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At least 811 records · Page 45Linked to original sources
PubMed1983

An analysis of the regulatory mechanisms in fetal heart rate changes, using a mathematical analysis-model.

To elucidate the effects of regulatory mechanisms on heart rate changes in the human fetus in utero, we devised a mathematical model involving factor analysis, a type of multivariate analysis. From the viewpoint of mathematics, a set of fetal heart rate (FHR) values has two different properties, scalar and vector. We studied the instantaneous FHR values for 96, 704 beats in sequence, obtained from a normal fetus at 33 weeks of gestation. The scalar components of the FHR changes appear to be composed of around 4,000 beats, among which a few isolated properties may be present. These findings indicate the underlying baseline heart rates, which differ in biological origin. The distribution of the beat-to-beat differences included the "core fluctuation" ranging up to +/- 3 beats per minute. According to the factor analysis for the vectorial components, it has also become evident that there were at least two different characteristics in FHR changes, indicating the existence of acceleration and deceleration mechanisms.

Analysis of Variance↗
PubMed1981

[Potential use of a mathematical modeling method for the analysis of immunological phenomena].

The paper reviews mathematical models of immunological processes associated with reactions of the total immunity system and its single formations: infectious diseases, in vivo experiments with cell cultures, cell proliferation and differentiation in the thymus, primary and secondary immune responses to the antigen, immunodeficient states, etc. It also gives models of immunological reactions in vitro: precipitation, agglutination, plaque formation, etc. The paper contains a short description of potentialities of mathematical models of biological processes.

Aerospace Medicine↗
PubMedDate not supplied

[Problem of sphere formation in mathematical models of morphogenesis].

The model of a process of morphogenesis is described, being a new link in the series of mathematical models of morphogenesis based on the local interactions of cells (see [6]) and the first space model of the series. A corresponding mathematical problem is formulated. The results of the proper computer calculations are published, showing that the chosen rule of motion solves the problem of sphere formation for a very large class of initial states of all investigated types of nets. The processes taking place in solving the problem of sphere formation are considered.

Computers↗
PubMed1980

Aerosol deposition in the respiratory tract of the rat. Experimental results and mathematical modelling.

The deposition fraction in the respiratory tract of rats were determined experimentally using aerosol 85Srl2 in saline. The dimensions of the particles [MMD 1.63 /+- /+- 0.47 micron, Sg = 1.29] were measured by two independent methods. Rats weighing 200 g were exposed for a period of 60 min [t] in the inhalation apparatus PIANO 3 with a generator according to Lauterbach. From the volume activity [A] of 3 - 11 Bq/litre air a depot of 35-129 kBq was formed in the animals. Spirometric values measured with a modified Jäger ergospirometer were: V = 178.8 /+- 42.9 ml, VT = = 1.18 /+- 0.24 ml. f = 163.1 /+- 28.1 cycles/min. The total amount inhaled [Q] was calculated [Q = V.A.t], the deposited amount [D] was measured by a whole body counter. THe mean deposition fraction was 0.570 /+- 0.052 and was not related either to exposure time or to aerosol activity. In view of the broad validity of the conclusions for aerosols of round-shaped particles, the mean deposition fraction was determined with the help of a mathematical model according to Landahl. The theoretical values amounted to 0.609 [from 0.522 to 0.686]. The good agreement between the mean deposition fractions estimated by two independent methods indicates that on the basis of the probability theory and dimensional analysis, the mathematical model can also be used in humans for simulation deposition as one of the basis foundations for a quantitative evaluation of inhalation risk from any kind of aerosol.

Aerosols↗
PubMed1995

Automated textural analysis of nuclear chromatin. A mathematical morphology approach.

Nuclear grading of neoplasms has classically been involved in prognosis and must be established by combining different parameters, such as the textural pattern of chromatin, which is subjective and difficult to measure. Mathematical morphology (MM), a branch of mathematics dealing with shapes, and, in particular, the so-called top hat transformation, provides us with a helpful tool for quantitative assessment of chromatin texture. A sequence of MM operations (the top-hat transformation) was applied to Mayer-hematoxylin-stained cytologic smears made immediately after surgical removal to obtain a series of images at different levels of a granulometric chromatin fractionation. These images are related to the size (n = 1, 2, 4, 6 and 8) of a structuring element that performs these operations. A skeletonization of the intergranular area at level 4 was also performed to provide a shape-related image of chromatin grains. Using these granulometric images as a starting point, we defined a series of variables: TH(n) as the granulometric area at top-hat level n; GAD(n) as the grain-associated density at level n; THIOD(n) as the integrated optical density of the granular fraction at level(n); GIOD(n) as the grain-integrated optical density at level n; CP as a chromatin texture variable, chromatin pattern, that estimates the granular versus dispersed aggregation pattern; and CB, a shape descriptor that estimates the roughness of the isolated chromatin grains and is expressed as a coefficient related to the number of branches of the intergranular skeleton. The operation provides a set of variables descriptive of a wide range of chromatin texture properties.(ABSTRACT TRUNCATED AT 250 WORDS)

Breast Neoplasms↗
PubMed1993

[Scaphocephaly: mathematical and geometrical principles. Surgical incidences].

Authors have reported the mathematical and geometrical principles of cranioplasty used for the surgical treatment of patients with scaphocephaly. After a review of classical mathematical procedures utilized to modify the surface of spherical or hemispherical structures, and after some considerations about relevant properties of bone, the authors illustrate the possibility of a clinical application. The technique described and used in a series of 40 patients, is a simple adaptation of the principles used by engineers to build complex structure such as ships hulls, domes and airfoils. The very satisfactory results obtained, encouraged us to extend the application of the method reports to the reshaping of the skull in other cranio-facial malformations characterized by abnormal skull morphology.

Craniosynostoses↗
PubMed1993

[Application of the mathematical model to forecast the incidence rates of seasonal infectious diseases].

The incidence rates of infectious diseases were selected and analysed according to data from the Beijing Railway Area during 1981-1991. We put forward the mathematical model to forecast the incidence rate of dysentery each quarter in 1992. The best mathematical model was selected from analysis of precision, and very useful in the prevention and treatment of seasonal infectious diseases.

China↗
PubMedDate not supplied

The tumor-producing effect of automobile exhaust condensate and fractions thereof. Part III: mathematical-statistical evaluation of the test results.

This paper deals with the mathematical-statistical evaluation of experiments devoted to the following problems: 1. To what extent is the carcinogenic potency of automobile exhaust gas condensate dependent on the dose? 2. What fractions (groups of substances) of the automobile exhaust gas condensate are mainly responsible for the carcinogenic potency? 3. To what extent can the potency be explained by fractions (or single substances)? In order to answer the above questions, the working group planned animal experiments (cf. Misfeld and Timm, 1973) and obtained, prepared, and fractionalized automobile exhaust gas condensate (Grimmer, 1978). The exhaust gas condensate and its fractions were dropped onto the skin of female CFLP mice (Brune et al., 1978). In view of the problems posed above, the aim of the mathematical-statistical evaluation was to establish the dose-response relations, to assess the combined effect, and to estimate the relative potency and the assumed potency. In particular, the hypothesis (basis for the separation process) that the potency of the entire exhaust gas condensate is mainly attributable to the fraction which contains the polycyclic aromatic hydrocarbons (nitromethane phase) was examined.

Animals↗
PubMed1993

Textural analysis of lymphoid cells in serous effusions. A mathematical morphologic approach.

Nuclear texture of reactive and well-differentiated neoplastic lymphocytes from serous effusions was studied by an approach based on principles of mathematical morphology. Density features were obtained before and after gray level nuclear image transformation by morphologic closing (dilation followed by erosion) and application of a top-hat function, which detects light or dense spots with a determined width and contrast. Five cases of benign reactive lymphocytic serous effusions and 11 cases of effusions in well-differentiated lymphocytic lymphomas were analyzed retrospectively. Each lymphoid cell was characterized by 24 densitometric features. Rank-order transformation was used for linear discriminant analysis given non-normal distributions of variables. In a first model formed by pooling all cells, discriminant function distinguished between 110 reactive and 216 malignant lymphocytes in the learning set and between 111 reactive and 226 malignant lymphocytes in the test set with better than 81% accuracy in both. In a second model, correct classification of cases as reactive or malignant was achieved in 5/5 reactive and 11/11 malignant lymphoid effusions. The results indicate that mathematical morphologic transformations of the gray level image may be an effective adjunct to other textural descriptors of cellular atypia, especially in the differential diagnosis of lymphoid serous effusions.

Ascitic Fluid↗
PubMed1993

[Extracorporeal lithofragmentation and of direct contact. Development of mathematical models for calculating the energy and predicting the fragmentation].

The present experimental 'in vitro' study pursues the development of mathematical equations which, prior to lithofragmentation, would allow to estimate the amount of energy required and to predict the degree of fragmentation for each of the different sources of energy. A total of 114 calculi with 6 different compositions were analyzed by conventional X-rays (Rx), computerized axial tomography (CT) and dual X-ray densitometry (DO). Calculi were then fragmented using 4 different types of energy: electrohydraulic (LEH), piezoelectric (LEP), ultrasounds (US) and pulse laser (LAS). The correlation between imaging techniques parameters on the one side, and the amount of energy used and degree of fragmentation obtained on the other one, allow with a multiple linear regression analysis, both to develop mathematical equations to estimate the amount of energy required, and to predict the fragmentation rate.

Biophysical Phenomena↗
PubMed1979

[Mathematical decription of the human intravascular elimination of HAS after repeated infusions].

Serum concentrations of high molecular weight-hydroxyethyl starch (HMW-HES, Mw 450,000 d, Mn 71,000 d, Mw/Mn = 6.3, MS = 0.7) were determined in normovolemic subjects dosed with three consecutive daily 500 ml infusions, to mathematically calculate the influence of the two-variable (Mw and MS) HES drug design system, on elimination of this material from the intravascular space under controlled conditions. Following the initial 500 ml (6% solution) infusion, the intravascular clearance up to 24-hours post-injection, was well predicted by the exponential equation: y = 3.94 + 3.34e-0.15x. On days two and three, the clearances up to 24-hours post-injection, were described by the equations: y = 6.32 + 3.75e-0.15x and y = 9.39 + 5.41e-0.15x, respectively. From these mathematical models, it appears that up to 24-hours post-injection on each of the three infusion days, HMW-HES is cleared from the bloodstream in a similar manner. HMW-HES clearance from the blood on day three, however, exhibited a slightly faster rate of decline, as seen by the larger coefficient attributed to the exponential component. The serum concentration of HMW-HES, 480 hours (2.9 weeks) following the third and final infusion, was 2.3 +/- 0.3 (SD) mg ml-1. Thus, in the 480-hour interval following the third and final injection, the serum concentration of HMW-HES measured at 10 minutes after injection 3, had been reduced by 85%. This decline in serum concentration following the infusion of HMW-HES, appears to be greater than previously reported by other investigators.

Humans↗
PubMedDate not supplied

[Mathematical model of adaptation of the energy metabolism of a cell. Calculation of the influence of ATP on the activity and concentration of the initiator stage enzyme].

A simple kinetic model was constructed to study the adaptation of cell energy metabolism to a varying loading. In this model the initiatory step of energy metabolism, in which the initial substrate S is activated at the expense of ATP molecule energy, is catalyzed by an oligomeric enzyme E dissociable at high ATP concentration to monomers E1. It is assumed that the steady state level of monomers E1 in the cell is maintained by constitutive synthesis of E1 molecules, which balances their continuous hydrolysis by proteases. The properties of the kinetic model were studied using a mathematical model which is a system of nonlinear differential equations describing the change with time of the total enzyme E concentration and the concentration of ATP. The main isoclines of this system can intersect in one, two or three points. The mathematical analysis shows that the kinetic model considered exhibits adaptive properties. A sharp increase of the ATPase activity in the model initiates a transient process which leads to a rise in the total enzyme E concentration and in the efficiency of energy metabolism. As a result, the concentration of ATP drops only slightly. The establishment of a new level of the enzyme E concentration may proceed in the oscillatory fashion.

Adaptation, Physiological↗
PubMed1995

Application of mathematical morphology in angiologic studies.

Application of mathematical morphology in morphologic sciences was tested. Two aspects were evaluated, cognitive and utilitarian on analyzing enigmatic objects in TK and searching for particular elements in angiologic photos taken in infrared. The results prove many application possibilities of the method. Combination of modern techniques: infrared, Pickworths method, TK, and image transformation delivers many new data. Mathematical morphology selects interesting details and rejects redundant information.

Blood Vessels↗
PubMed1997

Comparative genetico-mathematic analysis of essential hypertension and coronary heart disease mode of inheritance: a study using direct methods testing.

Essential hypertension (EH) and coronary heart disease (CHD) very often exhibit familial recurrence pattern, which are estimated in the Bulgarian population at 63.11% for EH and at 48.90% for CHD. The author made comparative genetico-mathematical analysis of the inheritance patterns of the two diseases. Examining the pedigrees from a large number of families two data sets were formed and analyzed separately: a subgroup of families of probands with phenotypically unaffected parents, in which the genealogical pattern was most often consistent with a recessive model of inheritance and a subgroup of families of probands with one or both parents affected, in which the pedigree analysis resembled that of a disease with a monogenic dominant model of inheritance. The segregation coefficients obtained in the subgroup of families with two healthy parents most often varied from 0.298 to 0.362--results that consistently reject the hypothesis of recessive inheritance; the respective coefficients obtained by the same direct methods in the subgroup of families with one or both parents affected showed values from 0.279 to 0.468--findings rejecting the hypothesis of dominant model of inheritance. The author pointed out the identical relationships exhibited by genetico-mathematical testing of EH and CHD, a fact demonstrating the significant genetic proximity between the two diseases. Conclusions are made about the complex and specific relationships between genetic and environmental risk factors in the two diseases.

Adult↗
PubMed1997

Ploidy determination on histologic sections of breast cancer specimens by image analysis using mathematical correction algorithms.

Several mathematical correction algorithms were developed to solve the problem of the unavoidable measurement of fragmented nuclei when determining DNA ploidy on thin histologic slides. These algorithms were designed for model tissue and until now had not been tested thoroughly on malignant human tissue. We evaluated the use of mathematical correction algorithms applied to measurements on thin histologic sections of breast cancer specimens, with strict control of the section thickness. Fifteen cases of breast carcinoma with known ploidy (5 diploid, 5 tetraploid, and 5 aneuploid breast cancer samples) were included. From each tissue block, we made a single-cell preparation and cut a thin histologic section. We evaluated the thickness of each of these sections according to a recently developed protocol and included only sections with a thickness between 5 and 6 microns. We performed DNA measurements with a custom-made image analyzing system equipped with a 100x oil immersion objective. Histograms of tissue section measurements were corrected according to the algorithms of McCready and Papadimitriou and of Haroske et al. We compared these results with the uncorrected histograms and with the histograms of the single-cell preparations. We also measured the single-cell preparations with a commercially available high-resolution image cytometer. The correlation between both image cytometers used was high (r = 0.99). Histogram correction improved results of tissue section measurements in all of the nondiploid tumors when compared with the uncorrected histograms. There were no significant differences between the correction algorithms used (correlation to the single-cell measurements determined by a linear regression; r = 0.98 for both algorithms). No overcorrection of the histograms occurred. We conclude that reliable DNA tissue section measurements are possible on breast cancer specimens and that such measurements will contribute to our understanding of tumor cell kinetics in small tumor cell populations not detected in single-cell measurements.

Aneuploidy↗
PubMed1996

Biological inferences from a mathematical model for malignant invasion.

Invasive cells show changes in adhesion, motility and the protease-antiprotease balance. In this paper the authors derive a model based on a continuum approach that describes the behaviour of the invasive cells. The invasive cells are studied in the context of their interaction with normal cells, noninvasive tumour cells, ECM proteins and the proteases. The authors briefly describe the methods of mathematical analysis used and then go on to highlight the biological inferences drawn from the mathematical analysis. Based on the results from the modelling the authors suggest that the movement of cells under the simultaneous effects of a haptotactic gradient and a concomitantly created chemotactic gradient is oscillatory both with respect to the speed of invasion and the wave profile of the invasive cells. They further demonstrate that the average speed of invasion can be computed as a measure of the phenotypic properties of the cell and the matrix. They use the model to suggest an intuitive explanation for the occurrence of noninvasion with high protease expression on the basis of chemotactic gradients that prevent invasion. The authors have studied the effect of the diffusivity of the protease on an invading cell and shown that increase in diffusivity initially results in enhanced invasion, but extreme increases in protease diffusivity can result in noninvasion.

Animals↗
PubMed1976

[Studies for a mathematical model of the proliferation kinetics of mammary carcinomas by means of electronic data processing (author's transl)].

Continuing an earlier publication in which the growth of spontaneous mammary carcinomas in female mice of a C3H inbred strain was described, in the present paper the growth rate is expressed by a mathematical function, and is adapted by electronic data processing to the experimental values of 60 tumors classified into seven "growth types". For mathematical description the tumors were conveniently assumed to have a spherical shape, and the main reason for the reduction in volume increase with increasing tumor size was thought to be insufficient supply with oxygen and the essential nutrients S. Including the experimental data of all carcinomas investigated, the minimum concentration of S necessary for mitotic activity of the tumor cells was calculated to be 65% of the normal level. As the average for all the tumors investigated, a time of at least 33 hrs is required for the tumor volume to double.

Animals↗
PubMed2006

Optimal size and location for corneal rotational autografts: a simplified mathematical model.

OBJECTIVE: To calculate clinical guidelines for the optimal location and size of a rotational autokeratoplasty. METHODS: The ideal graft size and trephine decentration for a rotational autograft were calculated based on scar location using geometric models. Mathematical variables were set to maximize postoperative visual acuity and for generalization of the geometric model. This model was used in a rotational autokeratoplasty of a patient with a history of a corneal scar and diplopia. An 8-mm autograft was decentered 0.5 mm superiorly and rotated 180 degrees to relocate the scar to the superior aspect of the cornea, out of the patient's vision. RESULTS: For cases that satisfy the given variables, a graft diameter of 8 mm with a decentration of 0.5 mm balances maximization of scar removal and scar movement superiorly, with minimization of discrepancy in corneal thickness after rotation. For scars that are alpha degrees from horizontal, the graft should be rotated 180 - alpha degrees . By using these calculations, the autograft in this case successfully resolved the diplopia and improved visual acuity. CONCLUSIONS: A rotational autograft can be an effective alternative to standard penetrating keratoplasty for some patients with corneal scars. We establish a mathematical model for most clinical instances of a rotational autograft, in which an 8-mm graft with a decentration of 0.5 mm best satisfies the goals of surgery.

Adult↗