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Buckton KE, O'Riordan ML, Ratcliffe SG, et al. A G-banded study of chromosomes in liveborn infants. Ann Hum Genet 1980;43 :227-39. 5 Gosden CM, Wright MO, Paterson WG, Grant KA. Clinical details, cytogenetic studies and cellular physiology of a 69,XXX fetus with comments on the biological effect of triploidy in man. J Med Genet 1976; 13:371-80. 6 Gosden CM, Brock DJH. Morphology of rapidly adhering amniotic fluid cells as an aid to the diagnosis of neural tube defects. Lancet 1977;i: 919-22. 7 Gosden CM, Brock DJH. Combined use of alphafetoprotein and amniotic fluid cell morphology in early prenatal diagnosis of fetal abnormalities.

We study the models for calcium (Ca) dynamics developed in earlier studies, in each of which the key component is the kinetics of intracellular inositol-1,4,5-trisphosphate-sensitive Ca channels. After rapidly equilibrating steps are eliminated, the channel kinetics in these models are represented by a single differential equation that is linear in the state of the channel. In the reduced kinetic model, the graph of the steady-state fraction of conducting channels as a function of log10(Ca) is a bell-shaped curve. Dynamically, a step increase in inositol-1,4,5-trisphosphate induces an incremental increase in the fraction of conducting channels, whereas a step increase in Ca can either potentiate or inhibit channel activation, depending on the Ca level before and after the increase. The relationships among these models are discussed, and experimental tests to distinguish between them are given. Under certain conditions the models for intracellular calcium dynamics are reduced to the singular perturbed form epsilon dx/d tau = f(x, y, p), dy/d tau = g(x, y, p). Phase-plane analysis is applied to a generic form of these simplified models to show how different types of Ca response, such as excitability, oscillations, and a sustained elevation of Ca, can arise. The generic model can also be used to study frequency encoding of hormonal stimuli, to determine the conditions for stable traveling Ca waves, and to understand the effect of channel properties on the wave speed.

More than 8.6 million people suffer from neurological disorders that affect their gait and balance. Physical therapists provide interventions to improve patient’s functional outcomes, yet balance and gait are often evaluated in a subjective and observational manner. The use of quantitative methods allows for assessment and tracking of patient progress during and after rehabilitation or for early diagnosis of movement disorders. This paper surveys the state-of-the-art in wearable sensor technology in gait, balance, and range of motion research. It serves as a point of reference for future research, describing current solutions and challenges in the field. A two-level taxonomy of rehabilitation assessment is introduced with evaluation metrics and common algorithms utilized in wearable sensor systems.

A general formulation is presented for the verification of isotonic transport and for the assignment of a degree of osmotic coupling in any epithelial model. In particular, it is shown that the concentration of the transported fluid in the presence of exactly equal bathing media is, in general, not a sufficient calculation by which to decide the issue of isotonicity of transport. Within this framework, two epithelial models are considered: (1) A nonelectrolyte compartment model of the lateral intercellular space is presented along with its linearization about the condition of zero flux. This latter approximate model is shown to be useful in the estimation of deviation from isotonicity, intraepithelial solute polarization effects, and the capacity to transport water against a gradient. In the case of uphill water transport, some limitations of a model of fixed geometry are indicated and the advantage of modeling a compliant interspace is suggested. (2) A comprehensive model of cell and channel is described which includes the major electrolytes and the possible presence of intraepithelial gradients. The general approach to verification of isotonicity is illustrated for this numerical model. In addition, the insights about parameter dependence gained from the linear compartment model are shown to be applicable to understanding this large simulation.

Cell volume regulation during anisotonic challenge is investigated in a mathematical model of a tight epithelium. The epithelium is represented as compliant cellular and paracellular compartments bounded by mucosal and serosal bathing media. Model variables include the concentrations of Na, K, and C1, hydrostatic pressure, and electrical potential, and the mass conservation equations have been formulated for both steady-state and time-dependent problems. 53:348-365.) reported that the cells of frog skin exhibit osmotic swelling followed by a volume regulatory decrease (VRD) when the serosal bath is diluted to half the initial osmolality. Similar regulation is achieved in the model epithelium when both a basolateral cotransporter and a volume-activated CI permeation path are included. The observed transepithelial potential changes could only be simulated by allowing volume activation of the basolateral K permeation path. The fractional VRD, or shrinkage as percent of initial swelling, is examined as a function of the hypotonic challenge. The fractional VRD increases with increasing osmotic challenge, but eventually declines under the most severe circumstances. This analysis demonstrates that the VRD response depends on the presence of adequate intracellular chloride stores and the volume sensitivity of the chloride channel.

A modified Newton-Raphson method for solving finite difference equations for the renal counterflow system is described. The method has proved generally stable and efficient, and has given significant computational results for a variety of models: calculations on single solute models of the coupled vasa recta nephron counterflow system have shown that for large water and solute permeabilities of the exchanging membranes, behavior of the non-ideal system approaches that of the previously described ideal central core model. Concentration by salt and urea mixing in two solute models has been analyzed and previous conclusions from central core models have been found to remain valid in non-ideal systems. The numerical solutions have set some order of magnitude bounds on permeability requirements for concentration in different types of non-ideal systems. Finally, from the detailed concentration profiles it has been possible to relate the rate of free energy creation and dissipation from transmembrane transport of solutes and water to the net rate of free energy efflux from the counterflow system, and so to compute in a given model the fraction of power used for solute concentration.It has been proposed in previous papers (1-3) that the behavior of the intricately coupled nephrovascular counterflow system of the renal medulla (4) approaches as a limiting case that of a four-tube model: the vascular counterflow exchanger is represented by a single tube-the central core, closed at the papillary end and open at the corticomedullary junction-which exchanges with three other tubes corresponding respectively to ascending Henle's limb (AHL), descending Henle's limb (DHL), and collecting duct (CD). Under the assumption that total solute concentrations in core, DHL, and CD are nearly the same at each level of the medulla, it has been possible to develop an approximate analytic theory of the ideal central core concentrating engine and so of the medullary counterflow system. This assumption implies very high solute and water permeability of the vasa recta and very high osmotic water permeability and (or) solute permeability of DHL and CD. The behavior of non-ideal models with finite permeabilities will deviate from that of the ideal central core model. In general, the differential equations describing non-ideal models must be solved numerically. For certain single-solute models this has been done by converting the two-point boundary value problem to an initial value problem (5), but this method tends to be unstable, requiring very good initial estimates to converge, and does not extend readily to two-solute models.In this paper we outline a modified Newton-Raphson method for solving globally finite difference equations approximating the differential equations. The method has proved generally applicable to a variety of models of the renal counterflow system. In this paper we summarize some significant preliminary computational results. Detailed descriptions of both the method and the results are in preparation. [2) [3] [4] ...

A simple transporting epithelium is represented as a cellular compartment, compliant in all dimensions, and a paracellular channel, of arbitrary shape, between well-stirred mucosal ans serosal baths. The equations for mass balance, Poiseuille flow, and the Nernst-Planck equation are used to describe the continuous behavior of the system along cell and channel, whereas passive transport across membranes is given by the relations of Kedem and Katchalsky. Time-dependent terms are retained to permit study of transient phenomena. Boundary conditions at the baths demand only mass conservation and specify no a priori estimates of the system variables. A numerical model containing Na+,K+,Cl-, and impermeant cellular anions is formulated with membrane parameters taken from the literature on Necturus gallbladder. The differential equations are represented as a finite difference scheme and solved using Newton's method. It appears that apical cellular NaCl cotransport is necessary to obtain a reasonable cell chloride concentration. Investigation of the osmolality of the transepithelial flow shows that at steady state a leaky epithelium cannot separate baths of substantially different tonicity, although this does not guarantee isotonic transport between equiosmolar media. Changes in bath pressure, application of transepithelial electrical potential, and simulation of ion-substitution experiments are performed to understand the role of membrane permeabilities in determining the dynamic behavior of the epithelium.