Mathematical Models Of Biological Systems Research Articles

Review of "Mathematical Modeling of Biological Systems, by Harvey J. Gold", John Wiley & Sons

This book describes the process by which biologists can capture the properties of biological systems within the framework of mathematical structures. Even though it is mathematical in nature, the author places no strong mathematical demands upon the reader. This volume should be of interest to those who are developing models and conducting simulations in the biomedical field as well as in basic biology. The author draws primarily from biology in the development of the mathematical models in the book.

Reliability range of model parameters and its application to biological models

This paper deals with the analysis of the determinability of the parameters of mathematical models of biological systems and the estimation of the reliability range of the parameter vectors. The results of the analysis are used to design further experiments for improving the estimation of the parameters. This procedure was illustrated by the investigation of intravenous radiopalmitate kinetics in rats with a special regard to the speed of labelled fatty acid outflow from plasma and lipoprotein formation in the liver. On the basis of the course of parameter sensitivity functions a new theoretical experiment, contributing to a marked improvement of the parameter reliability estimation, was designed. The method was algorithmized in the HYPER and EIGEN programs developed for the EAI690 hybrid computer system.

Quantitative Description and Mathematical Modelling of Biological Systems by Means of Nonlinear Approximations – Demonstrated at the Example of the Body Length Growth of Man

AbstractAfter general remarks upon the biomathematical tasks of quantitative description or mathematical modelling of biological systems and phenomena on different levels of organization the growth process of body length of human beings serves as illustration of the possibilities of such mathematical treatments. A short survey is given about the attempts of using differential equations for reflecting basic principles of growth processes. Further on analytical functions (as the solutions of growth differential equations) preferably may be used for an objective quantitative reproducing of measured courses of growth variables. The values of parameters contained in such expressions will be calculated by nonlinear fitting procedures. In nearly all cases we got a very high numerical precision in approximating parts of the body length growth process of man which extends from conception until the age of 18. Our attempts of a phenomenologic‐mathematical modelling of this growth process mean a subdividing of the whole process in single growth spurts with a symmetric‐sigmoidal shape of their courses, and describing the single spurt by a hyperbolic tangent function. An advantage of this kind of modelling is the fact that each of the terms is valid for the whole time interval of growth. Within the process of forming the model heuristical hints are taken into consideration arising from biological background and which would supply the possibility of interpretation and verification of the analyzed growth spurts.

D'Arcy thompson's theorems and the shape of the molluscan shell

The paper deals with properties of mathematical models of biological systems. It is shown that under suitable conditions the number of parameters employed in the model depends only on the biological system and not on the particular model chosen. As an application the mathematical description of the formation of molluscan shells is discussed.

Kinetic analysis of calcium transport across the placenta.

ArticleKinetic analysis of calcium transport across the placenta.C F Ramberg Jr, M Delivoria-Papadopoulos, E D Crandall, and D S KronfeldC F Ramberg JrSearch for more papers by this author, M Delivoria-PapadopoulosSearch for more papers by this author, E D CrandallSearch for more papers by this author, and D S KronfeldSearch for more papers by this authorPublished Online:01 Nov 1973https://doi.org/10.1152/jappl.1973.35.5.682MoreSectionsPDF (2 MB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat Previous Back to Top Next Download PDF FiguresReferencesRelatedInformation Cited ByMaternal stress does not exacerbate long-term bone deficits in female rats born growth restricted, with differential effects on offspring bone healthKristina Anevska, Jean N. Cheong, John D. Wark, Mary E. Wlodek,* and Tania Romano*1 February 2018 | American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, Vol. 314, No. 2Strontium biokinetic model for the pregnant woman and fetus: application to Techa River studies21 August 2015 | Journal of Radiological Protection, Vol. 35, No. 3Bone Development and Mineral Homeostasis in the Fetus and Neonate: Roles of the Calciotropic and Phosphotropic HormonesChristopher S. Kovacs1 October 2014 | Physiological Reviews, Vol. 94, No. 4Fetal Mineral HomeostasisCalcium, Phosphorus, and Magnesium Transport Across the PlacentaHyperparathyroidism in PregnancyThe Endocrinologist, Vol. 15, No. 5Calcium, Phosphorus, and Magnesium Transport Across the PlacentaFetal Mineral HomeostasisL-type Ca2+ channels in fetal and adult ovine cerebral arteriesArlin B. Blood, Yu Zhao, Wen Long, Lubo Zhang, and Lawrence D. Longo1 January 2002 | American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, Vol. 282, No. 1Characteristics of Calcium Uptake by BeWo Cells, a Human Trophoblast Cell LinePlacenta, Vol. 22, No. 8-94. Biokinetic data and models16 November 2016 | Annals of the ICRP, Vol. 31, No. 1-3Doses to the Embryo and Fetus from Intakes of Radionuclides by the Mother16 November 2016 | Annals of the ICRP, Vol. 31, No. 1-3Distributing Working Versions of Published Mathematical Models for Biological Systems via the InternetMaternal-Fetal Calcium and Bone Metabolism During Pregnancy, Puerperium, and Lactation*Endocrine Reviews, Vol. 18, No. 6Fetal calcium homeostasis10 June 2010 | Equine Veterinary Journal, Vol. 29, No. S24Parathyroid hormone-related peptide (PTHrP) regulates fetal–placental calcium transport through a receptor distinct from the PTH/PTHrP receptor24 December 1996 | Proceedings of the National Academy of Sciences, Vol. 93, No. 26Calcium-binding properties of fetuin in fetal bovine serumJournal of Experimental Zoology, Vol. 270, No. 6Oxygen exchange in the chorioallantoic membrane, avian homologue of the mammalian placentaPlacenta, Vol. 14, No. 6Hyperparathyroidism and pregnancyJournal of General Internal Medicine, Vol. 7, No. 4Application of Models to Determination of Nutrient Requirements: Experimental Techniques Employing TracersThe Journal of Nutrition, Vol. 122Calcium and Phosphorus Metabolism in the Premature Infant29 August 2016 | Annals of Clinical Biochemistry: International Journal of Laboratory Medicine, Vol. 28, No. 2Development of endocrine pathways in the regulation of calcium homeostasisBaillière's Clinical Endocrinology and Metabolism, Vol. 3, No. 3Is there control of solute transport at placental level?Placenta, Vol. 9, No. 1Placental transfer of calcium to the ovine fetus and its regulation28 February 2007 | Proceedings of the Nutrition Society, Vol. 46, No. 2The effect of fetal thyroparathyroidectomy on the transport of calcium across the ovine placenta to the fetusPlacenta, Vol. 7, No. 5Calcium metabolism in pregnancy and the perinatal period: A reviewAmerican Journal of Obstetrics and Gynecology, Vol. 151, No. 1Mineral and Water Exchange between Mother and FetusEndocrine Regulation of Calcium Homeostasis During PregnancyClinics in Perinatology, Vol. 10, No. 3Foetal plasma magnesium levels during maternal hypo- or hypermagnesaemia in ewes9 March 2007 | British Journal of Nutrition, Vol. 42, No. 3Nutrition and PregnancyPerinatal Calcium Homeostasis: Neonatal Hypocalcemia and Bone DemineralizationClinics in Perinatology, Vol. 4, No. 2Methylmercury movements across the perfused guinea pig placenta in late gestationToxicology and Applied Pharmacology, Vol. 39, No. 1Calcium and phosphorus metabolism in ruminants with special reference to parturient paresis1 June 2009 | Journal of Dairy Research, Vol. 43, No. 3Studies in calcium metabolism in infants with intrauterine growth retardationThe Journal of Pediatrics, Vol. 86, No. 6 More from this issue > Volume 35Issue 5November 1973Pages 682-8 https://doi.org/10.1152/jappl.1973.35.5.682PubMed4203705History Published online 1 November 1973 Published in print 1 November 1973 Metrics

A general method for calculating the dynamics of linear mathematical models of biological systems

A general method for calculating the exact dynamics of linear mathematical models of biological systems is presented. As a byproduct of using the exact method, one is assisted in acquiring the skill to make a qualitative estimate of the form of system response by observing only the form of the system mathematical model.

New Mathematical Methods in the Life Sciences

Haldane stated only way of real advance in biology lies in taking as our starting point, not the separated parts of an organism and its environment, but the whole organism in its actual relation to environment, and defining the parts and in this whole implying their existing relationships to the other parts and activities [1]. Recognizing the dangers inherent in oversimplification, we might nevertheless say that in medicine we are dealing functionally with highly complex systems of chemical reactions and with control mechanisms that affect the varying rates of these reactions. A living animal is perhaps the most complex chemical factory that will ever be devised. Its highly dynamic character has been brought into even sharper focus by the recent introduction of isotope techniques. It is clear that new approaches should be sought for viewing the human body as a whole and to make it possible to integrate and evaluate the information that has been accumulated but not necessarily interrelated about thousands of parameters developed in the study of living systems. Indeed it is interesting to note that the most recent developments have evolved out of the analogy between the automation and control of complex industrial processes (and decision making in general) and the complex metabolic and control processes of the human body. We appear to be at that point in human understanding when the greatest progress will be made if many processes are considered in relation to each other. Mathematical models of biochemical processes should now be undertaken that view the human body as a whole, as well as consider a particular organ which may incorporate a number of such processes. The idea of building mathematical models of biological systems is, of course, not new. Lotka, Rashevsky, Henderson, Michaelis, and others were early investigators who proposed mathematical models of biological systems or who pioneered in the quantification of parts of such systems. But it is only in recent years that the field has attracted a great deal of attention because now better tools are at hand to develop the basic ideas. The emerging nuclear and space age presents an especially difficult challenge to biological science and medical art. The stresses that may be placed on organisms by the completely new and stringent environments associated with these technologies are largely unknown. To understand the effects of these environments on the whole organism, especially on the human system, will be difficult and slow, if not impossible, within the present state of the biological arts and sciences. The reason is partly our lack of knowledge of individual biological phenomena, and partly the present lack of a technique for integrating a very large number of environmental effects. We should not try to decide in advance which lack is more important. Mathematical techniques and computing facilities