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At least 1,261 records · Page 70Linked to original sources
PubMed1994

Mathematical model of TMA+ diffusion and prediction of light-dependent subretinal hydration in chick retina.

PURPOSE: To derive a mathematical model of TMA+ diffusion across the retina that can be used to estimate the amplitude and kinetics of the light-evoked increase in subretinal hydration and its effect on the concentration of other ions. METHODS: All experimental data were obtained in chick retina-pigment epithelium-choroid preparations as described in the accompanying paper. RESULTS: Diffusional properties of the retina were derived from the time course of [TMA+]o in the subretinal space (SRS) after changes in the retinal perfusate. Then, the SRS volume changes underlying the light-induced [TMA+]o response can be derived using a mathematical model of TMA+ diffusion. Complete retinal depth series of light-evoked [TMA+]o responses could be simulated by producing a corresponding expansion of the SRS. Volume changes inferred from the diffusion model were 2.2 to 3.8 times larger and more prolonged than could be derived directly from delta [TMA+]o. The model predicted up to a 20% peak increase in subretinal-space hydration during illumination. The effects of this volume increase on subretinal K+ and Ca2+ were estimated. These predictions were supported by inhibiting the volume increase with DIDS, which blocks retinal pigment epithelium basal membrane Cl- conductance. CONCLUSIONS: The primary source of light-evoked changes in extracellular TMA+ concentration recorded throughout the retina is an increase in hydration (volume) of the subretinal space. The response spreads to the inner retina by diffusion. Effects of TMA+ diffusion lead to large underestimates of the underlying volume changes. The light-evoked volume change alters the composition of the subretinal space and light-induced responses of other ions.

Animals↗
PubMedDate not supplied

Interrelation between Western type cancers and non-Western type cancers as regards their risk variations in time and space. V. Mathematical analysis of the environment-sensing signal transmission system in carcinogenesis.

The purpose of this study was to elucidate the nature of the control mechanism of human carcinogenesis by applying regression analysis technique to the world statistics of various human neoplasias. The information used in the present study covers 19 cancers in the tumor spectrum, 47 cancer registration areas in space, and the years 1978 to 1982 in time. The risk for each cancer was expressed in terms of the annual age-adjusted incidence rate (AAIR). Results obtained are as follows: 1) The regression analysis of the world statistics demonstrated the existence of 3 subfamilies of cancer: a) Western type subfamily including 13 cancers; b) non-Western type subfamily including 4 cancers; c) independent type subfamily including 2 cancers. 2) Further regression analysis of the world statistics data revealed the presence of a mathematical regularity that characterized the relationship between various cancers and their risk changes in 47 areas of the world. The mathematical regularity of the above intercancer linkage closely resembled that of intersteroidal linkage of urine that was derived from the law of mass action. On the basis of the calculation results with the intercancer linkage, the international risk differences of various cancers are explained by use of the equilibrium model that resembles that of the chemical equilibrium model. Evidence is also presented to suggest that the intercancer equilibrium is maintained through the interaction between a proto-oncogen and a tumor suppressor gene in carcinogenesis. The significance of the environment-dependent control mechanism of human carcinogenesis is discussed in the light of population ecology.

Female↗
PubMed1993

Lag phase in solid gastric emptying: comparison of quantification by physiological and mathematical definitions.

Lag phase is considered an important parameter of solid gastric emptying studies. However, different methodologies with their own normal values and physiologic implications are advocated for lag phase measurements. We applied both physiologic and mathematic approaches to quantify lag phases from identical image data sets for direct comparison of these two approaches. Gastric emptying studies were performed on 22 patients using a standard solid meal to calculate the lag phase in each using three different methods: (1) visual analysis to determine time when activity first appeared in the duodenum (LagPh); (2) time-activity curves to determine time of 2% decrease from peak stomach activity (LagCu); and (3) a mathematical definition using the modified power exponential method (TLAG). In addition, time of peak antral activity (AntPk) was calculated. The values for LagPh and LagCu were very similar (mean: 14.6 versus 15.2 min) and correlated well with each other (r = 0.89). TLAG using the power exponential showed different values (mean: 34.7 min) and correlated well only with AntPk (mean: 35.1 min; r = 0.92). We conclude that LagPh and LagCu estimate the time of onset of gastric emptying; the time when the smaller particles in the meal (< 1-2 mm) begin to leave the stomach (onset of variable emptying phase). On the other hand, TLAG and AntPk estimate total trituration time (time for most of meal to be processed) and signal the beginning of the constant gastric emptying phase.

Adult↗
PubMed1995

["Even", integral indicators in systemic mathematical analysis of fatigue].

The article considers 3 different points of view on systemic mathematical analysis of human fatigue process. In this case, the same physiologic information is processed according to various algorithms for integral and digital estimates of lowered performance and energy expenditure, as well as indirect characteristics of inhibition and excitation processes in the brain cortex. The mathematical results are applied in computer forecasting of individual occupational risk at the specific workplace.

Algorithms↗
PubMed1994

The mathematical basis for imaging cardia electrical function.

The essential difficulty of the source-imaging problem in electrocardiology is that the data (body surface potentials) depend continuously on the properties of complex uniquely determined equivalent sources (e.g., epicardial potentials) while such sources do not depend continuously on the data (precluding utility of direct inversion of the operator relating sources and data). This is in distinction to the standard digital tomographic imaging problems in radiology, which superficially resemble the electrocardiographic imaging problem in their requirement for solution of a linear integral equation. From the mathematical standpoint, the electrocardiographic imaging problem requires that an operator with a continuous inverse be constructed from the original operator. This may be accomplished either by slightly perturbing the original operator (the regularization approach), or by performing a calculation on the data (based on inherent source evolution singularities) which allows restriction of the admissible solution domain to a compact set (the topological approach). An understanding of the mathematical questions fundamental to this imaging problem is helpful in assessing its present status and in identifying promising directions for the development of a clinically useful technique.

Electrocardiography↗
PubMedDate not supplied

[A mathematical model of operative analysis and prognosis in outbreaks of hospital infections in newborn infants (exemplified by Klebsiella infection)].

The results of investigations on the development of a mathematical model (computer program) for the study (imitation) of outbreaks of hospital infections among newborns, caused by Klebsiella pneumoniae. The mathematical model, when "saturated" with real data of the outbreak, opens wide possibilities for the operative analysis and prognosis of morbidity and mortality levels among newborns at the intensive therapy departments of maternity clinics and hospitals. The possibilities of the model (computer program) are illustrated by the prognostic calculations of 3 outbreaks (hypothetical) of hospital infections at the intensive therapy department of the university clinic of Universitario del Valle, Cali (Colombia), resulting from violations of sanitary regulations by medical staff members.

Colombia↗
PubMed1996

Forces and moments in six-DOF at the human knee joint: mathematical description for control.

A mathematical description of six-degree of freedom (6-DOF) forces and moments with respect to a commonly utilized knee joint coordinate system was performed using a [6 x 6] Jacobian matrix developed in this study. The presented Jacobian allows the proper transformation of the forces and moments measured at a sensor coordinate system (attached to the tibia in this case) into the joint coordinate system and is dependent on the kinematics of the joint itself. Experimental application of the developed mathematics to A-P drawer tests of the intact knee confirmed that it is possible to determine the forces and moments applied to a human knee within the joint coordinate system during joint loading. More importantly, the inverse Jacobian was also determined for implementation in the force-moment control of the joint during testing using a robotic testing system. This approach is demonstrated for the joint coordinate system for the human knee in the current study, although it may be more generally applied to allow determination and control of forces and moments within any description of motions, and for any additional joints in the human body.

Aged↗
PubMed1996

[Mathematical model of supersaturation of mixed venous blood by gases on decompression].

The paper deals with the negative role of a symptomless gas-formation in the blood; there deduced an equation making it possible to calculate and limit supersaturation of the mixed venous blood and there developed a mathematical model with the use of which it is possible to assess the supersaturation of human mixed venous blood during decompression. It is established that as a result of limitation of supersaturation of the mixed venous blood under decompression there appears a series of short deep-water stops which increases the mode safety. The use of this equation in an integrated mathematical model of decompression furnishes an opportunity to develop the more adequate decompression modes.

Decompression↗
PubMed1997

A mathematical approach for estimating reference values for weight-for-age, weight-for-height and height-for-age.

Anthropometry is widely used to monitor infant growth and to estimate child nutritional status. Current evidence suggests that existent growth curves are not adequate for use with all infants and researchers sought to identify another data set suitable for development as a new international growth reference. In this article we cast about unconditional limits for growth monitoring from raw data on age, sex, height and weight. Anthrompometric data from children aged 1 to 9 years from two studies on malnutrition in Brazil was analyzed. Data on age, sex, weight, height and body mass index from 141 Amerindian children was used to develop mathematical models to predict percent of NCHS medians for weight-for-age, weight-for-height, and height-for-age using multiple linear regression. Data from 251 children in a non-indian seaside village was used for cross-validation. Six age-specific equations were obtained with coefficients of determination greater than 0.96. Coefficients of correlation between NCHS-derived and model-derived values into the validation data set were greater than 0.96 for weight-for-age, greater than 0.99 for weight-for-height, and near 1.00 for height-for-age. It remains to be seen if one can achieve universal linear models from more representative samples, using the approach described here. Perhaps establishing a mathematical relation among anthropometric data would result in absolute individual limits for growth monitoring. They may even be as important to infant nutritional assessment as growth reference values.

Aging↗
PubMedDate not supplied

The effect of follicle-stimulating hormone therapy on sperm quality: an ultrastructural mathematical evaluation.

We investigated the effect of follicle-stimulating hormone (FSH) administration on the ultrastructure of spermatozoa in order to evaluate the potential of FSH therapy for improving sperm quality. Forty-six patients exhibiting idiopathic oligoasthenoterato-zoospermia who attended the intrauterine insemination (IU), in vitro fertilization (IVF), or intracytoplasmic sperm injection (ICSI) program at our clinic received FSH in daily dosages of 150 IU over a period of 12 weeks. Using transmission electron microscopy, the ultrastructural analysis of spermatozoa was performed prior to the start of FSH therapy, after the treatment had been finished, and 6 weeks posttherapy. Applying a mathematical formula based on submicroscopic characteristics, we calculated the number of morphologically normal spermatozoa. After the FSH treatment, the examined subcellular organelles achieved a higher percentage of integrity. Follicle-stimulating hormone treatment leads to a higher number of morphologically normal spermatozoa. The electron microscopic findings indicate that treatment with pure FSH may be an effective way to improve sperm quality in cases with oligoasthenoterato-zoospermia. Applying the mathematical analysis based on the whole complex of the selected sperm characteristics, we obtained a way to evaluate the success of therapy for the first time.

Follicle Stimulating Hormone↗
PubMed1997

Predictions of mathematical models of tissue oxygenation and generation of singlet oxygen during photodynamic therapy.

Photodynamic therapy (PDT) is a relatively new protocol for cancer treatment which has recently been approved for limited clinical use. Traditionally, the success of treatment with PDT has been compared on the basis of total light delivery. Using the mathematical model of Henning et al. (Radiat. Res. 142, 221-226, 1995), we have determined that when oxygen is not depleted from the tissue, the concentration of singlet oxygen that is generated is directly proportional to the product of the light fluence rate (phi) and the concentration of the photosensitizer (Cs). Therefore, phiCs is an appropriate parameter for comparing the potential success of PDT protocols under these conditions. For a treatment of time t, the observed photodynamic effect resulting from singlet oxygen exposure should be directly related to phiCst. For high phiCs, the model predicts that oxygen depletion occurs within the tumor tissue. As a result, the photodynamic effect is no longer proportional to phiCst. We have expanded the model of Henning et al. to include the changes in oxygen concentration which occur within the capillary as blood flows through the tissue. Our new predictions with the mathematical model for optimal PDT treatment conditions are significantly different from those predicted by the previous models. Predictions of the model are given using parameters relevant for treatment of solid tumors with Photofrin.

Dihematoporphyrin Ether↗
PubMedDate not supplied

A mathematical model of the regulation of the G1 phase of Rb+/+ and Rb-/- mouse embryonic fibroblasts and an osteosarcoma cell line.

A mathematical model integrating the roles of cyclin D, cdk4, cyclin E, cdk2, E2F and RB in control of the G1 phase of the cell cycle is described. Experimental results described with murine embryo fibroblasts (MEFs), either Rb+/+ or Rb-/-, and with the RB-deficient osteosarcoma cell line, Saos-2, served as the basis for the formulation of this mathematical model. A model employing the known interactions of these six proteins does not reproduce the experimental observations described in the MEFs. The appropriate modelling of G1 requires the inclusion of a sensing mechanism which adjusts the activity of cyclin E/cdk2 in response to both RB concentration and growth factors. Incorporation of this sensing mechanism into the model allows it to reproduce most of the experimental results observed in Saos-2 cells, Rb-/- MEFS, and Rb+/+ MEFs. The model also makes specific predictions which have not been tested experimentally.

Animals↗
PubMed1997

[Current issues of mathematical modeling and advancement in radiology].

An analysis of certain issues in mathematical support and optimization of radiological procedures has pointed to many criteria involved in designing effective schedules of radiotherapy of neoplasms. TDF, CRE and ETD may be used for relevant evaluations. The greatest promise is held by such criteria as tumor tissue ablation (TTA) and radiation injury complications (RIC) in normal organs and tissue. This calls for development of suitable methods. Considering the high complexity of the body. It should be expected that body responses to radiation are determined by irradiation parameters and condition of target tissues. The report deals with a procedure for adapting mathematical models to on-line requirements. Newly-developed programming complexes are designed to help the medical radiologist integrate available data with his or her clinical findings.

Models, Theoretical↗
PubMed1998

A simple mathematical model applied to selection of the sodium profile during profiled haemodialysis.

BACKGROUND: Among dialysis patients in the last 10 years the incidence of intradialytic dysequilibrium syndrome and symptomatic hypotension has increased significantly. Profiled haemodialysis (PHD), a new dialysis technique based on intradialytic modulation of the dialysate sodium concentration according to pre-elaborated individual profiles, has been set up to reduce intradialytic imbalances and the incidence of dysequilibrium syndrome and symptomatic hypotension. The present paper illustrates a new mathematical model for solute kinetics, single-compartment for sodium and two-compartment for urea, aimed at improving the use of PHD. The model allows the sodium profile to be elaborated a priori, before each dialysis session, according to the patient's clinical needs and respecting the individual sodium mass removal and weight gain. METHOD: The mathematical model was first derived and then applied to determining a rational dialysate sodium profile. A procedure which allows the method to be tuned to individual clinical needs on the basis of routine measurements performed before each session is also presented. The proposed method was validated in vivo during seven dialysis sessions, each performed on a different patient. RESULTS: The comparison between data predicted by the model and those obtained in vivo shows a good correspondence in particular concerning the time pattern of blood urea and sodium. The comparison between the model prediction and in vivo determined sodium and urea plasma curves showed standard deviations (2.25 mEq/l for sodium and 0.87 mmol/l for urea) only slightly higher than those attributable to laboratory measurement errors. Moreover, in vivo implementation of PHD by our model enables one to remove an amount of sodium mass comparable with the a priori quantity predicted by the model.

Aged↗
PubMedDate not supplied

[Mathematical modeling of energy coupling in mitochondria in frames of proton-chemical hypothesis].

The dependence of ATP-synthesis and mitochondria respiration rates on membrane potential was analyzed in frames of proton-chemical hypothesis of oxidative phosphorylation. The mathematical and electrical models of the unit of energy coupling are proposed. Computer analysis of the mathematical model allowed to obtain the theoretical dependence of the rates of ATP synthesis and of the respiration on the membrane potential. Both of all are in good qualitative agreement with experimental data, contradicting chemiosmotic hypothesis.

Animals↗
PubMed1998

Genetico-mathematical analysis of the inheritance pattern of ulcer disease. A posteriori methods. The maximum likelihood method.

Inheritance pattern of ulcer disease was analysed genetico-mathematically using one of the a posteriori methods--the method of maximum likelihood. We studied the families of 351 hereditary predisposed probands of whom 57 with type II gastric ulcer disease, 27 with type III gastric ulcer disease and 267 with duodenal ulcer disease. The types of ulcer disease were determined according to H. Johnson. The analysis of the patients with duodenal ulcer also included the types of familial predisposition of the probands. The results yielded by the maximum likelihood method excluded to a great degree the possibility of monogenic transmission of ulcer disease. None to the three types of peptic ulcer showed autosomal recessive pattern of inheritance; it was not found even in the families with phenotypically healthy but hereditary predisposed parents. No evidence was found of autosomal dominant pattern of inheritance of the disease in all studied groups including the families with one sick parent. This is supported by the different values of the segregation coefficients in the families with one sick father and one sick mother. The absence of evidence for monogenic mode of inheritance of the disease indicated by the detailed genetico-mathematical analysis should be further evaluated by the criteria of polygenicity.

Humans↗
PubMedDate not supplied

[Experimental verification of a mathematical model of plasma protein and erythrocyte regeneration after blood loss].

The regeneration process after 40% bleeding is mathematically regular. Albumin, hemoglobin and red cells regeneration is expressed by the fraction-linear function. This law is true for albumin resotration only immediately after blood loss. Red cells and hemoglobin recovery begins only 3 days after acute bleeding, when albumin concentration rises by 90% of the normal level. Mathematical regularity of albumin regeneration was destroyed after the liver denervation or spleenectomy.

Animals↗
PubMed1998

Mathematical modeling of normal pharyngeal bolus transport: a preliminary study.

Dysphagia (difficulty in swallowing) is a common clinical symptom associated with many diseases, such as stroke, multiple sclerosis, neuromuscular diseases, and cancer. Its complications include choking, aspiration, malnutrition, cachexia, and dehydration. The goal in dysphagia management is to provide adequate nutrition and hydration while minimizing the risk of choking and aspiration. It is important to advance the individual toward oral feeding in a timely manner to enhance the recovery of swallowing function and preserve the quality of life. Current clinical assessments of dysphagia are limited in providing adequate guidelines for oral feeding. Mathematical modeling of the fluid dynamics of pharyngeal bolus transport provides a unique opportunity for studying the physiology and pathophysiology of swallowing. Finite element analysis (FEA) is a special case of computational fluid dynamics (CFD). In CFD, the flow of a fluid in a space is modeled by covering the space with a grid and predicting how the fluid moves from grid point to grid point. FEA is capable of solving problems with complex geometries and free surfaces. A preliminary pharyngeal model has been constructed using FEA. This model incorporates literature-reported, normal, anatomical data with time-dependent pharyngeal/upper esophageal sphincter (UES) wall motion obtained from videofluorography (VFG). This time-dependent wall motion can be implemented as a moving boundary condition in the model. Clinical kinematic data can be digitized from VFG studies to construct and test the mathematical model. The preliminary model demonstrates the feasibility of modeling pharyngeal bolus transport, which, to our knowledge, has not been attempted before. This model also addresses the need and the potential for CFD in understanding the physiology and pathophysiology of the pharyngeal phase of swallowing. Improvements of the model are underway. Combining the model with individualized clinical data should potentially improve the management of dysphagia.

Deglutition↗