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PubMed1987

[Mathematical modeling of protein loss during prolonged blood loss].

The dependence of protein losses on the initial condition and experimental conditions were studied in dogs on a model of repeated bloodletting. Various animals have an intensive increase in this value in the beginning and a gradual decrease at later stages. Four mathematical models adequately describing changes in losses depending on the number of bloodlettings and duration of arterial pressure compensation phase have been suggested.

Animals↗
PubMed2007

Comment on mathematical models which describe transcription and calculate the relationship between mRNA and protein expression ratio.

Mathematical models to describe transcription (Arnold et al. (2001); Biotech Bioeng 72:548-561) and translation (Mehra et al. (2003); Biotech Bioeng 84:822-841) in bacteria are modified in order to improve reaction kinetics and to include the number of polymerase molecules that are active on the DNA, as well as to include the number of ribosomes that are active on the nascent and on the completed mRNA, respectively.

Bacteria↗
PubMed2003

Mathematical modelling of adsorption and transport processes in capillary electrochromatography: open-tubular geometry.

A mathematical modelling approach for open-tubular capillary electrochromatography is presented. The spatially one-dimensional model takes into account (i) a coupling of (non)linear adsorption of positively or negatively charged analyte molecules (at a negatively charged capillary inner surface) with the equilibrium electrokinetics at this solid-liquid interface, (ii) mobile phase transport by electroosmosis and pressure-driven flow, as well as (iii) transport of species by electrophoresis and molecular diffusion. Under these conditions the local zeta-potential and electroosmotic mobility become a function of the concentration of the charged analyte. The resulting inhomogeneity of electroosmotic flow through the capillary produces a compensating pore pressure as requirement for incompressible mobile phase flow (i.e., for constant volumetric flow along the capillary). The results of the simulations are discussed in view of the surface-to-volume ratio of the capillary lumen, the analyte concentration (in combination with a Langmuir isotherm for the adsorption process), and buffer effects.

Adsorption↗
PubMed2006

Pesticide exposure assessment in rice paddies in Europe: a comparative study of existing mathematical models.

A comparative test was undertaken in order to identify the potential of existing mathematical models, including the rice water quality (RICEWQ) 1.6.4v model, the pesticide concentration in paddy field (PCPF-1) model and the surface water and groundwater (SWAGW) model, for calculating pesticide dissipation and exposure in rice paddies in Europe. Previous versions of RICEWQ and PCPF-1 models had been validated under European and Japanese conditions respectively, unlike the SWAGW model which was only recently developed as a tier-2 modelling tool. Two datasets, derived from field dissipation studies undertaken in northern Italy with the herbicides cinosulfuron and pretilachlor, were used for the modelling exercise. All models were parameterized according to field experimentations, as far as possible, considering their individual deficiencies. Models were not calibrated against field data in order to remove bias in the comparison of the results. RICEWQ 1.6.4v provided the highest agreement between measured and predicted pesticide concentrations in both paddy water and paddy soil, with modelling efficiency (EF) values ranging from 0.78 to 0.93. PCPF-1 simulated well the dissipation of herbicides in paddy water, but significantly underestimated the concentrations of pretilachlor, a chemical with high affinity for soil sorption, in paddy soil. SWAGW simulated relatively well the dissipation of both herbicides in paddy water, and especially pretilachlor, but failed to predict closely the pesticide dissipation in paddy soil. Both RICEWQ and SWAGW provided low groundwater (GW) predicted environmental concentrations (PECs), suggesting a low risk of GW contamination for the two herbicides. Overall, this modelling exercise suggested that RICEWQ 1.6.4v is currently the most reliable model for higher-tier exposure assessment in rice paddies in Europe. PCPF-1 and SWAGW showed promising results, but further adjustments are required before these models can be considered as strong candidates for inclusion in the higher-tier pesticide regulatory scheme.

Environmental Exposure↗
PubMed1977

Mathematical model of pituitary thyrotropic function.

A nonlinear differential equation is used to develop a mathematical model describing the time course of thyrotropin (TSH) concentral to real data shows that pituitary responsiveness to TRH is highest in euthyroidism, reduced in primary hypothyroidism, and lowest in hyperthyroidism.

Feedback↗
PubMed1992

Application and validation of a three-dimensional mathematical model of the human masticatory system in vivo.

A previously described three-dimensional mathematical model of the human masticatory system, predicting maximum possible bite forces in all directions and the recruitment patterns of the masticatory muscles necessary to generate these forces, was validated in in vivo experiments. The morphological input parameters to the model for individual subjects were collected using MRI scanning of the jaw system. Experimental measurements included recording of maximum voluntary bite force (magnitude and direction) and surface EMG from the temporalis and masseter muscles. For bite forces with an angle of 0, 10 and 20 degrees relative to the normal to the occlusal plane the predicted maximum possible bite forces were between 0.9 and 1.2 times the measured ones and the average ratio of measured to predicted maximum bite force was close to unity. The average measured and predicted muscle recruitment patterns showed no striking differences. Nevertheless, some systematic differences, dependent on the bite force direction, were found between the predicted and the measured maximum possible bite forces. In a second series of simulations the influence of the direction of the joint reaction forces on these errors was studied. The results suggest that they were caused primarily by an improper determination of the joint force directions.

Adult↗
PubMedDate not supplied

Mathematical modelling of growth of Escherichia coli at subinhibitory levels of chloramphenicol or tetracyclines.

A mathematical model is suggested to describe the subinhibitory effects of chloramphenicol upon growth of Escherichia coli. It represents a generalization of Monod's equation. Our model was constructed entirely on the basis of biochemical factors, such as the reversibility of the interaction between the drug and its ribosomal target or intracellular uptake. The subinhibitory effects of chloramphenicol were satisfactorily described by this law within the range of 0.4-2.4 micrograms/ml. After simplifying the equation, this model was extrapolated to provide an accurate description of the mode of action of other bacteriostatic antibiotics which also inhibit the 50-S ribosomal subunit (tetracycline and doxycycline). The expanded model seems to accurately typify the effect of these antibiotics, whereas bactericidal aminoglycosides follow a completely different growth law.

Chloramphenicol↗
PubMed2006

Mathematical models to assess strategies for the control of gastrointestinal roundworms in cattle 1. Construction.

Mathematical models were constructed to simulate the effect of Ostertagia ostertagi infections on the growth of young cattle. The equations are based on System Dynamics using the DYSMAP 2 software package in their construction. A pasture and animal growth model simulates the growth of pasture and the influences of management and climate on it; cattle feed intake and conversion into energy for maintenance and liveweight gain; the effect of the parasite burden on feed intake and utilization of energy. This model was then combined with one of the life cycle of O. ostertagi in order to determine the effect of worm burdens on animal growth rate in a range of farm conditions, such as stocking rate, grazing history of the pasture, and rainfall. By converting the resultant liveweight gain into a monetary value, an economic assessment of alternative worm control strategies can be made. In this paper the construction of the models with equations and assumptions is given in detail.

Algorithms↗
PubMed2002

A mathematical model predicts that calreticulin interacts with the endoplasmic reticulum Ca(2+)-ATPase.

A robust mathematical model developed from single cell calcium (Ca(2+)) dynamics has enabled us to predict the consequences of over-expression of endoplasmic reticulum-located chaperones. Model predictions concluded that calreticulin interacts with the lumenal domain of the sarcoplasmic and endoplasmic reticulum Ca(2+)-activated ATPase (SERCA) pump, altering pump affinity for Ca(2+) (K(1/2) switches from 247 to 431 nM) and hence generating Ca(2+) oscillations. Expression of calreticulin in the ER generated an average of six transient-decline oscillations during the Ca(2+) recovery phase, upon exposure to maximal levels of the agonist ATP. In contrast, normal cells produced a single Ca(2+) transient with few or no oscillations. By conditioning the model to experimental data, parameters for generation and decay of IP(3) and SERCA pump kinetics were determined. To elucidate the possible source of the oscillatory behavior three possible oscillators, 1) IP(3), 2) IP(3)R, and 3) SERCA pump, were investigated and parameters constrained by experimental data to produce the best candidate. Each of the three oscillators generated very good fits with experimental data. However, converting a normal exponential recovery to a transient-decline oscillator predicted that the SERCA pump is the most likely candidate for calreticulin-mediated Ca(2+) release, highlighting the role of this chaperone as a signal protein within the endoplasmic reticulum.

Calcium↗
PubMed2002

Mathematical modeling of PCB bioaccumulation in Perna viridis.

In the present work, we built a mathematical model of polychlorinated biphenyl (PCB) bioaccumulation in Perna viridis, namely, a one-compartment model with a time dependent incorporation rate R (microg g(-1) lipid per ppb water per day), with positive substrate cooperativity as the underlying physical mechanism. The temporal change of the PCB concentration Q (microg g(-1) lipid) in the soft tissues of the mussel depends on the competition of the input rate R Wand the output rate kQ, where W is the concentration of PCB in water (ppb water) and k is the elimination rate (per day). From our experimental data, k = 0.181 +/- 0.017 d(-1). The critical concentration in water Wc for positive substrate cooperativity was found to be approximately 2.4 ppb. Below Wc, R is a constant. For a water concentration of 0.5 ppb Aroclor 1254, R = 24.0 +/- 2.4 microg g(-1) lipid ppb(-1) d(-1). Above Wc, positive substrate cooperativity comes into effect and R becomes a function of time and dependent on the concentration Q in a form R = gammaQ/(Q + delta). This is the case for a water concentration of 5 ppb Aroclor 1254, where gamma = 15.1 microg g(-1) lipid ppb(-1) d(1) and delta approximately 200 microg g(-1) lipid. From this model, the uptake is exponentially increasing when the PCB concentration in the mussel is small compared to 200 microg g(-1) lipid, and hyperbolically increasing when the concentration is large compared to 200 microg g(-1) lipid, which are consistent with the experimental data. The model is useful for understanding the true processes taking place during the bioaccumulation and for risk assessment with higher confidence. Future experimental data which challenge the present model are anticipated and in fact desirable for improvement and perfection of

Animals↗
PubMed1993

A mathematical model for regeneration rate and initial delay following surgical repair of peripheral nerves.

A mathematical model is presented by which the regeneration rate and initial delay for peripheral nerve regeneration can be calculated from sensory pinch test data following surgical repair of peripheral nerves. The model is based on the assumption that experimental variations in regeneration distances between animals is due to the initial delay period--the time period before the regenerating fibers cross the suture line whereas the rate of regeneration is constant. This model which accounts for all observed data including 'regenerating failures' showed that nerve fibers in the rat sciatic nerve repaired with a fresh nerve graft regenerated at a rate of 1.5 mm/day after an initial delay of 3.6 days.

Animals↗
PubMed2003

MEAD (part I)--a mathematical model of the long-term dispersion of radioactivity in shelf sea environments.

A mathematical model (MEAD) that simulates the transport of radioactivity in shelf-sea environments is presented. In the model it is assumed that the radioactivity can be present in three phases and transport both within and between the phases is captured. The set-up of the model for the Irish Sea is described and results from a simple discharge scenario are presented for (137)Cs and (239)Pu. From these results it appears that MEAD provides a good representation of the transport of radionuclides in the Irish Sea.

Forecasting↗
PubMed1999

Development of a mathematical model for the water distribution in freeze-dried solids.

PURPOSE: Development of a mathematical model to provide information about the amount of water associated with a protein and an excipient in a lyophilized product. METHODS: The moisture content of the product and the mass fraction of each component were used to derive a model for the calculation of the mass of water associating with each component. The model was applied to lyophilized formulations of rhDNase containing various amounts of mannitol or lactose. The total water content was investigated by thermogravimetry, crystalline properties by X-ray powder diffraction and water uptake behaviour using a moisture microbalance system. RESULTS: Calculations based on the model suggest that in a lyophilized rhDNase-mannitol formulation where the sugar is crystalline, most of the water is taken up by the protein. However, in the lyophilized rhDNase-lactose formulation where the sugar is amorphous, water is taken up by both the sugar and protein to a comparative extent. At high relative humidities when the amorphous sugar undergoes crystallization, the model can accommodate such a change by allowing for the formation of an additional crystalline phase. CONCLUSIONS: The rhDNase-sugar formulations show excellent conformity to the model which provides quantitative information about the distribution of water in the lyophilized binary protein-excipient products.

Crystallography, X-Ray↗
PubMed2002

A mathematical model of the stability control of human thorax and pelvis movements during walking.

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.

Algorithms↗
PubMed1990

Epigenesis theory: a mathematical model relating causal concepts of pathogenesis in individuals to disease patterns in populations.

A mathematical modeling approach called epigenesis theory is presented which relates three aspects of pathogenesis to the population distribution of disease. The three aspects of pathogenesis involve how two or more measured variables interact. They are 1) whether the measured variables are related to the same causal action, 2) whether there is only one pathogenic process leading to disease, and 3) whether the measured variables contribute to the same pathogenic process. Epigenesis theory defines the following multivariable relations between two disease causes: 1) "Complementary" causes contribute different causal actions to the sole pathogenic process leading to disease. They have multiplicative relations. 2) "Separate process" causes contribute different causal actions to different pathogenic processes. They have the relations of simple independent action which are slightly less than additive. 3) "Intermediate" causes contribute different causal actions to the same pathogenic process in the presence of additional pathogenic processes where at most one of them may also participate. They have relations somewhere between multiplicative and simple independent actions. 4) "Cooperative-competitive" causes share the same causal action and act within the same pathogenic process. Their relations can change from greater than multiplicative to less than simple independent action at increasing dichotomization points of the measured variables. Epigenesis theory unifies the sufficient-component causes model and the simple independent action model and exceeds either model in the range of observations it can explain. It is most useful given directly causal measured variables and specific disease outcomes, but it will assist in etiologic investigations of nonspecific outcomes in which new disease classifications are proposed. While it is less useful given surveillance-type variables such as age or sex or outcomes resulting from numerous pathogenic processes such as death, it gains utility as more causal variables are entered into an analysis and as more cut points of continuous complementary, independent, or intermediate variables are distinguished.

Adult↗
PubMed1998

A mathematical model for skeletal muscle activated by N-let pulse trains.

A physiologically based mathematical model for skeletal muscle activated by neural impulses is presented. This model is developed specifically to capture the behavior for mammalian skeletal muscle activated by N-lets (sets of N high-frequency pulses with variable interpulse intervals). N-let pulse trains have been demonstrated as a possible means of producing contractions with reduced fatigue and fiber-type transformation, while maximizing the force-time integral per pulse (FTIpP) of electrically stimulated muscle. This model is developed by modeling the underlying biophysical processes responsible for the initiation and maintenance of force generation in muscle. The release and reaccumulation dynamics of calcium ions from the sarcoplasmic reticulum are modeled and proposed as the governing mechanism for the observed N-let effects. It is found that the new model is robust, numerically stable and easily implemented. Simulation results are presented that demonstrate the model's ability to capture a variety of the nonlinear summation, force and stiffness variation effects seen experimentally when activating skeletal muscle with N-lets. General properties of FES muscle are also predicted by the model. The significant insight provided by this model into the internal dynamics of skeletal muscle is used to assess a variety of mechanisms proposed for N-let behavior. It is postulated that the calcium release and reaccumulation dynamics, as incorporated in this model, are responsible for the N-let effects found in experiment.

Calcium↗
PubMed2004

A mathematical model of haemopoiesis as exemplified by CD34 cell mobilization into the peripheral blood.

A mathematical model for the kinetics of haemopoietic cells, including CD34+cells, is proposed. This minimal model reflects the known kinetics of haemopoietic progenitor cells, including peripheral blood CD34+ cells, white blood cells and platelets, in the presence of granulocyte colony-stimulating factor. Reproducing known perturbations within this system, subjected to granulocyte colony-stimulating factor treatment and apheresis of peripheral blood progenitor cells (CD34+ cells) in healthy individuals allows validation of the model. Predictions are made with this model for reducing the length of time with neutropenia after high-dose chemotherapy. Results based on this model indicate that myelosuppressive treatment together with infusion of CD34+ peripheral blood progenitor cells favours a faster recovery of the haemopoietic system than with granulocyte colony-stimulating factor alone. Additionally, it predicts that infusion of white blood cells and platelets can relieve the symptoms of neutropenia and thrombocytopenia, respectively, without drastically hindering the haemopoietic recovery period after high dose chemotherapy.

Antigens, CD34↗
PubMed2002

A mathematical model of rat collecting duct. I. Flow effects on transport and urinary acidification.

A mathematical model of the rat collecting duct (CD) has been developed by concatenating previously published models of cortical (Weinstein AM. Am J Physiol Renal Physiol 280: F1072-F1092, 2001); outer medullary (Weinstein AM. Am J Physiol Renal Physiol 279: F24-F45, 2000); and inner medullary segments (Weinstein AM. Am J Physiol Renal Physiol 274: F841-F855, 1998). Starting with end-distal tubular flow rate and composition, plus interstitial solute profiles, the model predicts urinary solute flows, including the buffer concentrations required to assess net acid excretion. In the model CD, the interstitial corticomedullary osmotic gradient provides the basis for the flow effect on the transport of several solutes. For substances that have an interstitial accumulation and that can have diffusive secretion (e.g., urea and NH(4)(+)), enhanced luminal flow increases excretion by decreasing luminal accumulation. For substances that are reabsorbed (e.g., K+ and HCO(3)(-)), and for which luminal accumulation can enhance reabsorption, increasing luminal flow again increases excretion by decreasing luminal solute concentration. In model calculations, flow-dependent increases in HCO(3)(-) and NH(4)(+) approximately balance, so net acid excretion is little changed by flow, albeit at a higher urinary pH. The model identifies delivery flow rate to the CD as a potent determinant of urinary pH, with high flows blunting maximal acidification. At even modestly high flows (9 nl x min-1. tubule-1, with 6% of filtered Na+ entering the CD), the model cannot achieve a urinary pH <5.5 unless the delivered HCO(3)(-) concentration is extremely low (<2 mM). Nevertheless, simulation of Na2SO4 diuresis does yield both an increase in net acid excretion and a decrease in urinary HCO(3)(-) (i.e., a decrease in pH) despite the increase in urinary flow. This model should provide a tool for examining hypotheses regarding transport defects underlying distal renal tubular acidosis.

Acids↗