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At least 883 records · Page 49Linked to original sources
PubMed1991

Age, time since menopause, and body parameters as determinants of female spinal bone mass: a mathematical model.

The study of mathematical models to describe bone mass behavior throughout life is a possibility for assessing the main factors of peak bone mass and bone loss. We developed a mathematical model to predict spinal bone mass behavior on a sample of 181 healthy Italian women whose lumbar bone mineral content was determined by Gd-153 dual photon absorptiometry. This model proved to be both efficient, showing the best fit (r = 0.7 on spinal bone mineral content) when compared to other previously suggested models, and also reliable as its fit remained the best when applied to a subsequent sample of 519 women whose lumbar spine was measured by dual X-ray photon absorptiometry. This model suggests that body height and body weight (but not age) are determinants of bone mass in premenopausal women. In postmenopausal women, an accelerated phase of bone loss starting at menopause is dependent on age and time since menopause, whereas body mass index acts as a protective factor. This model confirms the influence on spinal bone mass not only of age and time since menopause but also of body size parameters.

Absorptiometry, Photon↗
PubMedDate not supplied

Mathematical analysis of type-I and type-IIb muscle fiber force generation in renal hypertension.

Previous results from our laboratory have shown that isometric tension development is significantly lower in reduced renal mass (RRM) hypertensive rats when compared to sham-operated controls. The current study was designed to mathematically analyze isometric tetanic contraction profiles and determine the relative contribution of fast-glycolytic (FG) and slow-oxidative (SO) muscle fibers produced by the isolated gastrocnemius-plantaris-soleus muscle group of RRM and sham rats. Because renal hypertension has been shown to be associated with a reduction in microvascular density, we hypothesized that renal hypertension leads to a decrease in SO muscle fiber contribution to force generation. The mathematical model determined the force contribution of two independent muscle fiber components, SO and FG, to the contraction and relaxation phase of isometric tetanic contractions. Each phase was modeled as having an exponentially rising contraction phase during the stimulus period and an exponentially decaying relaxation phase when the stimulus was removed. Each fiber type's tension was also scaled by an envelope function describing the fatigue over the contraction bout. The model, which included 10 parameters, was fit to experimental data by using a nonlinear optimization method and described certain limited characteristics of both fiber types. Results from this model suggest that renal hypertension affects skeletal muscle force generation primarily by decreasing the SO muscle fiber contribution to the total developed tension, decreasing performance and increasing muscle fatigue in RRM rats.

Animals↗
PubMedDate not supplied

Left-to-right shunts. (Quantification, mathematical methods and their statistical comparison).

This work describes a non-traumatic technique for quantitative determination of left-to-right shunts. Various mathematical methods to evaluate the radioisotope concentration lung curve are considered. Data were collected with a gamma camera system connected to a computer. The first results were obtained from 18 patients at the Ospedali Riuniti in Parma, Italy. All the mathematical processes are described. The three methods used were based on: 1. the count ratio (C2/C1) between two pulmonary activity concentrations, 2. the gamma function fitting, 3. decreasing exponential. A comparison of the three methods shows that the gamma function method is the most reliable. In this kind of investigation the patient's radiation dose is low enough for it to be repeated so that the course of the disease can be followed.

Child↗
PubMedDate not supplied

In Haughton's footsteps: mathematical insights into bioengineering and rehabilitation.

Four attempts are outlined which the author has made to develop mathematical models for topics encountered in bioengineering and rehabilitation. The first is autoregulation in the kidney, for which a nonlinear oscillator model is derived, based on observations of flow noise made by Erol Basar. The second is a nonlinear observer based on the theory of automatic control, developed to study patterns of spastic torque in paralysed legs via the pendulum test. The third is a design study of a skeletal muscle reflex arc involving the muscle spindle dynamics and invoking a principle of optimum stability. The final topic is an attempt to lay the groundwork for a mathematical theory of the cross-bridge or sliding filament mechanism of muscular contraction.

Biomedical Engineering↗
PubMed2001

Mathematical models of eye movements in reading: a possible role for autonomous saccades.

An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory - almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes.

Algorithms↗
PubMed2003

[High resolution fluorescence microscopy in combination with mathematical modelling. First evidence of sub-cellular anesthetic effects on Ca2+ sparks in situ].

Volatile anesthetics used in daily clinical routine, are associated with a rare but life-threatening disease, malignant hyperthermia. To date it is well known that, with the exception of xenon and nitrous oxide, all volatile anesthetics have the potential to trigger calcium (Ca(2+)) release from the sarcoplasmic reticulum, thereby influencing the Ca(2+) homeostasis in muscle fibers. The effects of volatile anesthetics have been previously studied by recording Ca(2+)-activated force transients in muscle fibers and by quantifying the effects on isolated intracellular Ca(2+)-release channels (ryanodin receptors). The use of high resolution fluorescence microscopy methods in combination with spatio-temporal mathematical models allows the effects of volatile anesthetics on functional clusters of ryanodin receptors in mammalian skeletal muscle fibers to be studied in situ for the first time.Thus, the analysis of cellular Ca(2+)-activated force production and single channel properties in conjunction with mathematical models allows the quantification of the effects of volatile anesthetics on Ca(2+)-release in the natural physiological environment on the basis of the underlying molecular architecture. In addition to the basic understanding of alterations in the Ca(2+) homeostasis induced by volatile anesthetics in muscle and nerve cells, the results are also of direct clinical importance for the understanding of the pathogenesis of malignant hyperthermia,where ryanodin receptor mutations are currently thought to result in an increased Ca(2+) release under the influence of volatile anesthetics.

Anesthetics, Inhalation↗
PubMed2002

A mathematical model and mechanism of sublation of dye-surfactant ion complexes.

A study of dye-surfactant ion complexes, bromophenol blue (BB), an anionic dye, with hexadecyl pyridium chloride (HPC) complex, and methane violet (MV), a cationic dye, with sodium docedylbenzensulfonate complex (DBS), was carried out. On the base of the complete transport mechanisms, the Langmuir adsorption and the ion complex equilibrium in aqueous phase, a mathematic model for the ion complex system is obtained with the aid of the 4th Runge-Kuta method and the Mathematic 4.0 and Matlab programs. The effects of many parameters are investigated. A substantial difference is posed between the solvent sublation and solvent extraction. Furthermore, the simulation shows that the model is substantiated with experiments on the solvent sublation of the two kinds of complexes. The results are very different from the models proposed by Wilson et al., which predict very different experimental results.

Journal Article↗
PubMed2006

Mathematical tools in analytical mass spectrometry.

Over the last few decades, mass spectrometry has become a powerful tool for exploring various aspects of molecular processes occurring in biological systems. Such exploration is leading to a greater understanding of various complex life processes; unraveling these processes poses the greatest challenge to contemporary bioscience. With due respect to sample preparation, data analysis is rapidly becoming a major obstacle to the conversion of experimental knowledge into valid conclusions. It is interesting to note that many problems related to mass spectrometry can be solved using techniques from computer science, graph theory and discrete mathematics. The aim of this manuscript is to recollect several essays that demonstrate the power and the need to apply such skills to mass spectrometry data interpretation. Special attention is paid to situations where traditional chemical analysis reaches its limits but mathematical reasoning can still allow us to reach valid conclusions.

Journal Article↗
PubMed2005

A novel mathematical model identifies potential factors regulating bone apposition.

The development of pharmaceutical treatments for bone disease can be enhanced by mathematical models that predict their effects on matrix apposition during cancellous bone remodelling. Therefore, a mathematical model was constructed to simulate the rate of focal bone formation from the number of osteoid-forming osteoblasts at one microsite and their rate of activity. The number of mature osteoid-forming cells was simulated from a relationship describing the proliferation of preosteoblasts. Osteoblast activity was described by Michaelis-Menten enzyme kinetic equations adapted to describe cellular activity. The model incorporates the negative feedback effects on the rates of bone apposition due to the reduction in size of mature osteoblasts with continuing differentiation and the reduction in number of osteoid-forming cells with apoptosis and osteocyte formation. In addition, the rate of mineralisation is limited according to osteoid substrate availability. Results of sensitivity analysis revealed the amount of bone formed at one microsite to be more sensitive to changes in factors that controlled cell growth during proliferation and the number of mature osteoid-forming osteoblasts than to those that determined cellular activity. Matrix and osteocyte signalling were shown to have potentially important roles in controlling rates of osteoid apposition in normal, healthy bone. This simple model supports the critical role of controlled mitotic growth in normal bone apposition. It can also help to explain how the homeostatic processes of bone resorption and apposition during remodelling can be disrupted by growth factors that affect the mitotic fraction and division time of proliferative preosteoblast cells.

Cell Proliferation↗
PubMed1999

Toward a mathematical description of bone biology: the principle of cellular accommodation.

Mathematical theories for bone biology or more specifically, bone mass regulation, should be viewed with considerable interest because they provide powerful tools for prediction of bone mass changes in response to mechanical or humeral stimuli. Frost [1] put forward one such theory when he postulated that bone mass is a controlled mechanical feedback system called the "mechanostat." He suggested that certain hormones and biochemical agents act on bone biology by changing the thresholds (or minimum effective strains) of the mechanostat. Critical examination of the mechanostat theory indicates that it does not conform well with certain experimental observations. In the present paper, a new theory is presented that addresses some of the flaws in the mechanostat. The new theory is based upon the assumption that bone cells react strongly to transients in their environment, but eventually "accommodate" to steady state signals. This cellular accommodation, represented by a relaxation function, forms the basis for mathematical rate equations that describe bone mass changes in response to external stimuli. Importantly, the cellular accommodation theory can have the property of "path dependence," meaning that final bone mass will be dependent upon the temporal sequence of preceding mechanical loading/hormonal events. Bone tissue demonstrates path dependence in its responses to mechanical loading and anabolic agents. Theoretically, it is possible to exploit the nonlinear character of path dependence to maximize the osteogenic effect of various therapeutic regimens. An experimental approach to test this possibility is described.

Adaptation, Physiological↗
PubMed2002

Quantitative assessment of agricultural runoff and soil erosion using mathematical modeling: applications in the Mediterranean region.

Three mathematical models, the runoff curve number equation, the universal soil loss equation, and the mass response functions, were evaluated for predicting nonpoint source nutrient loading from agricultural watersheds of the Mediterranean region. These methodologies were applied to a catchment, the gulf of Gera Basin, that is a typical terrestrial ecosystem of the islands of the Aegean archipelago. The calibration of the model parameters was based on data from experimental plots from which edge-of-field losses of sediment, water runoff, and nutrients were measured. Special emphasis was given to the transport of dissolved and solid-phase nutrients from their sources in the farmers' fields to the outlet of the watershed in order to estimate respective attenuation rates. It was found that nonpoint nutrient loading due to surface losses was high during winter, the contribution being between 50% and 80% of the total annual nutrient losses from the terrestrial ecosystem. The good fit between simulated and experimental data supports the view that these modeling procedures should be considered as reliable and effective methodological tools in Mediterranean areas for evaluating potential control measures, such as management practices for soil and water conservation and changes in land uses, aimed at diminishing soil loss and nutrient delivery to surface waters. Furthermore, the modifications of the general mathematical formulations and the experimental values of the model parameters provided by the study can be used in further application of these methodologies in watersheds with similar characteristics.

Agriculture↗
PubMed2001

Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber.

The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [7]. Its purpose is to characterize genetic variants that occur in many biological experiments. In this paper, a mathematical model which describes the spatial distribution of a bacterial population within the DGC is developed. Mathematical analysis of the model concerning positivity and boundedness of the solutions are given. An ADI (Alternating Direction Implicit) method is constructed for finding numerical solutions of the model and carrying out computer simulations. The numerical results of the model successfully reproduced the patterns that were observed in the experiments using the DGC.

Bacteria↗
PubMed1996

A mathematical model for drug administration by using the phagocytosis of red blood cells.

A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood cells is proposed. The model is based on the following assumption: At time t = 0 a preassigned red blood cell population n(0,a) = phi (a), a > 0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a > or = a (a = 120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than a. Within the red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on the mathematical properties and on the formulation of the control problem.

Drug Therapy↗
PubMed2001

The effect of mathematical modeling on critical velocity.

The purpose of this investigation was to examine the effects of mathematical modeling on critical velocity (CV) estimates and the oxygen consumption (VO2), heart rate (HR), and plasma lactate values that corresponded to the five CV estimates. Ten male subjects performed a maximal, incremental treadmill test to determine maximal VO2, and four randomly ordered treadmill runs for the estimation of CV. Two linear, two nonlinear, and one exponential mathematical models were used to estimate CV. Regression analyses were used to determine the VO2, HR, and plasma lactate values that corresponded to the five CV estimates from the relationships for VO2, HR, and plasma lactate versus running velocity from the maximal, incremental test. The nonlinear, three-component model (Nonlinear-3) resulted in a mean CV that was significantly (P < 0.05) less than the mean values derived from the other four models, and was the lowest CV estimate for each subject. The percent of maximal VO2, HR, and plasma lactate values that corresponded to the Nonlinear-3 model were 89%, 93%, and 63%, respectively. These findings indicate that CV estimates differ by as much as 20% depending upon the model used to determine the characteristics of the velocity/time relationship. Future studies are needed to determine which model provides the most valid estimate of the demarcation point between heavy and severe exercise.

Adult↗
PubMed1999

A mathematical model of the adaptive control of human arm motions.

This paper discusses similarities between models of adaptive motor control suggested by recent experiments with human and animal subjects, and the structure of a new control law derived mathematically from nonlinear stability theory. In both models, the control actions required to track a specified trajectory are adaptively assembled from a large collection of simple computational elements. By adaptively recombining these elements, the controllers develop complex internal models which are used to compensate for the effects of externally imposed forces or changes in the physical properties of the system. On a motor learning task involving planar, multi-joint arm motions, the simulated performance of the mathematical model is shown to be qualitatively similar to observed human performance, suggesting that the model captures some of the interesting features of the dynamics of low-level motor adaptation.

Algorithms↗
PubMed2001

Epileptiform activity in a neocortical network: a mathematical model.

A simple mathematical model describing the generation and propagation of epileptiform activity in a cerebral cortical network is presented. The model consists of a system of nonlinear delay differential equations. Physiological properties are taken into account as nonlinear transmission of signals at the synapse, temporal and spatial summation of incoming signals at the soma, active membrane characteristics, and dendritic and axonal propagation times. The influence of the connectivity and the temporal parameters on the oscillatory properties of the model is studied. The computer simulations are in agreement with experimental observations in cortical networks: whereas a weak excitatory or strong inhibitory synaptic connection strength produces a stationary status with short-lasting responses to external stimuli, increases in excitation or decreases in inhibition induce spontaneous and stimulus-evoked rhythmic discharges. Synaptic burst-like activity is observed only for an intermediate range of excitatory and inhibitory connection strengths and external inputs. The form and duration of the bursts can also be controlled by the temporal parameters. The results demonstrate that relatively simple mathematical equations are sufficient to model some of the network properties underlying the generation and propagation of epileptiform activity.

Epilepsy↗
PubMed2004

A mathematical model for preoperative planning of radiofrequency ablation of hepatic tumors.

BACKGROUND: Radiofrequency ablation (RFA) is rapidly evolving as an effective minimally invasive technique for the treatment of small and unresectable liver tumors. A potential cause of treatment failure is the inability to determine the optimum number of overlapping ablations needed to completely destroy tumors larger than the size of a single ablation. To clarify this relationship, we performed a mathematical evaluation that enables us to accurately estimate the number of ablations needed to completely ablate larger tumors. METHODS: This estimation is based on the assumptions that complete ablation of the surface of a target tumor, including its blood supply, would completely destroy the tumor and that the tumor and ablations produced are perfectly spherical. The smallest possible number of partially overlapping ablations that would completely cover the surface of the target tumor is the same as the number of faces on a regular polyhedron that has a circumscribing diameter equal to or greater than the diameter of the target sphere. RESULTS: This mathematical analysis shows that for a 5-cm ablation device, tumors with diameters ranging between 3.01 and 3.30 cm will require at least four ablations. Tumors between 3.31 and 4.12 cm require six overlapping ablations, and tumors between 4.13 and 6.23 cm require 12 overlapping ablations. The number of ablations needed for larger tumors and for 3-, 4-, 6-, and 7-cm ablation devices are also determined. CONCLUSION: The smallest number of ablations required to completely ablate a spherical target tumor larger than the size of the ablation sphere increases dramatically as tumor size increases. Because this model is geometrically optimized, even a small change in the position of the ablation spheres with respect to the target sphere can leave potentially unablated tumor and thus result in treatment failure.

Catheter Ablation↗
PubMed1999

Diagnostic in normal pressure hydrocephalus: A mathematical model for determination of the ICP-dependent resistance and compliance.

The internationally accepted calculation methods concerning cerebrospinal fluid dynamics proceed from a pressure independent resistance to cerebrospinal fluid outflow. In a new model we focus our attention on the pressure dependency of resistance. In our calculation model we are monitoring the complete pressure course p(t) over the time during and after the infusion. The comparison of the pressure rise On(p) during the infusion and the descent Off(p) after the infusion at the same pressure level allows one to construct all formulas for the compliance C(p) and resistance R(p). The computerized analysis of the results of the intrathecal infusion test using our mathematical computation leads to a simplification of this investigation. The simultaneous measurement of the resistance and compliance during a single investigation allows one to minimize the patient's discomfort. In contrast to the classical methods it is not necessary that the ICP reaches a plateau. Our mathematical method diverges with the description of a pressure dependent slope of the function for the resistance from the static examination models. For that we are able to take the non-linearity of the cerebrospinal fluid resorption into consideration.

Computer Simulation↗