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K A Lindsay

Publications and source records attributed to K A Lindsay.

At least 19 recordsLinked to original sources
PubMed2005

Increased computational accuracy in multi-compartmental cable models by a novel approach for precise point process localization.

Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional models assign a single potential to a compartment. This potential is associated with the membrane potential at the centre of the segment represented by the compartment. All input to that segment, independent of its location on the segment, is assumed to act at the centre of the segment with the potential of the compartment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the location of input to a segment on the model solution by partitioning the effect of this input between the axial currents at the proximal and distal boundaries of segments. For a given neuron, the new and traditional approaches to compartmental modelling use the same number of locations at which the membrane potential is to be determined, and lead to ordinary differential equations that are structurally identical. However, the solution achieved by the new approach gives an order of magnitude better accuracy and precision than that achieved by the latter in the presence of point process input.

Computer Simulation↗
PubMed2004

A note on the discrepancy between the predicted and observed speed of the propagated action potential in the squid giant axon.

The Hodgkin-Huxley model for the ionic currents in the membrane of the squid giant axon has become the standard model for the electrophysiological behaviour of many excitable cells. A strong test of the model predicted a travelling wave speed of 18.76 m/s for the propagated action potential in an axon with a reported speed of 21.2 m/s. This discrepancy between prediction and observation was considered satisfactory when the model was proposed 50 years ago, appears not to have been re-evaluated, but is unsatisfactory for a mature and important model. The separate and combined influences of measurement error and biological variability on the discrepancy between prediction and observation are quantified, as is the effect of using of a one-dimensional model to represent a three-dimensional axon. The main tool in this investigation is the use of simulation to study the behaviour of the Hodgkin-Huxley membrane model. These studies show that measurement error in combination with biological variability cannot account for the discrepancy between prediction and observation. Also, calculation shows that the one-dimensional description of the behaviour of the axon is adequate. Further calculation shows that the travelling wave description of the propagated action potential is valid only for sufficiently long axons. In shorter axons the propagated action potential is predicted to travel faster than the travelling wave; consequently under suitable experimental conditions the discrepancy between prediction and observation may be negligible.

Action Potentials↗
PubMed2004

From Maxwell's equations to the cable equation and beyond.

Maxwell's equations are taken as the starting point for the development of a mathematical model of a dendrite. The three-dimensional model of the evolution of the dendritic membrane potential based on these equations gives rise to a hierarchy of one-dimensional membrane equations. Under sufficiently strong assumptions, the first membrane equation is identical to the conventional cable equation. The second membrane equation explicitly includes the influence of dendritic taper and non-axial gradients in the intra-cellular potential. The procedure of starting from a three-dimensional model and extracting from it a one-dimensional approximation provides a prescription of how to incorporate three-dimensional properties of a dendrite in a one-dimensional representation, by contrast with an approach which aims to modify the traditional cable equation to take account of three-dimensional structure. Finite element methods are used to solve the membrane equations. An example based on a simple model of a tapered dendrite with differently placed distributions of synaptic input suggests that the effect of taper on the spike train output from the model is more important for distal synapses than those closer to the soma.

Animals↗
PubMed2003

Analytical and numerical construction of equivalent cables.

The mathematical complexity experienced when applying cable theory to arbitrarily branched dendrites has lead to the development of a simple representation of any branched dendrite called the equivalent cable. The equivalent cable is an unbranched model of a dendrite and a one-to-one mapping of potentials and currents on the branched model to those on the unbranched model, and vice versa. The piecewise uniform cable, with a symmetrised tri-diagonal system matrix, is shown to represent the canonical form for an equivalent cable. Through a novel application of the Laplace transform it is demonstrated that an arbitrary branched model of a dendrite can be transformed to the canonical form of an equivalent cable. The characteristic properties of the equivalent cable are extracted from the matrix for the transformed branched model. The one-to-one mapping follows automatically from the construction of the equivalent cable. The equivalent cable is used to provide a new procedure for characterising the location of synaptic contacts on spinal interneurons.

Action Potentials↗
PubMed2002

An investigation into the influence of boundary condition specification in finite difference methods on the behaviour of passive and active neuronal models.

Neuronal models provide a major aid to understanding the behaviour of individual neurons and networks of neurons. The solution of the model equations by finite difference methods is widespread because of the inherent simplicity of the technique. Error in the finite difference approach due to spatial and temporal discretisation is shown to be equivalent to a mis-specification of membrane current density. The effect of this mis-specification on the accuracy of the solution to the model equations is shown to depend on the structure of the model and its input, as well as the size of the discretisation intervals themselves. Through a theoretical analysis, illustrated by a number of examples on passive and active dendrites, this article demonstrates that the accuracy with which core current is implemented numerically at segment end-points in elementary models influences the behaviour of the numerical solution of these models, and consequently any physiological conclusions drawn from them.

Animals↗
PubMed2001

The interaction between membrane kinetics and membrane geometry in the transmission of action potentials in non-uniform excitable fibres: a finite element approach.

By solving the partial differential equations for an axonal segment using a finite element method, the interaction between membrane kinetics and axonal inhomogeneities, measured by their influence on propagated action potentials and stochastic spike trains, is investigated for Morris-Lecar and Hodgkin-Huxley membrane models. To facilitate comparisons of both kinetic models, parameter values are matched to give approximately the same speed for propagated action potentials. In all cases examined, the Morris-Lecar membrane model is more sensitive to geometric inhomogeneities than the comparable Hodgkin-Huxley membrane model. This difference in sensitivity can, in part, be attributed to significant differences in the membrane current supplied by each kinetic model ahead of the action potential. Also, the Morris-Lecar membrane model did not generate reflected action potentials whereas these were observed over a narrow range of geometric parameters for the comparable Hodgkin-Huxley membrane model. Simulations using stochastic spike train input showed that the presence of a sharp flare could significantly modify the statistical characteristics of the spike train output. The behaviour of action potentials governed by Morris-Lecar kinetics were more sensitive to changes in axonal geometry than those generated by comparable Hodgkin-Huxley kinetics. As a consequence of the fine balance between membrane kinetics and axon geometry, local changes in membrane properties, such as those caused by synaptic activity, can be expected to have a strong influence on the behaviour of stochastic spike trains at regions of changing axonal geometry.

Action Potentials↗
PubMed2001

The effect of tissue-specific growth patterns of target stem cells on the spectrum of tumours resulting from multistage tumorigenesis.

A multistage mathematical model of tumorigenesis has been developed to explore the effects of target cell growth pattern on the proportions of tumours deriving from different tissues (the tumour spectrum). Analytical modelling techniques have shown that the effect of the target cell growth pattern on the tumour spectrum also depends on the number of stages (gene mutations) necessary for malignant change in cells of each tissue type. This suggests the existence of temporal "windows of opportunity" for tumours of different types in relation to stage number and growth kinetics. Models of this kind are applicable to cancer-prone transgenic (e.g. p53 deficient) mice, where homozygotes and heterozygotes differ in one carcinogenic stage, and differ also in the spectrum of tumours observed. Generally, tumours deriving from target stem cells which are developmentally short-lived will arise more frequently in homozygotes than heterozygotes. Such models may also be applicable to human syndromes (e.g. Li-Fraumeni) in which susceptibility to cancer is inherited.

Animals↗
PubMed2001

Equivalence transformations for dendritic Y-junctions: a new definition of dendritic sub-unit.

A sequence of equivalence transformations is used to represent the mathematical model of a simply branched neuron with non-homogeneous membrane properties and non-uniform geometry by an entirely equivalent model of an unbranched structure. The analysis indicates how neuronal morphology, in combination with its biophysical properties, shapes neuronal output in response to current input. The equivalence transformations described here reveal the types of operations that are likely to feature in the analysis of complex multi-branched structures, neuronal or otherwise. These transformations provide a new definition of dendritic sub-unit and a basis of a mechanism for characterising local and non-local signal processing within dendritic structures. It is anticipated that the capacity to transform biological neurons into an equivalent unbranched structure will make an important contribution to the understanding of the functional role of neuron geometry as well as to the construction of silicon neurons with realistic biological properties.

Dendrites↗
PubMed2001

Dendritic subunits determined by dendritic morphology.

A theoretical framework is presented in which arbitrarily branched dendritic structures with nonhomogeneous membrane properties and nonuniform geometry can be transformed into an equivalent unbranched structure (equivalent cable). Rall's equivalent cylinder is seen to be one part of the equivalent cable in the special case of dendrites satisfying the Rall criteria. The relation between the branched dendrite and its equivalent unbranched representation is uniquely defined by an invertible mapping that connects configurations of inputs on the branched structure with those on the unbranched structure, and conversely. This mapping provides a new definition of dendritic subunit and provides a mechanism for characterizing local and nonlocal signal processing within dendritic structures.

Animals↗
PubMed2001

Radiation carcinogenesis modelling for risk of treatment-related second tumours following radiotherapy.

Radiobiological modelling of the risk of radiation-induced tumours following high dose radiation implies a general form for the dose-response relationship. Generally, risk will rise with radiation dose at low doses, reach a maximum value and then decline with further increase in dose. The magnitude of risk and the dose at which this risk is maximum are strongly dependent on the kinetics of repopulation by surviving normal and mutant cells and on genetic factors likely to differ between tissues and between individuals. The most reliable way to reduce the risk of second tumours is to reduce radiation dose further at sites where the dose is already low. These sites are usually distant from the primary treatment volume. For illustrative purposes, we have compared the predicted relative risks of second tumours at "distant sites" for treatment plans giving similar dose distributions (dose volume histograms) at the primary site. We suggest that dose reduction to distant sites could be of significant benefit in reducing the risk of second tumours. Further improvement will require more detailed knowledge of the radiation sensitivities and mutagenicities, together with the repopulation kinetics of the various cell lineages within the treatment volume.

Cell Death↗
PubMed2000

The dose-response relationship for cancer incidence in a two-stage radiation carcinogenesis model incorporating cellular repopulation.

PURPOSE: To investigate the role of cellular repopulation in the dose-response relationship for radiation carcinogenesis resulting from high doses of radiation. METHOD: A two-stage mathematical model of radiation carcinogenesis was developed and used to explore the effects of differing assumptions about repopulation by surviving normal stem cells and by one-stage mutants. RESULTS: Characteristically, cancer incidence at any fixed time after irradiation increases with radiation dose, reaches a peak and then declines with dose (the decline reflecting radiation cell-killing). The optimal dose for cancer incidence, and the incidence level at this dose, are strongly influenced by repopulation kinetics. If repopulation does not occur, or is impaired owing to radiation damage to tissues, the highest value of cancer incidence is reduced, and this value occurs at a lower dose than if repopulation had been complete. A similar result is found if repopulation by one-stage mutants is impaired relative to unmutated cells, or if tissue recovery is assisted by immigration of unirradiated cells. CONCLUSIONS: Differing repopulation kinetics can account for differing dose-response relationships after large doses of radiation. These findings are relevant to the occurrence of 'second tumours' following radiotherapy and to the interaction of radiation with other agents.

Algorithms↗
PubMed2000

Gender bias in self-report personality disorder inventories.

There has been considerable controversy and research regarding gender biases in the diagnosis of personality disorders, but few studies have explored whether personality disorder self-report inventories might contain gender biases. The current study investigated whether items from three commonly used inventories evidence a potential for gender bias. Subjects were from outpatient mental health clinics. Items were considered gender biased if they exhibited gender differences and failed to correlate with or, more importantly, correlated negatively with dysfunction. Thirty-eight items evidenced potential bias, the majority of which were from Narcissistic scales. The implications of the results for the clinical assessment of purportedly maladaptive personality traits and for the construction of personality disorder scales are discussed.

Adult↗
PubMed1999

Responses to constant work exercise in patients with chronic heart failure.

OBJECTIVE: To describe the kinetics of metabolic gas exchange at the onset and offset of low level, constant work exercise in patients with chronic heart failure. SETTING: Tertiary referral centre for cardiology. PATIENTS: 10 patients with chronic heart failure and 10 age matched controls. METHODS: Each subject undertook maximum incremental exercise testing with metabolic gas exchange measurements, and a fixed load exercise test at 25 watts with metabolic gas exchange measurements before, during, and after the test. A monoexponential curve was fitted to the data to describe the kinetics of gas exchange at onset and offset of fixed load exercise. OUTCOME MEASURES: Peak oxygen consumption; time constants of onset and offset for metabolic gas exchange variables during constant load exercise. RESULTS: Peak oxygen consumption (mean (SD)) was higher in controls (26.1 (4.3) v 15.3 (5.3) ml/kg/min; p < 0.001) than in heart failure patients. Oxygen consumption during steady state was the same in both groups (9.2 (1.8) ml/kg/min in controls v 8.6 (1.6) in patients). The time constant of onset was the same in each group, but the time constant of offset was longer in patients (1.29 (0.14) v 0.82 (0.07); p < 0.005). There was a relation between peak oxygen consumption and time constant of offset (R = 0.56; p < 0.001). CONCLUSIONS: The dynamics of gas exchange at the onset of low level exercise are normal in heart failure, but the recovery is delayed. The delay is related to the reduction in exercise capacity. A patient may spend a greater portion of the day recovering from exercise, and may not begin the next bout from a position of true recovery, perhaps contributing to the sensation of fatigue.

Aged↗
PubMed1998

Stochastic modelling of tumorigenesis in p53 deficient mice.

Stochastic models of tumorigenesis have been developed to investigate the implications of experimental data on tumour induction in wild-type and p53-deficient mice for tumorigenesis mechanisms. Conventional multistage models in which inactivation of each p53 allele represents a distinct stage predict excessively large numbers of tumours in p53-deficient genotypes, allowing this category of model to be rejected. Multistage multipath models, in which a p53-mediated pathway co-exists with one or more p53-independent pathways, are consistent with the data, although these models require unknown pathways and do not enable age-specific curves of tumour appearance to be computed. An alternative model that fits the data is the 'multigate' model in which tumorigenesis results from a small number of gate-pass (enabling) events independently of p53 status. The role of p53 inactivation is as a rate modifier that accelerates the gate-pass events. This model implies that wild-type p53 acts as a 'caretaker' to maintain genetic uniformity in cell populations, and that p53 inactivation increases the probability of occurrence of a viable cellular mutant by a factor of about ten. The multigate model predicts a relationship between the time pattern of tumour occurrence and tumour genotype that should be experimentally testable. Stochastic modelling may help to distinguish 'gatekeeper' and 'caretaker' genes in other tumorigenic pathays.

Animals↗
PubMed1997

Modeling the lifespan of human T lymphocyte subsets.

T lymphocytes may be classified as naive or memory cells, depending on whether they possess immunological memory. The central tenet of this work is that memory lymphocytes revert to naive lymphocytes in vivo. This phenomenon is modeled by a mechanism qualitatively similar to Demoivre's law of human mortality. Additionally, both lymphocyte subsets undergo decay. Model parameters and their standard errors are estimated by maximizing a likelihood function constructed by Kalman filtering of the experimental data on the assumption that it is contaminated by measurement noise of constant relative error.

Cell Death↗
PubMed1997

A two-stage model for childhood acute lymphoblastic leukemia: application to hereditary and nonhereditary leukemogenesis.

A differential equation model is developed to represent a two-stage mutational process leading to childhood acute lymphoblastic leukemia (ALL). Leukemogenesis is modeled as transformation of target stem cells that initially grow rapidly in the embryo but plateau and then decline in postnatal childhood. Inheritance of the first of two leukemogenic mutations is allowed as a possibility in a small minority of leukemic patients who would characteristically develop leukemia at an early age. The model is shown to be capable of providing good fits to incidence data for childhood ALL; these fits allow estimation of some parameters of the model. The analysis shows that individuals inheriting one of the two mutations necessary for ALL would be likely to experience "multiclonal leukemogenesis"; that is, the parallel development of several leukemic clones arising from multiple independent leukemic events. The model suggests that between two and ten such clones would typically have developed in such individuals by the time of diagnosis. The main conclusions of the deterministic investigation were confirmed by stochastic modeling. The existence of multiclonal leukemogenesis is in principle testable by molecular biological methods (clonality analysis) that rely on the random inactivation of one of two X-chromosomes in normal female subjects. It is expected that the mathematical methods developed here will also be useful for more general (N-stage) models of malignant transformation of stem cell populations undergoing growth or decline.

Aging↗
PubMed1995

Sex and gender bias in self-report personality disorder inventories: item analysis of the MCMI-II, MMPI, and PDQ-R.

There has been considerable controversy and research regarding sex bias in the diagnosis of personality disorders, but little has involved self-report inventories. Thus this study investigated items from the Millon Clinical Multiaxial Inventory-II (Millon, 1987), the Minnesota Multiphasic Personality Inventory (Morey, Waugh, & Blashfield, 1985), and the Personality Diagnostic Questionnaire-Revised (Hyler & Rieder, 1987). Subjects (N = 189) completed the Histrionic, Dependent, Antisocial, and Narcissistic scales from these inventories, along with the Bem Sex Role Inventory (Bem, 1974) and the Symptom Checklist-90-Revised (Derogatis, 1977). Items were considered to evidence sex or gender bias if they (a) failed to correlate with dysfunction and (b) exhibited sex or gender role differences. At least 13 items evidenced sex bias (76 items using a more liberal threshold). The majority were from Narcissistic scales; few Histrionic items evidenced sex or gender bias. Implications with respect to sex-bias assessment and item construction are discussed.

Journal Article↗