exact solutions to the equations for the case of constant rate parameters and constant error distributions. The solutions allow the direct assessment of the effect of mutations on the “selective value” parameters discussed by Eigen as well as the distribution of the molecular species selected in steady state. In addition we show that the selection process may be characterized by an extremal principle.

Notes: Abstract The electromagnetic molecular electronic resonance (EMER) frequencies of the molecular chains of α-chymotrypsin are calculated. The chain length relations and coupling positions suggest a possible energy transfer, at the EMER frequencies, from one chain to the other. Photon enzyme activation data indicate that the energy corresponding to the EMER frequencies of its molecular chains is used by α-chymotrypsin for its enzyme function.

Notes: Abstract Based on Wei's dipole flip-flop model and with the assumption that the dipole is coupled to the membrane matrix, the cathode-make-excitation, the anode-break-excitation and the cathode-gap-excitation can be explained in a systematic way. The istrength-duration relations for these three processes are derived.

Notes: Abstract It is usually stated that only systems with multiple steady states can exhibit hysteresis. For protein conformations, this would violate the idea that, in fixed environments, primary structure uniquely determines tertiary structure. It is shown that hysteresis-like phenomena can be exhibited by systems possessing only a single steady-state configuration. This property is placed in a more general theoretical setting of recognition and classification systems, and some implications for processes such as memory, learning and pattern generation (morphogenesis) are discussed.

Notes: Abstract The natural historical literature contains a considerable body of work which indicates that harvesting (or predation) can alleviate competitive instabilities. In order to arrive at an understanding of this, the appropriate bifurcation structure for a rather general family of two-dimensional competitive systems is here investigated. The results of this analysis suggest that, in more complicated ecosystems with many competing species, (1) there is a good chance that harvesting at moderate rates will increase species diversity if one species is dominant in the unharvested system, while an increase in diversity is not likely to result from harvesting from a system with no dominant species, (2) whenever harvesting does increase species diversity, maximal diversity will occur at moderate harvesting rates, with less diversity at both very high and very low harvesting rates.

Notes: Abstract The Weber-Fechner law (response of an organism is a linear function of log of stimulus) has been widely used for description of physiological and psychological data for many years. It is shown here that the Weber-Fechner law is derivable in a simple way from the Elovich equation (−dx/dt=m exp(nx), which is observed experimentally in numerous physiological and biochemical systems, and which has a simple derivation from solid state charge transport across interfaces in these systems. It therefore seems reasonable to interpret data conforming to the Webner-Fechner law to imply that the observed phenomenon is rate-limited by interfacial charge transport in the cell. By a similar analysis, the Loewenstein equation, which may be considered an exact form of the Weber-Fechner law applicable to data over a wider range of values of the variables, is derived from a more exact form of the Elovich equation.

Notes: Abstract A simple similarity transformation of the Leslie matrix renders certain properties obvious. In particular the characteristic polynomial, characteristic vectors and principal vectors can be explicitly written out. Bounds for the dominant root are given.

Notes: Abstract A mathematical description of the process of adherence to glass of the rat thymus lymphocytes is presented. It is based on the result of previous work in which the process was studied in the course of the flow of the51Cr labelled cell suspension through the glass-bead column. The concentration of cell suspension, flow velocity and medium temperature were constant; the experiments were performed with different lengths of the bead bed. The amount of cells captured on the glass beads' surface was calculated as a function of time. Two approaches to the mathematical description of the process are presented. The first one is based on the linear equation of kinetics of cell retention on the elementary thin layer and on the transport equation of the flow of the suspension through the column. In the second one, the differential equation of the adhesion, derived from the experimental data, is discussed.

Notes: Abstract A simple population model consisting of one adult and two larval stages with cannibalism or competition among the larval stages is presented. The solutions are found to be either periodic or of a steady state nature depending on the ratios of fertility and cannibalism among the larvae. Two similar cannibalism pressure functions are compared and the conditions that lead to steady or periodic solutions, or to extinction, are examined.

Notes: Abstract Thyroid hormone synthesis shows two important characteristics at each iodine organification step: iodine fixation to thyroglobulin tyrosyl residues in the vicinity of the thyroid cell microvilli, and the storage of thyroglobulin in the follicular lumen. In order to study the influence of kinetic parameters (chemical reactions, diffusion coefficient) and, of the structure (follicular radius and reactional space width) we have determined the impulsional response of a diffusion sphere exchanging matter with a compartment where the chemical reactions are taking place. This study gives the starting point of a mathematical model of hormonal secretion by a thyroid follicle. Moreover it suggests a simple way of estimating the thyroglobulin diffusion coefficient by the mean transit time determination. Finally, we discuss respectively the validity limits of a compartmental description of the model, and of a continuous description by an infinite sum of exponentials of a system where chemical reactions interfere with a storage process by diffusion.

Notes: Abstract In order to represent the biological evolution of a predator-prey ecology it is necessary to add to the equations of population dynamics terms corresponding to spontaneous mutation. Using a Volterra-Lotka ecology as an example, a model is developed for this. It is based on the assumption of two levels of description; a local one containing mutation probabilities, and the other the macroscopic average equations for the whole system. Diffusion processes link the two. The “evolutionary state” of a species is interpreted as an average effectiveness in terms of a genetic parameter space and it is shown that as a result of random mutations the ecosystem drifts irreversibly through this space.

Notes: Abstract A number of recent experiments have revealed the existence of mutants with different free run periods in their circadian rhythms. Parameter variations in mathematical models can be used to simulate such changes. In addition, phase response curves (PRC) are derived and the effect of parameter variation in their shape is studied. It is shown that changes in global parameters can also distort their shape. Therefore one cannot conclude that genetic experiments provide evidence in favor of “chronon” models since “kinetic” models can also simulate their outcome.

Notes: Abstract A methematical description of a coupling between a chemical reaction, the diffusion through a cellular membrane and a fluid flow is presented. This coupling may occur at the membrane levels of the cells bathed by fluid flows (e.g. endothelial cells). By such a coupling, the fluid flow and the diffusion can act as drivers of some intracellular endergonic reactions.

Notes: Abstract The classical epidemic equations of Kermack and McKendrick are cast into dimensionless form. This allows discussion of the assumptions underlying the standard approximate solutions.

Notes: Abstract A study is made of blood flow by assuming that the blood constitutes a suspension of cells in plasma instead of a simple homogeneous fluid. A macroscopic theory governing the motion of plasma in a plasma-cell system is derived from the local volume averaging method for a system without mass transfer between the phases, and its characteristic length is much larger than the size of the cells. The equations governing the motion of the local averaged fluid quantities include one additional term in the equation of motion and two additional terms in the energy equation. These terms represent, respectively, the force exerted upon the fluid by the particles, and the rate of heat transfer and work done upon the fluid by the particles. The theory is applied to obtain the effective viscosity as the explicit function of the volume concentration of the cells by assuming that the cells behave like rigid spherical particles with slip-collision, and the plasma is an incompressible Newtonian fluid. Comparison with existing experimental results shows a good agreement. The theory is also used to obtain the effects of cell distribution upon the overall effective viscosity in a circular tube. The quantitative result shows that there is a decrease in overall effective viscosity as the concentration of cells increases toward the center of the tube, and the overall effective viscosity is smaller than the flow with evenly distributed cells.

Notes: Abstract The distribution of the two-compartment, reversible system with time-dependent transitions is proposed and verified. Inasmuch as the required probabilities cannot, in general, be expressed in closed form, a method of approximating these probabilities is described. An example with specific inverse functions of time is presented.

Notes: Abstract The airway system of the lung from the mouth to the pulmonary membrane is modelled by matching a cylindrical model of a pathway through the respiratory region of the lung onto a one-dimensional trumpet model for the conducting airways. The concentration of O2 in gas expired from this model airway system is investigated following an inspiration of air at two different flow rates (10 litres/min and 85 litres/min). In each case, expiration occurs at the same constant flow rate as that during the previous inspiration. The inspirations, which are studied in an earlier paper, are each of 2 sec duration and begin at a lung volume of 2300 ml and a lung oxygen tension of 98 mm Hg. The equations are solved numerically and plots of expired O2 concentration against time and against expired volume are shown. It is found that at 85 litres/min, gas mixing in the lung is complete after about 0.7 sec of expiration whereas at 10 litres/min, about 2.6 sec of expiration is required for complete equilibration. It is suggested that the experimental alveolar plateau slope is not in general caused by a slow approach to equilibrium of gas concentrations; except at very low flow rates in the early part of the concentration/time plateau.

Notes: Abstract On the basis of an abstract, simple bistable reaction system (‘homogeneous Eccles-Jordan trigger’) used as anRS flip-flop, an abstract homogeneousastable flip-flop is devised. It can be run also as amonostable flip-flop and as aT flip-flop. The qualitative behavior of the three systems can be understood, in the limiting case, with the aid of Poincaré's notion of bifurcation of steady states. The reaction system is proposed as a paradigm for a specific class of ‘decomposable’ chemical and dynamical systems (so-called DC-type dynamical automata). Two possible biological applications are mentioned.

Notes: Abstract The stochastic theory of a nonlinear game is presented which incorporates some of the essential properties of living systems: metabolism, reproduction and mutability. The steady state distribution function as well as the complete time development are given explicitly. The second law of thermodynamics is generalized to a certain class of nonequilibrium systems. An order parameter is introduced as a measure of the system's internal organization. From the point of view of phase transition theory, the model exhibits a transition at the absolute zero of temperature, with critical behaviour showing up in the low temperature region.

Notes: Abstract A theory for environmental systems is defined on the basis of two elements, termed ‘environmental unity’ and ‘behavior’. Environmental systems are regarded as non-living systems, each one related with only one biological system. We construct a material-energetic environmental diagram, which is introduced in terms of the theory of categories, thereby giving rise to a new categoryE. By means of two biological conditions, and the definition of static property of the biological system (related to its own environment), a set of theorems is obtained, exhibiting mathematical consequences for the represented theory.

Notes: Abstract Complementary variational principles are derived for the pressure boundary value problems in Weinbaum's (1965) model of the human eye. These principles can be used to obtain accurate solutions for the pressure.

Notes: Abstract The bat wing is used as an experimental preparation and as a self-contained vascular bed. The number, dimensions, and distribution of the vessels of the real vascular bed are included into an analyzable, representative geometric configuration. Based on theoretical analysis and experimental data, equations are developed and utilized to characterize the pressure-flow relationships for each branching order of the vascular field. The geometric configuration and associated describing equations are used to determine the resistance distribution of the microvascular bed. The predicted values are compared with experimentally determined quantities in normal and hypertensive animals.

Notes: Abstract The geometry of the human bronchial tree has been described as a network formed by successive dichotomous branching with constant branching angles and geometrically decaying branch lengths. Models having these properties and with randomly distributed branching planes are constructed. The distribution of the end points of the model networks are described by computing the variance of the distributions in the direction of the axis of the network and in the transverse directions. It is found that, for a given decay ratio, there is a branching angle for which the volume filled by the end points is a maximum. The advantages of the network with the decay ratio and branching angle of the human bronchial tree are discussed.

Notes: Abstract The steady state distribution of oxygen tension in thein vivo cornea is estimated in the present study by using a nonlinear oxygen consumption rate equation of the Michaelis-Menten type. Such a rate expression is more accurate than the previous simplified versions in predicting the oxygen consumption rate. It is found that for an open eye with or without contact lens, the oxygen tensions predicted previously are in good agreement with these predicted in the present work. However, for a closed eye with or without contact lens, the previous predictions underestimate the oxygen tension.

Notes: Abstract The dual reciprocal and antagonistic organization of B- and D-neurons of the afferent visual system is obtained using differentiation and integration as mathematical equivalents of visual information processing by an impulse frequency code. The spatial and temporal derivatives lead to the transient responses. A constant and a time-dependent term proportional to the luminance distribution describe the sustained response components and the shift-effect of retinal on- and off-center ganglion cells. Receptive field properties of lateral geniculate cells and their antagonistic shift-effect are obtained by passing the retinal output, i.e. the difference between B- and D-neurons' activity, once again through the same operations. However, the factor of proportionality is applied to the retina alone. The surprisingly small difference between retinal and geniculate receptive field properties on the one hand and the dramatic change from a synergistic to an antagonistic shift-effect on the other hand are thereby explained. The theory offers an understanding of a a possible functional significance of the shift-effect as a mechanism of transientrestoration of visual information, which prevents the system from total fading by means of shifts of the retinal image, normally produced by eye movements.

Notes: Abstract Applications of randomly connected networks are reviewed briefly. The connectivity of a random network has been defined in a variety of ways including output connectivity, total or network connectivity, connectance, expected path length and radius. One or more of these definitions may prove more convenient in a given experimental system. Interrelations among these definitions are derived and displayed and asymptotic results provided in the form of two theorems. Computer simulations were used to explore the range of application of these asymptotic approximations. The results were used to determine the output connectivity of the neurons of the brain.