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Specific features of hard palate mucosa relief are described, major elements of the relief, their variants and location shown. A mathematical model of hard palate relief is suggested. The possibility of using the scheme of hard palate relief structures as an additional criterion in forensic medical personal identification is statistically proved.
This study is concerned with the construction of a mathematical model of mandibular movement on the Hanau articulator and a complete denture occlusion simulation system (CDOSS) in the field of dental restoration. On the basis of the theory of spatial mechanisms, degrees of freedom in the kinematic chain of the Hanau articulator are analysed, and a hypothesis of constraints is presented to obtain constrained motion. Then, a series of mathematical expressions are derived to describe the three dimensional mandibular movement on the Hanau articulator. By adopting techniques and tools such as laser scanning, computer graphics, and computer databases, a 3D digitized model of complete denture is reconstructed, and a CDOSS is developed. With the aid of this software, the visualization and diagnosis of mandibular movement can be easily realized. One edentulous case discussed in this study shows that CDOSS provides a useful tool to deal with the functional aspects of occlusal morphology in a diagnostic and therapeutic sense.
The results of cytogenetic analysis of unfertilized human oocytes in an in-vitro fertilization programme are to a large extent influenced by the methodology used. Exact conclusions cannot be drawn due to technical and interpretational errors. A mathematical model was constructed, therefore, to estimate the weight of these errors and to calculate the exact frequency of first meiotic non-disjunction in IVF oocytes. Of 246 prepared oocytes only 105 could be karyotyped exactly. Using the classical method of calculation, an aneuploidy frequency of 39% was obtained. By applying the maximum likelihood method a correlation between the frequency of first meiotic non-disjunction and the interpretational error level was found. Loss of chromosomes by anaphase lagging seemed to be undetectable, but the probability of chromosome loss due to fixation and unhomogeneous spreading was found to be 20%. Accepting an error level of 10-20%, the true non-disjunction frequency expected should range between 20 and 40%. This model yields a standard curve which can offer a basis for comparison of results obtained in different studies.
Using experimental data of AgI sol and poly(2-methyl-5-vinylpyridine) chloride, we show that there is good agreement between the developed mathematical model of suspension flocculation by polyelectrolytes and the experimental data. The rate constants of bridging and nonbridging aggregation of particles and of floc breakup, as well as their ratios, have been determined. It has been shown that the role of the nonbridging mechanism, as compared with that of the bridging one, diminishes when molecular mass of polyelectrolyte increases from 1.4 x 10(5) to 9.3 x 10(5).
After a brief description of the main anatomical structures subserving the oculomotor responses during combined vestibular and optokinetic stimulations, a mathematical model is presented. With respect to a previous model by Schmid et al. (1980), a more accurate definition of the roles of the neural mechanisms involved in oculomotor control in different conditions of visual-vestibular interaction is given. The model is proved to be able to predict not only oculomotor responses, but also single unit average responses in the vestibular nuclei and in the vestibulo-cerebellum. Experimental data available in the literature on monkeys and cats are used for model validation.
The effect of luminal flow rate and peritubular pH on Na and K transport is investigated in a mathematical model of the rabbit cortical collecting tubule. The model is used to simulate a 0.4-cm segment of tubule comprised of principal cell, alpha- and beta-intercalated cells, and lateral interspace. Calculations produce luminal profiles of Na, K, Cl, HCO3, and phosphate, as well as of electrical potential and pH. Parameter sets are developed that permit representation of both unstimulated and deoxycorticosterone acetate-stimulated tubules. A series of simulations is performed in which initial luminal flow rate is varied over the range of values between 0.1 and 30 nl/min. A marked flow-dependent enhancement of Na reabsorption and K secretion is seen, especially at lower flows, while Cl and HCO3 transport remain relatively constant. In experimental studies, it has been observed that metabolic alkalosis stimulates and metabolic acidosis inhibits K secretion, while leaving Na transport relatively unaffected [B. A. Stanton and G. Giebisch. Am. J. Physiol. 242 (Renal Fluid Electrolyte Physiol. 11): F544-F551, 1982; K. Tabei, S. Muto, Y. Ando, Y. Sakairi, and Y. Asano. J. Am. Soc. Nephrol. 1: 693, 1990; and K. Tabei, S. Muto, H. Furuya, and Y. Asano. J. Am. Soc. Nephrol. 2: 752, 1991]. Model calculations indicate that, when ion permeabilities are fixed and not dependent on pH, the impact of peritubular HCO3 on K secretion cannot be simulated. When junctional Cl permeability decreases with increasing interspace pH (E. M. Wright and J. M. Diamond. Biochim. Biophys. Acta 163: 57-74, 1968) in the model, there is a marked stimulation of K secretion with alkalosis and inhibition with acidosis. Furthermore, inclusion of a pH-dependent apical Na permeability [L. G. Palmer and G. Frindt. Am. J. Physiol. 253 (Renal Fluid Electrolyte Physiol. 22): F333-F339, 1987] that increases with increasing principal cell pH significantly reduces the change in Na+ reabsorption seen with the pH-dependent junctional Cl permeability alone. In these calculations, a pH-dependent apical K permeability [W. Wang, A. Schwab, and G. Giebisch. Am. J. Physiol. 259 (Renal Fluid Electrolyte Physiol. 28): F494-F502, 1990] that increases with increasing principal cell pH shows relatively little impact on K secretion.
A two-chamber mathematical model of 137Cs uptake and removal from the body of cattle chronically consuming contaminated fodder has been developed; the model takes into account age dependence of radionuclide absorption from the gastro-intestinal tract. The model parameters were taken from the experiment on calves with chronic peroral uptake of contaminated fodder. In accordance with the model and experiment, 137Cs transfer factor to the muscular tissue one month after birth reaches a maximum value of 56% of the daily uptake per 1 kg of the tissue. By the model, the equilibrium processes of uptake and removal set in two years after the calves birth. The equilibrium TF for muscles in adults approximates 2.8% of the daily uptake per 1 kg tissue. Because of 137Cs absorption from the gastrointestinal tract changes with age, doses of internal exposure of calves over the first two years will be about 5 times higher than doses for any one of the two subsequent years.
A new generalized conception of an organism is given. Based on this conception, a new mathematical model of ontogenesis of an individual and the survival of the age cohort of population was proposed. By using real data on the dynamics of the survival of the age cohort of population, the model enables one to determine the parameters characterizing the relationship man-environment in the context of survival and calculate the dynamics (from birth to death) of the model variables of the state of the organism.
The authors assess the functional potentialities of a mathematical model of transport of labeled colloids in the body. Some additions to and modifications of the model were analyzed. They made it possible to get 4 diagnostically important indices: the rate of colloid excretion from the vascular bed, the rate phagocytosis, RES volume, and the rate of RP accumulation by the liver. Besides, the authors presented the results of a computerized experiment for the determination of maintenance characteristics of a program developed for computer. The iteration algorithm for parameter identification based on a method of linearization of minimized function, was used in the program. They also formulated recommendations for a choice of arbitrary components of a calculation procedure and the use of a method of barrier functions, developed as a result of prolonged maintenance of the program.
In order to describe spontaneous wave-like contractions of a single isolated cardiomyocyte a mathematical model is proposed, which relates this phenomenon to propagation of calcium ion concentration wave along the cell. Free diffusion of Ca2+ ions as well as their reversible binding to regulatory proteins in contractile apparatus, Ca2+ accumulation in sarcoplasmic reticulum, and Ca-induced Ca2+ release are included in the governing equations. The model agrees with some observations. It predicts also some effects which may by a subject of future experimental research.
The SPLEN-K (INZOMA) computing system, based on the mathematical model of a heterogeneous elastic body with linear plastic reinforcement helps estimate the design of coated dentures with due consideration for the individual features of the jaws and teeth, articulation, and occlusion. The open module type of this system permits its modifications and improvements, allows introduction of individual changes in the planned denture design, helps rapidly estimate the changes in the strained-deformed state and assess the correctness of the result from the computed data. The reliability of estimations was assessed in special tests. Practical results of theoretical studies are adequate to clinical and experimental data.
OBJECTIVE: The objective of the study was to improve with respect to accuracy and smoothness the three-dimensional model of the spinal midline which has been calculated from rasterstereographic back surface data. DESIGN: A new mathematical model using frequency-modulated sine curves has been applied to existing rasterstereographic and radiographic data in an in vivo study. BACKGROUND: Analysis of back shape (measured by rasterstereography) enables a three-dimensional model of the spinal midline to be calculated. The model is based on the so-called symmetry line which coincides approximately with the line of the spinous processes. In addition the surface rotation on the symmetry line is taken as an estimate for vertebral axial rotation in scoliosis. METHODS: Four hundred and seventy-eight pairs of radiographs and rasterstereographs of scoliotic patients have been evaluated and compared using the new model. The radiographs were digitized manually, delivering curves of lateral deviation and vertebral rotation. Analysis of back shape from the rasterstereographs delivers a three-dimensional model of the spinal midline, the frontal projection of which is to be compared with the radiographic curve. Likewise, vertebral rotation and surface rotation are compared. RESULTS: The use of frequency-modulated sine curves improved the results as compared to the existing procedure with respect to prediction accuracy of lateral deviation (typically from sigma(x) = 4.6 mm to sigma(x) = 4.0 mm, P < 10(-10)). The prediction of axial rotation was not significantly improved (sigma(varrho) thick approximate 3.8 degrees ). In addition, the smoothness of the curves is considerably improved. The prediction accuracy proved to be independent of the scoliosis type as represented by apex height (r = -0.09 ellipsis + 0.03). CONCLUSION: The use of frequency-modulated sine curves improves significantly the accuracy and smoothness of the spinal model curves.
Most conventional digesters used for animal wastewater treatment include continuously stirred-tank reactors. While imperfect mixing patterns are more common than ideal ones in real reactors, anaerobic digestion models often assume complete mixing conditions. Therefore, their applicability appears to be limited. In this study, a mathematical model for anaerobic digestion of cattle manure was developed to describe the dynamic behavior of non-ideal mixing continuous flow reactors. The microbial kinetic model includes an enzymatic hydrolysis step and four microbial growth steps, together with the effects of substrate inhibition, pH and thermodynamic considerations. The biokinetic expressions were linked to a simple two-region liquid mixing model, which considered the reactor volume in two separate sections, the flow-through and the retention regions. Deviations from an ideal completely mixed regime were represented by changing the relative volume of the flow-through region (a) and the ratio of the internal exchange flow rate to the feed flow rate (b). The effects of the hydraulic retention time, the composition of feed, the initial conditions of the reactor and the degree of mixing on process performance can be evaluated by the dynamic model. The simulation results under different conditions showed that deviations from the ideal mixing regime decreased the methane yield and resulted in a reduced performance of the anaerobic reactors. The evaluation of the impact of the characteristic mixing parameters (a) and (b) on the anaerobic digestion of cattle manure showed that both liquid mixing parameters had significant effects on reactor performance.
Transcranial doppler studies show that microscopic cerebral artery air emboli (CAAE) are present in virtually all patients undergoing cardiac surgery. Massive cerebral arterial air embolism is rare. If it occurs, hyperbaric oxygen therapy (HBO) is recommended as soon as surgery is completed. We used a mathematical model to predict the absorption time of CAAE, assuming that the volumes of clinically relevant CAAE vary from 10(-7) to at least 10(-1) mL. Absorption times are predicted to be at least 40 h during oxygenation using breathing gas mixtures of fraction of inspired oxygen approximately equal to 40%. When CAAE are large enough to be detected by computerized tomography, absorption times are calculated to be at least 15 h. Decreases in cerebral blood flow caused by the CAAE would make the absorption even slower. Our analysis suggests that if the diagnosis of massive CAAE is suspected, computerized tomography should be performed, and consideration should be given to HBO therapy if the CAAE are large enough to be visualized, even if patient transfer to a HBO facility will require several hours.
In this paper, a simple mathematical model developed in H.A. Levine, B.D. Sleeman, M. Nilsen-Hamilton [J. Math. Biol., in press] to describe the initiation of capillary formation in tumor angiogenesis is extended to include the roles of pericytes and macrophages in regulating angiogenesis. The model also allows for the presence of anti-angiogenic (angiostatic) factors. The model is based on the observation that angiostatin can prevent the degradation of fibronectin in the basal lamina by inhibiting the catalytic action of active proteolytic enzyme. That is, it is proposed that the inhibitor 'deactivates' the protease but that it does not reduce the over all concentration of the protease. It consequently explores the possibility of preventing neovascular capillaries from migrating through the extra-cellular matrix toward the tumor by inhibiting protease action. The model is based on the theory of reinforced random walks coupled with Michaelis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived angiogenic factors into proteolytic enzyme which in turn degrade the basal lamina. A simple catalytic reaction is proposed for the degradation of the basal lamina by the active proteases. A mechanism, in which the angiostatin acts as a protease inhibitor is discussed which has been substantiated experimentally. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase.
The authors present a physico-mathematical model of a human femur, under "monopodal" static constraints, using the finite elements method. Three examples are considered: a normal femur, a femur implanted with a short-stem prosthesis without cement, and a femur implanted with a long-stem prosthesis without cement. The lines of isoconstraints were compared in the three examples, as well as the main constraints (direction and intensity). From the results, the authors suggest that a prosthesis made of titanium is currently best even though its YOUNG's modulus differs from that of the bone. A prosthesis of composite material is possible in the future. While the intensity of the constraints is nearly the same at the level of the epiphysis for the short-stem and long-stem prosthesis it seems that the short-stem prosthesis fitted accurately without cement is the best solution. The introduction of a hip prosthesis modifies the normal curve of the loaded femur by changing the center of this curve.
This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue (phase), together with the physical stresses in each component. The theory requires constitutive relations to specify the material properties of each phase, and also requires relations to specify the stresses developed due to mechanical interactions, both within each phase and between different phases. An application of the theory is given to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. Stability analysis techniques show that the interplay of the forces between the tissue constituents results in two different regimes: either the cells form aggregates or disperse through the scaffold.
The early development of solid tumours has been extensively studied, both experimentally via the multicellular spheroid assay, and theoretically using mathematical modelling. The vast majority of previous models apply specifically to multicell spheroids, which have a characteristic structure of a proliferating rim and a necrotic core, separated by a band of quiescent cells. Many previous models represent these as discrete layers, separated by moving boundaries. Here, the authors develop a new model, formulated in terms of continuum densities of proliferating, quiescent and necrotic cells, together with a generic nutrient/growth factor. The model is oriented towards an in vivo rather than in vitro setting, and crucially allows for nutrient supply from underlying tissue, which will arise in the two-dimensional setting of a tumour growing within an epithelium. In addition, the model involves a new representation of cell movement, which reflects contact inhibition of migration. Model solutions are able to reproduce the classic three layer structure familiar from multicellular spheroids, but also show that new behaviour can occur as a result of the nutrient supply from underlying tissue. The authors analyse these different solution types by approximate solution of the travelling wave equations, enabling a detailed classification of wave front solutions.