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Model-free association analysis of a rare disease.

Model-free methods of testing for association of a disease with alleles at a marker locus were used to analyze simulated data for a rare disease locus and 360 marker loci distributed at 2 cM intervals along six chromosomes. After adjustment for multiple tests, there was no evidence of significant heterogeneity of parental allele frequencies between a sample of parents with at least one affected child and a sample of parents with no affected children. Several significant deviations from Hardy-Weinberg equilibrium were detected after Bonferroni correction but these were Type I errors. After adjusting for multiple tests, the model-free test for association detected significant associations of alleles at two loci with the disease. These associations were in fact part of the generating model for the simulated data. However, these methods were unable to detect two other major loci contributing to the disease since these loci were not associated with any of the marker loci.

Alleles

A mathematical model describing the generation of oxygen radicals in mitochondria during ischemia-reperfusion.

A mathematical model for the generation of free radicals by mitochondria in ischemia-reperfusion is proposed. Computations show that normally two stable equilibrium states exist: the intact state, and the state characterized by damage to mitochondrial structures and a high rate of radical formation. Transition from one state to another occurs after hypoxia of a certain degree of severity and duration. The model also describes a number of phenomena observed during development of reperfusion injuries and drug therapy.

Free Radicals

Fabrication of titanium implant-retained restorations with nontraditional machining techniques.

Traditional laboratory techniques are being supplemented by modern precision technologies to solve complex restorative problems. Electrical discharge machining combined with laser scanning and computer aided design-computer aided manufacturing can create very precise restorations without the lost wax method. A laser scanner is used to create a three-dimensional polyline data model that can then be converted into a stereolithography file format for output to a stereolithography apparatus or other rapid prototyping device. A stereolithography-generated model is used to create an electric discharge machining electrode via copper electroforming. This electrode is used to machine dental restorations from an ingot of titanium, bypassing the conventional lost wax casting process. Retaining screw access holes are machined using conventional drilling procedures, but could be accomplished with electric discharge machining if desired. Other rapid prototyping technologies are briefly discussed.

Computer-Aided Design

A model for the generation of movements requiring endpoint precision.

A model is proposed in which movement accuracy is regulated by means of corrective actions taken at discrete intervals throughout the course of a movement. A movement, as represented by its tangential velocity profile, cna be decomposed into a series of one or more submovements. Each submovement consists of a prototype velocity profile which can be scaled in magnitude and duration. For planar two-joint movements, we demonstrate that these submovements can be mathematically represented either in terms of velocity profiles or in terms of the underlying joint torque profiles. In either case, the submovements superimpose linearly to produce the composite movement. The model provides a very good fit to tangential velocity profiles recorded from human subjects during three-dimensional arm movements with constraints on accuracy and speed. The model assumes that when a submovement is present, its onset is associated with a change in the direction of the hand path and/or a zero crossing or inflection in at least one of the components of the velocity vector. The model is consistent with a strategy in which precision is achieved by periodic discrete actions which redirect the moving arm in order to bring the hand closer to the target. Since submovements were also observed in slow movements where accuracy constraints had been relaxed, we hypothesize that the strategy of superimposing a series of submovements to make one composite movement may be a general one. We suggest that it would be particularly appropriate for the process of learning a new motor skill.

Adult

The within-host cellular dynamics of bloodstage malaria: theoretical and experimental studies.

The properties of a mathematical model of bloodstage infection with a single strain of malaria were investigated. Analysing the cell population dynamics in the absence of a host immune response we demonstrate a relationship between host and parasite parameters that defines a criterion for the successful invasion and persistence of the parasite. Important parameters are the rates of merozoite production and death and those of erythrocyte production, death and invasion. We present data from experiments designed to evaluate the erythrocyte invasion rate in a rodent malaria system. The model generates patterns of parasitaemia in good qualitative agreement with those seen in Plasmodium berghei infections. The sole force behind the rise and fall in parasitaemia in the model without immunity is the density of susceptible erythrocytes, suggesting that resource availability is an important determinant of the initial pattern of infection in vivo. When we incorporate a simple immune response into the model we find that immunity against the infected cell is much more effective at suppressing parasite abundance than immunity against the merozoite. Simulations reveal oscillating temporal patterns of parasite abundance similar to P. c. chabaudi infection, challenging the concept that antigenic variation is the sole mechanism behind recrudescing patterns of infection.

Animals

Theoretical considerations in relation to the treatment of brain tumours by means of local hyperthermia generated by ultrasound fields.

Brain tumours comprise a significant fraction of all tumours in the human body. Despite the development of technology in clinical oncology, these tumours still present a difficult challenge. The margin between destruction of tumour and damage to normal tissue is narrow in the brain. The price paid for producing tissue damage outside the tumour is high in terms of quality of survival. Results of many experiments with ultrasound hyperthermia show that this new technique is successful for treating certain types of malignant tumours. In the case of brain tumours, applying focused fields should have the advantage of selectively destroying the tumour and leaving surrounding tissues intact. Previous attempts at applying ultrasound to the field of neurosurgery are reviewed. Those factors which have effects on the generation of thermal fields in brain tissues are considered in relation to the possible treatment of human brain tumours. Calculated thermal fields in a 2-D brain model generated by an applicator built in our laboratory are also presented.

Brain

Effects of circulating renin substrate on renal function in isolated perfused rat kidney.

The effects of two different amounts of pure rat angiotensinogen were investigated in a closed circuit isolated perfused rat kidney. In response to angiotensinogen, circulating levels of angiotensin I (AI) and angiotensin II (AII) immunoreactive materials were found to increase in a time and dose-dependent manner. Vasoconstrictor and renin inhibitory effects were observed in parallel with the increase in AII. Glomerular filtration rate decreased after administration of angiotensinogen to a greater extent than renal flow and filtration fraction. The characterization by high performance liquid chromatography of peptides generated showed the liberation of AI, des-Asp1AI, AII and des-Asp1AII (AIII). These findings demonstrate that administration of angiotensinogen in an isolated perfused kidney model generates AI and that renal converting enzyme and aminopeptidases are able to convert AI to AII, AI to des-Asp1AI, and des-Asp1AI and/or AII to AIII. Changes in circulating level of angiotensinogen influence the activity of the renin-angiotensin system and, therefore, renal function.

Angiotensin I

On the effect of the intracellular calcium-sensitive K+ channel in the bursting pancreatic beta-cell.

Based on the observation that the calcium-activated K+ channel in the pancreatic islet cells can also be activated by the membrane potential, we have formulated a mathematical model for the electrical activity in the pancreatic beta-cell. Our model contains two types of ionic channels, which are active above the subthreshold glucose concentration in the limit-cycle region: a Ca2+-activated, voltage-gated K+ channel and voltage-gated Ca2+ channel. Numerical simulation of the model generates bursts of electrical activity in response to a variation of kCa, the rate constant for sequestration of intracellular calcium ions. The period and duration of the bursts in response to kCa are in good agreement with experiment. The model predicts that a combined spike and burst pattern can be created using only single species of inward and outward currents, the inactivation kinetics (i.e., h) in the inward current is not a necessary condition for the generation of the pattern, and a given pattern or intensity of electrical activity may produce different levels of intracellular Ca2+ depending on the set of certain electrical parameters.

Animals

A molecular thermodynamic approach to predict the secondary structure of homopolypeptides in aqueous systems.

Under physiological conditions, many polypeptide chains spontaneously fold into discrete and tightly packed three-dimensional structures. The folded polypeptide chain conformation is believed to represent a minimum Gibbs energy of the system, governed by the weak interactions that operate between the amino acid residues and between the residues and the solvent. A semiempirical molecular thermodynamic model is proposed to represent the Gibbs energy of folding of aqueous homopolypeptide systems. The model takes into consideration both the entropy contribution and the enthalpy contribution of folding homopolypeptide chains in aqueous solutions. The entropy contribution is derived from the Flory-Huggins expression for the entropy of mixing. It accounts for the entropy loss in folding a random-coiled polypeptide chain into a specific polypeptide conformation. The enthalpy contribution is derived from a molecular segment-based Non-Random Two Liquid (NRTL) local composition model [H. Renon and J. M. Prausnitz (1968) AIChE J., Vol. 14, pp. 135-142; C.-C. Chen and L. B. Evans (1986) AIChE J., Vol. 32, pp. 444-454], which takes into consideration of the residue-residue, residue-solvent, and solvent-solvent binary physical interactions along with the local compositions of amino acid residues in aqueous homopolypeptides. The UNIFAC group contribution method [A. Fredenslund, R. L. Jones, and J. M. Prausnitz (1975) AIChE J., 21, 1086-1099; A. Fredenslund, J. Gmehling, and P. Rasmussen (1977) Vapor-Liquid Equilibrium Using UNIFAC, Elsevier Scientific Publishing Company, Amsterdam], developed originally to estimate the excess Gibbs energy of solutions of small molecules, was used to estimate the NRTL binary interaction parameters. The model yields a hydrophobicity scale for the 20 amino acid side chains, which compares favorably with established scales [Y. Nozaki and C. Tanford (1971) Journal of Biological Chemistry, Vol. 46, pp. 2211-2217; E. B. Leodidis and T. A. Hatton (1990) Journal of Physical Chemistry, Vol. 94, pp. 6411-6420]. In addition, the model generates qualitatively correct thermodynamic constants and it accurately predicts thermodynamically favorable folding of a number of aqueous homopolypeptides from random-coiled states into alpha-helices. The model further facilitates estimation of the Zimm-Bragg helix growth parameter s and the nucleation parameter sigma for amino acid residues [B. H. Zimm and J. K. Bragg (1959) Journal of Chemical Physics, Vol. 31, pp. 526-535]. The calculated values of the two parameters fall into the ranges suggested by Zimm and Bragg.

Models, Molecular

Optimisation of transcutaneous cardiac pacing by three-dimensional finite element modelling of the human thorax.

The goal of the study is to determine by finite element analysis (FE) the optimal electrode placement, size and electrolyte resistivity that minimise the pain experienced by patients during successful transcutaneous cardiac pacing (TCP). The three-dimensional FE model generated for this purpose has 55,388 nodes, 50,913 hexahedral elements and simulated 16 different organs and tissues, as well as the properties of the electrolyte. The model uses a non-uniform mesh with an average spatial resolution of 0.8 cm in all three dimensions. To validate this model, the voltage across 3 cm2 Ag-AgCl electrodes is measured when currents of 5 mA at 50 kHz are injected into a subject's thorax through the same electrodes. For the same electrode placements and sizes and the same injected current, the FE analysis produced results in good agreement with the experimental data. The optimisation analysis tested seven different electrode placements, five different electrode sizes and six different electrolyte resistivities. The analysis indicates that the anterior-posterior electrode placement, electrode sizes of about 90 cm2 and electrolytes with resistivity of about 800 omega.cm yield the most uniform current distribution through the skin, thus having the best chances to minimise the pain delivered to the patient during successful TCP. The anterior-anterior electrode placement is the second most efficient.

Cardiac Pacing, Artificial

[Geometrical modeling of the spine and the thorax for the biomechanical analysis of scoliotic deformities using the finite element method].

In order to study the biomechanical behavior of the whole human spine and thorax, as well as orthopaedic treatment effects, a new generation model is proposed, which includes a precise functional representation of the posterior part of the spine, while respecting computational capabilities. This paper presents the geometrical aspects of this model. The latter is built using an hybrid method which combines steroradiographic 3-D reconstructions of the spine and thorax [1] to serial CT scan 3-D reconstructions of typical human vertebrae and sternum [4] and published morphometric data of ribs [2, 3]. These anatomical structures were deformed in order to fit as well as possible the personalized data of scoliotic patients using geometrical transformations as well as interpolation or extrapolation techniques. In the posterior part, articular facets are modelled and parameterized as elementary surface shapes (plane, cylinder, sphere). For the articular facet geometry of a given normal subject, results revealed that the zygapophyseal facets are better represented by planes for T1 to T11 and by portions of cylinders for T12 to L5, which is in concordance with the literature [5, 6]. Evaluation of this modelling approach was done on 2 cadaveric vertebral segments. Parametric data obtained from the model were compared to precise measurements done on the vertebrae using a 3-D digitizer, and concordance was found. These personalized geometric informations were then used to build a finite element model [7], which will be useful to study scoliotic deformities as well as personalized orthopaedic treatments.

Humans

Extending the multiple indicator dilution method to include slow intracellular diffusion.

The traditional multiple indicator dilution (MID) method is extended to incorporate cytoplasmic concentration gradients due to slow intracellular diffusion of the permeable molecule. The new model is governed by a system of partial differential equations that are solved using Laplace transformation. An analysis of the transformed solution shows that the traditional MID method is a special case of the extended model. We then use simulation analysis to show that the traditional MID model and the new diffusion model generate similar outflow curves. However, when the traditional MID equations were used to analyze outflow curves generated using a system in which intracellular diffusion is slow compared to other transport processes, the recovered rate constants for the transmembrane and excretion processes were incorrect. The diffusion model permits estimation of the rate of intracellular transport of amphipathic molecules from suitable indicator dilution data.

Animals

A dimension reduction framework for understanding cortical maps.

We argue that cortical maps, such as those for ocular dominance, orientation and retinotopic position in primary visual cortex, can be understood in terms of dimension-reducing mappings from many-dimensional parameter spaces to the surface of the cortex. The goal of these mappings is to preserve as far as possible neighbourhood relations in parameter space so that local computations in parameter space can be performed locally in the cortex. We have found that, in a simple case, certain self-organizing models generate maps that are near-optimally local, in the sense that they come close to minimizing the neuronal wiring required for local operations. When these self-organizing models are applied to the task of simultaneously mapping retinotopic position and orientation, they produce maps with orientation vortices resembling those produced in primary visual cortex. This approach also yields a new prediction, which is that the mapping of position in visual cortex will be distorted in the orientation fracture zones.

Animals

Experimental verification of a mathematical model for pelleted growth of Streptomyces coelicolor A3(2) in submerged batch culture.

A published mathematical model for growth of pellets of filamentous microorganisms has been tested by comparison of model predictions with experimental data on growth of Streptomyces coelicolor in liquid batch culture. The original model considered the classification of pellets into a range of size classes. Growth resulted in movement of pellets to classes of increasing size, while shear forces produced mycelial fragments which entered the smallest size class, from which they grew to form further pellets. This model did not correctly describe changes in pellet size distributions during growth and was therefore modified in two ways. In the first, new pellets were assumed to be formed by the break-up, by shear forces, of existing pellets into two pellets of equal size, rather than removal of small hyphal fragments from the pellet surface. The second modification assumed that the outer shell of active mycelial biomass had a density less than 1 g cm-3 and that hyphal density within this shell decreased with distance from the pellet centre. The modified model generated predictions which agreed closely with experimental data on biomass concentration, pellet size distribution, pellet number and pellet radius during batch growth, thereby supporting the assumptions on which the model was based. The model did not accurately describe final biomass concentration, through lack of consideration of autolysis of mycelia at the centre of larger pellets in which growth was limited by diffusion of nutrients. Attempts to incorporate autolysis into the model improved prediction of biomass concentration but were not based on sound biological assumptions and increased the complexity of the model. Further experimental work is required for accurate description of the effects of autolysis on pellet growth.

Models, Theoretical

Theory of rodent navigation based on interacting representations of space.

We present a computational theory of navigation in rodents based on interacting representations of place, head direction, and local view. An associated computer model is able to replicate a variety of behavioral and neurophysiological results from the rodent navigation literature. The theory and model generate predictions that are testable with current technologies.

Animals

Influence of parathyroid hormone and calcitonin on tissue zinc homeostasis in the rat.

Tissue zinc accumulation kinetics and compartmental analysis models were evaluated in thyroparathyroidectomized (TPTX) rats treated with parathyroid extract or calcitonin. The animals were injected with 65Zn and studied at multiple time intervals. SAAM-25 was utilized to generate models from the plasma specific activity decay curves. Calcitonin had a marked effect to decrease the fractional influx and efflux transfer coefficients in the model and inhibit tissue zinc accumulation in several, but not all, tissues. Parathyroid extract increased accumulation in all tissues studied, but had minimal effects on the model. It is concluded that parathyroid hormone acts nonspecifically and that calcitonin appears to have specific influences on zinc homeostasis.

Animals

Adoptive transfer of human lymphoid cells to severely immunodeficient mice: models for normal human immune function, autoimmunity, lymphomagenesis, and AIDS.

Though the development of human-to-mouse xenotransplant models is in its infancy, astonishing progress has been made in a short period of time. Two experimental applications have been developed: short-term transfer of human lymphocytes to generate models for autoimmunity and infectious diseases, and long-term engraftment of tissues with self-renewal potential. Human PBL-SCID mice have been used by multiple laboratories to study normal and autoimmune antibody responses, and have been shown to be readily infectable with HIV-1. SCID mice grafted with fetal tissue have been developed for studies of HIV-1 infection and its therapy as well as for studies of human hematopoietic cell differentiation. Human tumors appear to grow better in SCID mice than in nude mice, and hu-PBL-SCID mice can develop EBV-related B cell lymphoproliferative disease that resembles the immunoblastic lymphomas appearing in immunosuppressed transplant recipients. There is some evidence of mouse NK cells responding to the human xenograft, and of human T and B cells responding to mouse xenoantigens in these models, but these responses are not generally strong enough to have a major impact on human immune function. The use of these surrogate human models is expected to have a major impact on the understanding and treatment of human disease.

Acquired Immunodeficiency Syndrome

An assessment of critical anthropometric dimensions for predicting the fit of a half-mask respirator.

The purpose of this study was to determine if facial dimensions for a group of subjects were predictive of the fit factors measured while one brand of half-mask respirator was worn. Fit factors and 12 facial dimensions measured on 30 female and 38 male subjects were analyzed by correlation coefficients; weighted, multiple linear regression; and discriminant analysis. Data were analyzed for all subjects, gender subgroups, a race subgroup (whites only), and race/gender subgroups. Significant correlation coefficients with the log-transformed fit factors were found for four dimensions; four dimensions had significant coefficients in four or more multiple linear regression models. Only two dimensions had significant coefficients in four or more discriminant analysis models. Menton-subnasale (lower face) length was the only dimension included in all three of these groups. Gender-specific regression models had very high coefficient of determination values (R2 > 0.85). Discriminant analysis of the data for all subjects and race/gender subgroups found very good predictive scores for statistical software-generated models and menton-subnasale length alone; these scores were significantly better than those for the model with the respirator test panel dimensions (face length and lip width). These analyses found that facial dimensions were good predictors of respirator fit for those subjects wearing one brand of half-mask respirator. Lower face length was consistently indicated as being correlated or associated with fit. These results would indicate that dimensions other than those currently used may be more appropriate to define a half-mask respirator test panel.

Adult