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Surkis, A., C. S. Peskin, D. Tranchina, and C. S. Leonard. Recovery of cable properties through active and passive modeling of subthreshold membrane responses from laterodorsal tegmental neurons. J. Neurophysiol. 80: 2593–2607, 1998. The laterodorsal tegmental nucleus (LDT) is located in the dorsolateral pontine reticular formation. Cholinergic neurons in the LDT and the adjacent pedunculopontine tegmental nucleus (PPT) are hypothesized to play a critical role in the generation of the electroencephalographic-desynchronized states of wakefulness and rapid eye movement sleep. A quantitative analysis of the cable properties of these cells was undertaken to provide a more detailed understanding of their integrative behavior. The data used in this analysis were the morphologies of intracellularly labeled guinea pig LDT neurons and the voltage responses of these cells to somatic current injection. Initial attempts to model the membrane behavior near resting potential and in the presence of tetrodotoxin (TTX, 1 μM) as purely passive produced fits that did not capture many features of the experimental data. Moreover, the recovered values of membrane conductance or intracellular resistivity were often very far from those reported for other neurons, suggesting that a passive description of cell behavior near rest was not adequate. An active membrane model that included a subthreshold A-type K+ current and/or a hyperpolarization-activated cation current (H-current) then was used to model cell behavior. The voltage traces calculated using this model were better able to reproduce the experimental data, and the cable parameters determined using this methodology were more consistent with those reported for other cells. Additionally, the use of the active model parameter extraction methodology eliminated a problem encountered with the passive model in which parameter sets with widely varying values, sometimes spanning an order of magnitude or more, would produce effectively indistinguishable fits to the data. The use of an active model to directly fit the experimentally measured voltage responses to both long and short current pulses is a novel approach that is of general utility.

Mesopontine cholinergic neurons have been implicated in the initiation and maintenance of rapid eye movement sleep via their efferent connections to the thalamus and the medial pontine reticular formation. As a first step toward understanding how these modulatory neurons integrate synaptic input, we have investigated the dendritic architecture of laterodorsal tegmental nucleus neurons. The principal cells of the guinea-pig laterodorsal tegmental nucleus were identified electrophysiologically in a brain slice preparation, then were intracellularly injected with biocytin and reconstructed using a computer-aided tracing system. The somata were large (27 +/- 3 microns; n = 11) and gave rise to an average of 4.8 primary dendrites which, in most cases, emerged from the soma in a pattern that was radially symmetric in the plane of the slice. Primary dendrites had an average of 3.7 endings. A single axon arose from either the soma or a proximal dendrite and exited the nucleus with a medial and/or lateral trajectory. Some axons also gave rise to a local terminal plexus composed of fine fibers bearing numerous punctate swellings that ramified profusely within the neuron's dendritic field. Total dendritic area averaged about 10(5) microns2, and therefore the average contribution of the soma to the total surface area (20%) was significantly larger than the values reported for many other cell types. Dendritic diameters were non-uniform in three respects. Some processes were sparsely spiny. Most processes were varicose, with the degree of varicosity increasing substantially in secondary and tertiary dendritic segments. There was also a large degree of taper in dendritic processes; those processes with a non-negative taper had an average diameter decrease of 40 +/- 25%. Dendritic processes deviated from the criteria necessary for a Rall equivalent cylinder approximation due to non-uniformity in morphotonic path length, failure to conform to the Rall 3/2 branching rule and non-uniformity of dendritic diameter. An analysis was done to assess the impact of dendritic varicosities on the extraction of cable parameters for these cells. Voltage traces were simulated by solving the cable equation for a varicose dendrite and then membrane parameters were recovered using an equivalent cylinder model. Errors in the extracted values of specific membrane conductance and specific membrane capacitance were quite small (or = 5%), while larger errors were seen for electrotonic length (or = 21%) and intracellular resistivity (or = 5%). These data indicate that the principal cells of the laterodorsal tegmental nucleus, while possessing a relatively simple dendritic structure in terms of number and branchiness of dendrites, display a heterogeneity of dendritic process types. Processes range from smooth to markedly varicose, and can be aspiny or sparsely spiny. The possibility that the dendritic varicosities function as sites of either electrical or chemical compartmentalization is discussed. The degree of error resulting from a Rall equivalent cylinder approximation in light of these varicosities indicated that a generalized cable model approach may prove more effective in estimating their cable parameters.

The two-headed motor protein kinesin hydrolyzes nucleotide to move unidirectionally along its microtubule track at speeds up to 1000 nm/s (Saxton et al., 1988) and develops forces in excess of 5 pN (Hunt et al., 1994; Svoboda et al., 1994a). Individual kinesin molecules have been studied recently in vitro, and their behavior has been characterized in terms of force-velocity curves and variance measurements (Svoboda and Block, 1994a; Svoboda et al., 1994b). We present a model for force generation in kinesin in which the ATP hydrolysis reactions are coordinated with the relative positions of the two heads. The model explains the experimental data and permits us to study the relative roles of Brownian motion and elastic deformation in the motor mechanism of kinesin.

At this Symposium on Biological Fluid Dynamics, it is appropriate to ask whether there is any common theme that unites the diverse problems that arise in the study of living systems interacting with fluids. The answer that immediately comes to mind is this: biological fluid dynamics invariably involves the interaction of elastic flexible tissue with viscous incompressible fluid. (In many cases the tissue is not only elastic, it is also active, i.e. capable of doing work on the fluid). This paper describes the immersed boundary method, which is a general framework for the computer simulation of biofluid dynamic systems. This method has already been applied to blood flow in the heart (including the computer-assisted design of prosthetic cardiac valves), platelet aggregation during blood clotting, aquatic animal locomotion, wave propagation along the basilar membrane of the inner ear, and flow in collapsible tubes. In the immersed boundary method, the elastic (and possibly active) biological tissue is treated as a part of the fluid in which additional forces (derived from the tissue stresses) are applied. Because the tissue is represented in terms of its force field, the method remains straightforward, even when the geometry of the biological tissue is complicated, dynamic and not known in advance.

We propose that protein translocation across membranes is driven by biased random thermal motion. This "Brownian ratchet" mechanism depends on chemical asymmetries between the cis and trans sides of the membrane. Several mechanisms could contribute to rectifying the thermal motion of the protein, such as binding and dissociation of chaperonins to the translocating chain, chain coiling induced by pH and/or ionic gradients, glycosylation, and disulfide bond formation. This helps explain the robustness and promiscuity of these transport systems.

The heart is modeled as a system of elastic and/or contractile fibers immersed in a viscous incompressible fluid. Simulated heart walls and valves are constructed by arranging the fibers according to an idealized version of the actual distribution of muscle fibers in the heart walls and collagen fibers in the valve leaflets. Then the combined motion of the fluid-fiber system is predicted through the numerical solution of its coupled equations of motion. Fluid equations are solved by a finite difference method on a fixed, regular computational lattice. Fiber points move freely through this lattice without being constrained to lie at the lattice intersections. Communication between fibers and fluid involves interpolation of the fluid velocity to the fiber points and the spreading of the fiber forces to the computational lattice of the fluid. Both of these operations make use of a smoothed approximation to the Dirac delta function. The entire method is suitable for implementation on vector, parallel, or parallel-vector hardware. Applications include the investigation of normal cardiac function, the simulation of disease processes affecting the mechanical function of the heart or its valves, and the computer-assisted design of prosthetic cardiac valves.

A non-stationary optimal smoothing filter for digital nuclear medicine image data, degraded by Poisson noise, has been derived and applied to temporal simulated and clinical gated blood pool study (GBPS) data. The derived filter is automatically calculated from a large group (library) of similar GBPS which are representative of all studies acquired according to the same protocol in a defined patient population (the ensemble). The filter is designed to minimize the mean-square difference between the filtered data and the true image values; it provides an optimal trade-off between noise reduction and signal degradation for members of the ensemble. The filter is evaluated using a computer simulated ensemble of GBPS. Libraries of Poisson-degraded and non-degraded studies were generated. Libraries of up to 400 Poisson-degraded simulated studies were used to estimate optimal temporal filters that, when applied to Poisson-degraded members of the ensemble not included in the libraries, reduced the mean-square error in the raw data by 65%. When the non-degraded studies were used instead to compute the optimal filter values, the corresponding reduction in the error was 83%. Libraries of previously acquired clinical GBPS were then used to estimate optimal temporal filters for an ensemble of similarly acquired studies. These filters were subsequently applied to studies of 13 patients (not in the original libraries) who received multiple sequential repeat studies. Comparisons of both the filtered and raw data to averages of the repeat studies demonstrated that optimal filters calculated from 400 and 800 clinical studies reduced the mean-square error in the clinical data by 56% and 63% respectively.

The empirical differential equation that describes the kinetics of monazomycin-induced voltage-dependent conductance is derived using a standard chemical kinetic formulation and the assumption that monazomycin entry into and exit from the membrane is autocatalytic. The predicted form of gating currents is shown and numerical calculations for this process are made using a range of values for two unmeasured variables. A form of "memory" is then demonstrated, along with the ability of the theoretical equation to explain the nature of the memory.

The pressure-flow relations of large amplitude pulsatile water flows across an orifice have been investigated theoretically and experimentally. By retaining the unsteady term in the one-dimensional equation of motion, and by allowing the jet area to be a function of distance in the continuity equation, a lumped parameter relationship between pressure drop and flow has been developed which reflects the influence of inertia and dissipation. The results are applicable to the analysis of natural and prosthetic heart valves under normal and pathologic conditions. Within the physiologically possible conditions of frequency and flow rate, unsteady separated flows exhibit the same energy losses as comparable steady separated flows. Thus, the flow is quasi-steady, even when the waveforms and temporal relations indicate a significant inertial influence.

Isometric relaxation in cardiac sarcomeres is characterised by an early, very slow phase of tension fall which is terminated by a 'give' in tension. A 'give' which occurs during relaxation in cardiac muscle can not be attributed to decrease in myofilament overlap. After the 'give' asynchronous motion occurs between sarcomeres, but the duration and extent of their displacement is limited. Intriguingly, the effect of isotonic displacements on the early fall in the velocity of sarcomere shortening indicates that an internal resistance increases near the peak of contraction. The complex shape of the sarcomere's complete force-velocity relation, with lengthening motions in particular, was consistent with an idealized model of cross-bridge cycling. The sarcomere's resistance to stretch is high at low velocity, but it diminishes to reveal yielding at larger velocities. Relative to tension, the resistance to yielding does not decrease during relaxation, and it may actually increase. The decay of isometric tension after a controlled stretch also slows during relaxation. Consequently, cycling slows in those cross-bridges which form (or persist but produce less force) later in contraction. Changes in cross-bridge properties may restrict sarcomere shortening, prolong activation, but promote a disequilibrium which favors rapid relaxation in cardiac muscle.

This paper describes an analytic and a numerical method for the aortic sinus problem. Both methods are based on the dynamics of point vortices, and both exploit a particular conformal mapping from a model aortic sinus to the upper half plane. The analytic description is based on an isolated point vortex in equilibrium with a free stream. This inviscid model is used to study the stability of the aortic sinus vortex and to elucidate the mechanism of aortic valve closure, but it cannot be used to study the formation of the sinus vortex and it gives a somewhat incorrect picture of the flow pattern. These difficulties are overcome by the introduction of a numerical method for the aortic sinus problem with fluid viscosity. We use Chorin's vortex method combined with conformal mapping. The conformal mapping approach gives an explicit formula for the vortex velocities and it resolves the singularities associated with the corners of the domain. This method is then used to study the formation of the sinus vortex and to confirm the predictions of the point vortex model with respect to the role of the vortex in valve closure.

This paper describes the use of the new technique of computer testing to study the simulated performance of flat and curved pivoting disc prosthetic mitral valves. The design parameters considered are the radius of curvature of the occluder and the position of the pivot point. The performance criteria are the net stroke volume, the mean forward pressure difference, and the peak anterior velocity. The last of these criteria may be important in the prevention of small-orifice valve thrombosis. The best overall valve in the study has a radius of curvature equal to 1.5 times the diameter of the occluder and a pivot point located 0.39 mitral-ring diameters from the anterior border of the mitral anulus. The maximum angle of opening of this optimal valve is limited to about 70 degrees by fluid-mechanical forces. Nevertheless, the inclusion of a redundant stop in the mechanical design of the valve is indicated, since the computer experiments also reveal excessive opening and failure to close in valves with nearby parameter values. These studies illustrate the usefulness of computer testing in prosthetic valve design.