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PubMedDate not supplied

Mathematical analysis of contribution of bone remodeling to adhesive performance.

The alkyl-2-cyanoacrylates have been used to repair tissues such as bone. The failure of bonding observed with the application of such adhesives is attributable to a variety of factors including the aqueous environment of the bond. A mathematical analysis of the contribution of the aqueous environment to bonding performance is elaborated. Mathematical modeling may accurately approximate experimental variables that contribute to the performance of biomaterials.

Body Water↗

PubMedDate not supplied

The Gow-Gates technique for mandibular block anesthesia. A discussion and a mathematical analysis.

Reliable profound mandibular block anesthesia is questionable when depositing the anesthetic solution at the lingula. Complications can occur and the needle may impact a number of important anatomical structures by deep penetration. The Gow-Gates technique for mandibular anesthesia obviates these problems.In this paper the Gow-Gates technique is reinterpreted using a geometrical approach based on lines and planes and is proved mathematically. In so doing a simple yet concise method of reaching the injection site is presented with a definite relationship between the anatomical pathway of the needle and a formal geometrical and mathematical pattern.

Anesthesia, Dental↗

PubMed1987

[Mathematical model of the immunostimulation of tumor growth].

A mathematical model of immune system that takes into consideration the subpopulation of suppressor lymphocytes was proposed. The possibility of stable balance in the process of carcinogenesis is shown. The prospects of mathematical formalization of the immune processes are discussed.

Humans↗

PubMed1986

[Mathematical model of brain edema and optimal control of intracranial pressure].

It is necessary to analyse various parameters responding to hypertonic solutions such as mannitol or glycerol, in order to achieve the best therapeutic results for patients having increased intracranial pressure (ICP). The responding model system for the ICP composing of multi-compartments of blood and brain tissue was mathematically introduced. By analysing the changes of the ICP under administration of glycerol using this system, the mathematical model for brain edema was developed. The cause of water transfer in this model system was indicated as the difference of the osmotic pressure and determined as ICP increasing factor, V. It was demonstrated that this theoretical model responded quite similarly to human ICP monitored by sumulating this system for clinical cases. The ICP controller was further developed. The automatic control of ICP was clinically achieved by using this controller. The minimal effective dose of glycerol can be automatically administered by presetting a desirable ICP for each patient.

Aged↗

PubMedDate not supplied

[Discrete and continuous mathematical models of intraspecific behavior in the pharmacoethology of the mouse].

An algorithm and software library were compiled in order to interpret the intraspecies agonistic animal behaviour in terms of discrete or continuous mathematical model. Applied aspects of the use of mathematical models in pharmacoethology were shown on concrete examples. The ways of construction of standard prototypes, and the integrative criteria of psychotropic drugs action were developed. The possibility was shown of identification of unknown substances by comparing with standard drugs by calculating the norm of standardized matrices.

Aggression↗

PubMed1985

New prospects in CT image processing via mathematical morphology.

New prospects are foreseen in CT image processing via mathematical morphology (M.M.). M.M. is a set theory based upon the concept of "structuring elements" and allows texture analysis and pattern recognition by performing sequences of neighborhood transformations. This results in a wide range of quantifications. Mathematical morphology applied to CT densitometry allows obtaining the mean density of an organ after its automatic extraction from the background. This operation eliminates the approximations due to the manual selection of the Region of Interest (ROI). Precision, reliability and reproducibility are therefore improved. In this study, we performed the automatic isolation of a sole vertebral body in thoracic or abdominal CT slices to quantify numerous parameters, among them, density of the vertebral trabecular and cortical bones. On scans of the second and third metacarpals, morphomathematical analysis allowed quantification of the parameters of bone evolution: mean cortical density, directional cortico-diaphyseal index, and medullar area. In a different connection, M.M. has allowed automatic segmentation of lung parenchyma, the measurement of its mean density and the determination of the relative importance of the vascular network.

Absorptiometry, Photon↗

PubMedDate not supplied

[Study of the efficacy of assisted circulation control by mathematical and physical modeling methods].

The efficiency of the assisted circulation control has been studied by mathematical and physical simulation. It has been assessed by simulating a transient process within the circulation system that imitated the left ventricular failure. The control system for regulation of the assisted circulation process based on the mathematical models is shown to be capable of maintaining the main hemodynamic parameters and the left ventricular relief at the present level in heart failure.

Assisted Circulation↗

PubMed1985

Mathematical representation of the velocity curve of sprint running.

Some remarks are tendered on the commonly accepted equations of motion for sprint running. All these involve combinations of one or more exponentials. An alternate form, not discussed in the sports literature, is investigated but though sound, is considered to be mathematically unsuitable. The re-examination of some available data on sprinting suggests that a reformulation of the original differential equation leads to a new solution which is a simple hyperbolic function. This equation may prove a better mathematical model than that commonly accepted as the velocity curve of sprint running. Parameters of the curves are discussed for trainability.

Humans↗

PubMed1979

A mathematical model of speedskating performance improvement for goal setting and program evaluation.

An analysis of world class performance improvement over chronological time was used to develop mathematical curves of performance for each speedskating event. The equations were calculated using an unconstrained non-linear least squares iterative curve-fitting technique. A non-linear model was selected to satisfy the principle of diminishing returns, that is, it is more difficult to achieve a unit of performance improvement as performance approaches the theoretical limits of man. Minimum criteria of acceptance for each curve were: 1) the coefficient of determination must be 0.90; 2) the year 2000 predicted value must be less than the current world record; and 3) the curve must be progressive, i.e. satisfy the principle of diminishing returns. Satisfactory curves were calculated for seven of the eight male and female events studied. A four year Olympic cycle was noted and a definite change in performance trend was identified as occurring in the mid 1960's. The calculated mathematical curves can be used in three applications: 1) setting objective individual goals and evaluating these goals; 2) evaluating and comparing training programs on successive years; and 3) evaluating total programs.

Female↗

PubMed1977

Mathematical analysis of concentration-response relationships. Method for the evaluation of the ED50 and the number of binding sites per receptor molecule using the logit transformation.

The mathematical analysis of concentration-response relationships is performed by means of the mass law and the drug-receptor theory. It is demonstrated that the calculation of the median effective dose (ED50), which is decisive for the pharmacological characterisation of a certain drug, may only be effected by means of the logit transformation. In addition, it is shown that this transformation is most suitable to evaluate in a mathematically simple way the number of drug binding sites of the receptor molecule.

Binding Sites↗

PubMed1977

[Critical remarks on an essay by K.T. Kalveram, "Factor analysis. Critical comments on a theoretical concept and its mathematical reformulation"].

The following contribution is a critical discussion of a paper by K. T. Kalveram Uber Faktorenanalyse. Kritik eines theoretischen Konzepts und seine mathematische Neuformulierung", which was published in this journal in 1970. In the following it is shown that Kalveram's attempt of a mathematical reformulation must be considered a failure, even if mathematical misrepresentations are not taken into account.

Factor Analysis, Statistical↗

PubMed1980

[Construction and study of mathematical models of the dynamics of bacterial biomass growth taking into account the effect of interchangeable metabolic links].

Systemic approach was used as a basis for developing mathematical models for the dynamics of the growth of bacterial biomass with regard to the intracellular substrate pool in case of ramification of metabolic links. The results obtained by calculations with the use of such model were compared with the experimental results of the batch cultivation of E coli M 17. The mathematical models were shown to give a qualitatively correct description characterizing process of the growth of bacterial biomass under conditions of the limited supply of inorganic phosphorus and magnesium.

Bacteria↗

PubMed1978

[Mathematical relationship between the dimensions of the auditory ossicles and fetal age].

Having applied morphometric data obtained on more than 400 auditory ossicles from prefetuses and fetuses at different stages of intrauterine development, the dynamic changes of the greatest size of the malleus, incus and stapes were investigated in age aspect. Increase in size of the auditory ossicles was stated to occur unevenly, every bone having certain periods of the most intensive growth. Mathematical relation of the auditory ossicles growth has been revealed and presented graphically, in an equation. This relation makes it possible to establish mathematically the dementions of the auditory ossicles at any stage of their development. And, according to the auditory ossicles dementions, it is possible to ascertain the fetus age, the data useful for medicolegal practice.

Ear Ossicles↗

PubMed1984

[Mathematical simulation of the blood coagulation system].

The Blood coagulation system was converted to a mathematical model which was described using differential equations. The calculated output patterns of the mathematical model against various input stimulations were compared with results of in vitro assay. The simulated results of (1) Hemophilia A, (2) anticoagulation effect of antithrombin III and (3) anticoagulation effect of heparin corresponded to the results of in vitro assay and clinical reports. However, the simulated result of (4) anticoagulation effect of synthesized arginine derivative No. 805 (MD-805) did not correspond to the results of in vitro assay. Therefore, a new series simulation of MD-805 was done, supposing that MD-805 had an inhibitory activity not only on coagulation factor IIa but also VIIa. The new simulation pattern closely resembled the results of in vitro assay. From these facts, it was theoretically indicated that MD-805 also has an inhibitory activity on VIIa.

Adult↗

PubMedDate not supplied

[Possibilities of using a mathematical method for determining the biological value of protein mixtures].

The authors have devised a mathematical method that allows for the calculation of the best correlations of proteins in a mixture, the determination of amino acid content of the final protein composition and the evaluation of the enrichment effect whatever the characteristics of the reference aminogram and the number of amino acids in it. The indicators of biological value of protein mixtures determined by the mathematic method are in good agreement with the data obtained in biological studies.

Dietary Proteins↗

PubMed1983

Mathematical analysis of isotope labeling in the citric acid cycle with applications to 13C NMR studies in perfused rat hearts.

Rat hearts have been perfused in vitro with 5 mM glucose and either 5 mM acetate or 1 mM pyruvate to achieve steady state conditions, followed by replacement of the acetate with 90% enriched [2-13C]acetate or pyruvate with 90% enriched [3-13C]pyruvate. The hearts were frozen different times after addition of 13C-substrate and neutralized perchloric acid extracts from three pooled hearts per time point were used to obtain high resolution proton-decoupled 13C NMR spectra at 90.55 MHz. The 13C fractional enrichment of individual carbons of different metabolites was calculated from the area of the resolved resonances after correction for nuclear Overhauser enhancement and saturation effects. A mathematical flux model of the citric acid cycle and ancillary transamination reactions was constructed with the FACSIMILE program, and used to solve unknown flux parameters with constant pool sizes by nonlinear least squares analysis of the approximately 200 simultaneous differential equations required to describe the reactions. With [2-13C] acetate as substrate, resonances and line splittings due to 13C-13C spin coupling of the C-2, C-3, and C-4 carbons of glutamate were well resolved. The half-times to reach maximum 13C enrichment were 2.6 min for glutamate C-4 and 8 min for glutamate C-2 and C-3. From these data, a well determined citric acid cycle flux of 8.3 mumol/g dry weight X min was calculated for an observed oxygen consumption of 31 mumol/g dry weight X min. With [3-13C]pyruvate as substrate, resonances of aspartate C-2 and C-3 and of alanine C-3 were well resolved in addition to those of glutamate C-2, C-3, and C-4. Nonlinear least squares fitting of these data to the model gave nonrandomly distributed residuals for the 13C fractional enrichments of glutamate C-4, suggesting an incomplete model, but a well determined cycle flux of 11.9 mumol/g dry weight X min for an oxygen uptake of 35 mumol/g dry weight X min. Our studies demonstrate the practicality of 13C NMR, used in conjunction with mathematical modeling, for the measurement of metabolic flux parameters in living systems.

Animals↗

PubMed1982

Kinetics of killing Listeria monocytogenes by macrophages: correlation of 3H-DNA release from labeled bacteria and changes in numbers of viable organisms by mathematical model.

Conventional methods of assessing antibacterial activities of macrophages by viable counting are limited by the precision of the statistics and are difficult to interpret quantitatively because of unrestrained extracellular growth of bacteria. An alternative technique based on the release of radioactive DNA from labeled bacteria has been offered as overcoming these drawbacks. To assess it for use with macrophages I have made a correlation with the conventional viable counting method using a mathematical model. Opsonized Listeria monocytogenes labeled with 3H-thymidine were exposed to rat macrophages for periods up to 4 hr. Numbers of viable bacteria determined after sonication increased exponentially in the absence of live cells and this growth rate was progressively inhibited by increasing numbers of macrophages. After a lag period of 30-60 min soluble 3H appeared in the supernatant, the amount increasing with time and numbers of macrophages. To correlate these data I developed a mathematical model that considered that changes in numbers of viable organisms were due to the difference between rates of 1) growth of extracellular bacteria and 2) killing within the macrophage. On the basis of this model curves of best fit to the viable counts data were used to predict the release of radioactivity, assuming that death of a bacterium led to the total release of its label. These predictions and the experimental data agreed well, the lag period of 30-60 min between death of the bacterium and release of radioactivity being consistent with intracellular digestion. Release of soluble radioactivity appears to be an accurate reflection of the number of bacteria killed within the macrophage.

Animals↗

PubMedDate not supplied

Use of mathematical models for the evaluation of two- and three-drug combination chemotherapy in murine tumor models.

In parallel with an ongoing clinical trial in patients with metastatic mammary carcinoma, we compared the three-drug combination of cyclophosphamide, tegafur, and methotrexate with the two-drug combination of cyclophosphamide and tegafur in the murine L1210 leukemia and B16 melanoma models. The obtained data based on a central composite design were calculated by mathematical models, which estimate optimum dose combinations for survival by restricting side effect constraints (loss of weight, leukopenia). The main results were as follows: (a) long-term survival can be reached only by accepting a relatively high toxicity in each case, and (b) in the L1210 model the three-drug combination was superior to the two-drug combination, while in the B16 melanoma cyclophosphamide as a single agent offered the best results. The experimental yields are in accordance with preliminary results of the clinical trial. The mathematical model used offers the possibility of comparing drug combinations in a relatively economic way.

Animals↗