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PubMed1991

Fractals and medicine.

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Image Interpretation, Computer-Assisted↗
PubMed1986

Computer-assisted predictive mathematical relationship among metrazol dose and time and mortality in mice.

A microcomputer program in BASIC for predicting mortality in mice administered metrazol is designed. A formula published by the author to express the mathematical relationship among the drug dose, the time after administration, and the biological response was used in this program. Analysis of the actual and the computer-assisted predicted mortalities has shown that the program is fairly accurate and reliable in expressing tolerance of mice as a function of the dose and the time.

Animals↗
PubMed1989

A mathematical model for the computation of the oxygen dissociation curve in human blood.

The mathematical relations developed by various researchers for the oxygen dissociation curve are reviewed. Using well-known mechanisms of chemical kinetics of various species in the blood, we have developed a mathematical formula to compute the oxygen dissociation curve in the blood showing its dependence on the pH and PCO2. The functional form, proposed here, is much simpler in comparison to those available in the literature for use in the mathematical modelling of O2 transport in the pulmonary and systemic circulations. In the process, the well-known Hill's equation has been generalized showing an explicit dependence on PCO2 and pH. It is shown that the oxygen dissociation curve computed from our comparatively simpler equation, fits in fairly well with the documented data and shows realistic shift with PCO2 and pH.

Hemoglobins↗
PubMed1989

Computer-assisted predictive mathematical relationship among plasma acetaminophen concentration and time and hepatotoxicity in man.

A microcomputer program in BASIC for predicting hepatoxicity in man resulting from a single overdosage ingestion of acetaminophen was designed. A formula used in this program is derived from the data reported by Prescott and his coworkers (Lancet i (1971) 519-522). Analysis of the actually reported and the computer-assisted predicted data has shown that the computer-assisted predictive formula may be clinically helpful in determining if the plasma acetaminophen level is in the toxic or nontoxic range.

Acetaminophen↗
PubMed1989

Computer-assisted predictive mathematical relationship between time after diagnosis and survival probability in patients with chronic leukemias.

A microcomputer program in BASIC for predicting the survival probability by the time after diagnosis in patients with chronic leukemias is designed. Formulas used in this program are derived from the data published by Feinleib and MacMahon (Blood 15 (1960) 332-349). A general equation previously published by the author is applied in this study to calculate the survival probability. Analysis of the computer-assisted predicted and Feinleib and MacMahon's observed data has shown that the program is fairly accurate and reliable with a close agreement in expressing survival probability as a function of the time after diagnosis. The computer-assisted predictive formulas can determine the relationship between the time and the survival probability, and may be of value for prognostic evaluation of patients with chronic leukemias.

Chronic Disease↗
PubMed1975

Theory of image reconstruction in computed tomography.

Mathematical methods are of central importance in the new technologies of radiographic and radioisotopic image reconstruction. The most important procedures are classified as Back-projection, iterative, and analytical (Two-dimensional Fourier, Filtered Back-projection). Back-projection played an important historical role but is no longer used because of sizable artifacts. Analytical methods excel in speed and accuracy when a large number of projections are available and are extensively used in x-ray imaging. Iterative reconstruction is more attractive when the number of views is limited, if noise is significant, and if additional factors, e.g., gamma-ray attenuation, are present. For these reasons, iterative methods are widely used in radioisotope imaging.

Computers↗
PubMed1990

Mathematical model for the computation of alveolar partial pressure of carbon monoxide.

A mathematical model is formulated for computing alveolar partial pressure of carbon monoxide (PACO) from that in the atmospheric air. The model takes into account parameters like inspired/expired air flow rates, diffusion capacity of the lung, concentration of CO in the atmospheric air, blood flow rate and the non-linear CO dissociation curve. The effect due to the presence of O2 in the blood on CO dissociation curve is also incorporated. It is shown that for a given atmospheric CO concentration, PACO increases exponentialy with time and attains asymptotic value. Alveolar PCO increases further with the increase in the atmospheric CO concentration. The model can also be used to compute carboxyhaemoglobin levels in the blood as a function of exposure time and the results are comparable with the CFK equation and the values measured experimentally.

Carbon Monoxide↗
PubMed1991

Ear canal cross-sectional pressure distributions: mathematical analysis and computation.

Cross-sectional pressure distributions, natural acoustic modes, and associated cutoff frequencies are determined for real ear-canal geometries using an asymptotic theory in combination with a numerical method. The technique is particularly well suited to obtain the higher modes, which are trapped near both ends of the ear canal. Results detail the influence of the canal geometry and frequency on the spatial distribution of the pressure. Adult ear-canal geometries are determined near the concha from ear-mold sections using a light microscope interfaced to a video-data-acquisition system. Computed results compare favorably to the exact solutions for circular and square acoustic waveguides. The cutoff frequency of the two adult ear canals studied averaged 20% less than the cutoff frequency of a circular tube of identical cross-sectional area. Inserting a probe microphone into the canal decreases the rate of decay of circumferential nonplanar modes while increasing the rate of decay of radial modes. Relative to the pressure beyond the tube, insertion increases the plane-wave component of the pressure around the tube by a multiplicative factor approximately equal to the square root of the original area divided by the occluded area. Eccentric placement of the probe tube has a relatively small influence on the cutoff frequency. The transition of the pressure distribution at the entrance to a simple plane wave in the core region of the canal is calculated and shown graphically for the actual geometry of two adult subjects.

Computer Simulation↗
PubMed1991

[The differential diagnosis of sarcoidosis of the respiratory organs using mathematical methods and computers].

A system for detecting sarcoidosis has been proposed on the basis of the results of a primary examination, which comprises a combination of programs for determining whether sarcoidosis may occur in various X-ray syndromes (enlarged intrathoracic lymph nodes, disseminated process, infiltrative or pneumonia-like shadow and cavity formation). The system has been developed with the help of a program-algorithm complex which enables one to make the dialogue system of the decision-make support on the basis of statistical methods of "image recognition" containing basic structural elements of the expert systems. Program development proceeds from the findings obtained in 406 patients with sarcoidosis of respiratory organs and 723 patients having similar clinical and X-ray picture of the disease. The diagnostic efficiency of the system was 89% in disseminated processes, 90% in enlarged intrathoracic lymph nodes and cavitary changes, and 96.2% in infiltrative changes.

Diagnosis, Differential↗