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PubMed2002

Ambulatory venous pressure measurements: new parameters derived from a mathematic hemodynamic model.

PURPOSE: The mechanism of venous pressure decrease during exercise still remains unclear. To explore the components involved with the regulation of ambulatory venous pressure, we reinvestigated the pattern of pressure decrease during tiptoe exercise with a newly developed mathematic model. METHODS: Seventeen healthy limbs of 16 volunteers (normal group) and 35 limbs of 33 patients with signs and symptoms of chronic venous insufficiency were studied. Seventeen limbs had superficial venous incompetence (SVI), and 18 showed deep venous incompetence with or without concomitant superficial venous reflux. All subjects were examined with ambulatory venous pressure measurements. As parameters obtained from serial phasic changes in pressure during tiptoe movements, the pressure reduction fraction per step (decreasing component) and the pressure increase per step (increasing component) were calculated with application of the mathematic hemodynamic model and assessed comparatively in the three groups with different types of reflux (normal, SVI, and deep venous incompetence group). RESULTS: The pressure increase per step was significantly different in each of the three groups (P <.0001, with analysis of variance), whereas no apparent difference was seen in the mean pressure reduction fraction per step among the groups. With addition of the inflation of ankle cuff, the value of pressure increase in limbs with SVI was significantly reduced (P =.0004, with Wilcoxon signed rank test), although no changes were seen in the pressure reduction fraction in each group. CONCLUSION: Our results indicate that the pressure reduction fraction, representing calf muscle pump function, is independent of the existence or site of valve incompetence. On the other hand, the pressure increase, corresponding to the degree of reflux during exercise, correlates strongly with the severity of venous insufficiency. The theoretic model can separate the two components responsible for ambulatory venous pressure changes, calf muscle pump function and venous reflux, and provide better understanding of venous hemodynamics.

Blood Pressure Monitoring, Ambulatory↗
PubMed2006

An opposite role for tau in circadian rhythms revealed by mathematical modeling.

Biological clocks with a period of approximately 24 h (circadian) exist in most organisms and time a variety of functions, including sleep-wake cycles, hormone release, bioluminescence, and core body temperature fluctuations. Much of our understanding of the clock mechanism comes from the identification of specific mutations that affect circadian behavior. A widely studied mutation in casein kinase I (CKI), the CKIepsilon(tau) mutant, has been shown to cause a loss of kinase function in vitro, but it has been difficult to reconcile this loss of function with the current model of circadian clock function. Here we show that mathematical modeling predicts the opposite, that the kinase mutant CKIepsilon(tau) increases kinase activity, and we verify this prediction experimentally. CKIepsilon(tau) is a highly specific gain-of-function mutation that increases the in vivo phosphorylation and degradation of the circadian regulators PER1 and PER2. These findings experimentally validate a mathematical modeling approach to a complex biological function, clarify the role of CKI in the clock, and demonstrate that a specific mutation can be both a gain and a loss of function depending on the substrate.

Animals↗
PubMed1995

Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: application to the feedbacks of blood coagulation.

A hierarchy of enzyme-catalyzed positive feedback loops is examined by mathematical and numerical analysis. Four systems are described, from the simplest, in which an enzyme catalyzes its own formation from an inactive precursor, to the most complex, in which two sequential feedback loops act in a cascade. In the latter we also examine the function of a long-range feedback, in which the final enzyme produced in the second loop activates the initial step in the first loop. When the enzymes generated are subject to inhibition or inactivation, all four systems exhibit threshold properties akin to excitable systems like neuron firing. For those that are amenable to mathematical analysis, expressions are derived that relate the excitation threshold to the kinetics of enzyme generation and inhibition and the initial conditions. For the most complex system, it was expedient to employ numerical simulation to demonstrate threshold behavior, and in this case long-range feedback was seen to have two distinct effects. At sufficiently high catalytic rates, this feedback is capable of exciting an otherwise subthreshold system. At lower catalytic rates, where the long-range feedback does not significantly affect the threshold, it nonetheless has a major effect in potentiating the response above the threshold. In particular, oscillatory behavior observed in simulations of sequential feedback loops is abolished when a long-range feedback is present.

Blood Coagulation↗
PubMed1997

The problem of the spreading of a liquid film along a solid surface: a new mathematical formulation.

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds-i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Journal Article↗
PubMed1999

Competition for antigenic sites during T cell proliferation: a mathematical interpretation of in vitro data.

By fitting different mathematical T cell proliferation functions to in vitro T cell proliferation data, we studied T cell competition for stimulatory signals. In our lymphocyte proliferation assays both the antigen (Ag) availability and the concentration of T cells were varied. We show that proliferation functions involving T cell competition describe the data significantly better than classical proliferation functions without competition, thus providing direct evidence for T cell competition in vitro. Our mathematical approach allowed us to study the nature of T cell competition by comparing different proliferation functions involving (i) direct inhibitory T-T interactions, (ii) Ag-specific resource competition, or (iii) resource competition for nonspecific factors such as growth factors, and access to the surface of Ag-presenting cells (APCs). We show that resource competition is an essential ingredient of T cell proliferation. To discriminate between Ag-specific and nonspecific resource competition, the Ag availability was varied in two manners. In a first approach we varied the concentration of APCs, displaying equal ligand densities; in a second approach we varied the Ag density on the surface of the APCs, while keeping the APC concentration constant. We found that both resource competition functions described the data equally well when the Ag availability was increased by adding APCs. When the APC concentration was kept constant, the nonspecific resource competition function yielded the best description of the data. Our interpretation is that T cells were competing for "antigenic sites" on the APCs.

Algorithms↗
PubMed1995

Mathematical model of serine protease inhibition in the tissue factor pathway to thrombin.

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation.

Animals↗
PubMed2006

Mathematical modeling of polyamine metabolism in mammals.

Polyamines are considered as essential compounds in living cells, since they are involved in cell proliferation, transcription, and translation processes. Furthermore, polyamine homeostasis is necessary to cell survival, and its deregulation is involved in relevant processes, such as cancer and neurodegenerative disorders. Great efforts have been made to elucidate the nature of polyamine homeostasis, giving rise to relevant information concerning the behavior of the different components of polyamine metabolism, and a great amount of information has been generated. However, a complex regulation at transcriptional, translational, and metabolic levels as well as the strong relationship between polyamines and essential cell processes make it difficult to discriminate the role of polyamine regulation itself from the whole cell response when an experimental approach is given in vivo. To overcome this limitation, a bottom-up approach to model mathematically metabolic pathways could allow us to elucidate the systemic behavior from individual kinetic and molecular properties. In this paper, we propose a mathematical model of polyamine metabolism from kinetic constants and both metabolite and enzyme levels extracted from bibliographic sources. This model captures the tendencies observed in transgenic mice for the so-called key enzymes of polyamine metabolism, ornithine decarboxylase, S-adenosylmethionine decarboxylase and spermine spermidine N-acetyl transferase. Furthermore, the model shows a relevant role of S-adenosylmethionine and acetyl-CoA availability in polyamine homeostasis, which are not usually considered in systemic experimental studies.

Acetyl Coenzyme A↗
PubMed2003

Mathematics and the gap junctions: in-phase synchronization of identical neurons.

A close consideration of some mathematical results with regards to neuronal synchronization mechanisms are examined. It is well known that intercellular coupling via gap junctions normally occurs between identical neurons, such as the coupling between inhibitory interneurons belonging to the same class. It is unknown why this should happen. The theory of coupled oscillators offers some explanations to answer the questions of the functional role of electrical interactions mediated by gap junctions and the necessity to couple identical neurons. The inference presented here from the mathematical results is that only if the cells are identical will their firing synchronize in-phase. Thus, we propose the concept that the functional role of gap junctional electrical coupling is to synchronize neurons in-phase and therefore this type of coupling will be found between neurons belonging to the same class.

Action Potentials↗
PubMed1985

Mathematical models of central pattern generators in locomotion: I. Current problems.

As a background for subsequent studies of mathematical models of central pattern generators in locomotion (Stafford & Barnwell, 1985a, b) relevant aspects of the literature on locomotion are reviewed, concepts of locomotion discussed, and extant models considered. Advantages and disadvantages of present models are discussed, and the need for mathematical models is emphasized. It is shown that realistic models of pattern generation in locomotion must take numerous factors into account, including phases of step cycle, muscle sequencing, gait and interlimb coordination, initiation and cessation of locomotion, and many aspects of neuromuscular control and function.

Journal Article↗
PubMed2000

Mathematical leadership vision.

This article is an analysis of a new type of leadership vision, the kind of vision that is becoming increasingly pervasive among leaders in the modern world. This vision appears to offer a new horizon, whereas, in fact it delivers to its target audience a finely tuned version of the already existing ambitions and aspirations of the target audience. The leader, with advisors, has examined the target audience and has used the results of extensive research and statistical methods concerning the group to form a picture of its members' lifestyles and values. On the basis of this information, the leader has built a "vision." The vision is intended to create an impression of a charismatic and transformational leader when, in fact, it is merely a response. The systemic, arithmetic, and statistical methods employed in this operation have led to the coining of the terms mathematical leader and mathematical vision.

Humans↗
PubMed1994

A nonlinear mathematical model for the development and rupture of intracranial saccular aneurysms.

Mathematical models of aneurysms are typically based on Laplace's law which defines a linear relation between the circumferential tension and the radius. However, since the aneurysm wall is viscoelastic, a nonlinear model was developed to characterize the development and rupture of intracranial spherical aneurysms within an arterial bifurcation and describes the aneurysm in terms of biophysical and geometric variables at static equilibrium. A comparison is made between mathematical models of a spherical aneurysm based on linear and nonlinear forms of Laplace's law. The first form is the standard Laplace's law which states that a linear relation exists between the circumferential tension, T, and the radius, R, of the aneurysm given by T = PR/2t where P is the systolic pressure. The second is a 'modified' Laplace's law which describes a nonlinear power relation between the tension and the radius defined by T = ARP/2At where A is the elastic modulus for collagen and t is the wall thickness. Differential expressions of these two relations were used to describe the critical radius or the radius prior to aneurysm rupture. Using the standard Laplace's law, the critical radius was derived to be Rc = 2Et/P where E is the elastic modulus of the aneurysm. The critical radius from the modified Laplace's law was R = [2Et/P]2At/P. Substituting typical values of E = 1.0 MPa, t = 40 microns, P = 150 mmHg, and A = 2.8 MPa, the critical radius is 4.0 mm using the standard Laplace's law and 4.8 mm for the modified Laplace's law.(ABSTRACT TRUNCATED AT 250 WORDS)

Aneurysm, Ruptured↗
PubMed1995

Normal pressure hydrocephalus: an analysis of aetiology and response to shunting based on mathematical modeling.

The dynamics which maintain the state of enlarged cerebral ventricles and normal intracranial pressures (normal pressure hydrocephalus) are not completely understood, making the response to cerebrospinal fluid diversion difficult to predict. Using our previously described mathematical model of intracranial physiology which allows nonlinear relationships of pressure, volume, and flow in 7 distinct compartments, we desired to determine factors which could be responsible for the development and maintenance of the steady state of normal pressure hydrocephalus. Using typical starting values for CSF volume, pressure, and flow, the model indicates that this condition cannot be sustained, in spite of high CSF outflow resistance, unless capillary flow resistance is elevated. This condition can be the result of arterial hypertension. The additional modeling of a CSF diversion device demonstrates predicted time courses for ventricular size reduction which are consistent with clinical observations. We conclude that certain vascular conditions may allow for the maintenance of an enlarged ventricular size, and that mathematical modeling can assist in identifying factors for clinical study that may maintain normal pressure hydrocephalus even after treatment by CSF diversion.

Cerebral Ventricles↗
PubMed2000

Mean pressures and flows in the human intracranial system as determined by mathematical simulations of a steady-state infusion test.

In order to understand the fluid dynamics within the human intracranial system, the relatively small flow of extracellular fluid into, and out of, the interstitial brain tissue must be determined. Due to the magnitude of these flows, it is difficult to measure them clinically. Through a steady-state infusion simulation run on a mathematical model, values for these small flows may be calculated based on clinical data regarding the conductance of cerebrospinal fluid outflow. In this way, the mathematical model allows information to be obtained regarding these small mean flows, as well as the remaining mean flows and mean pressures throughout the intracranial space, with minimal reliance on data from intrusive procedures.

Blood-Brain Barrier↗
PubMed2003

The baton exchange during the 4 x 100 m relay: a mathematical analysis.

Using mathematical analysis, we examined the three baton exchanges that occur during a 4 x 100 m relay. Identical representative 100 m running performances were assumed for each of four elite male athletes, and the calculations were made for optimal or near-optimal positions of the baton exchanges and starting positions of the athletes running the second, third and fourth legs as determined by Ward-Smith and Radford (2002). In this paper, we focus on the calculation of the checkmark position and demonstrate the complexity of the baton exchange process. The results of the mathematical analysis show that, for optimal performance, the checkmark should be located differently for each of the three exchanges in a single race, and is further affected bylane draw and free distance (the distance between the runners at the baton exchange). For a representative free distance of 1 m at each exchange, the checkmark distance ranges from a minimum of 11.04 m at the third exchange in Lane 1 to 12.20 m for the first exchange in Lane 8. Failure by teams and their coaches to consider adequately the complexities of the baton exchanges may help explain why 25.5% of teams in recent World Championships were disqualified or did not finish.

Humans↗
PubMed2005

A mathematical model for ocular tear and solute balance.

PURPOSE: In this paper we develop a mathematical model that can predict the steady-state tear film thickness and the dynamic tear film thickness and the solute concentration after instillation of a solute-laden fluid in the eye. METHODS: The mathematical model developed in this paper is based on a balance between the inflow and outflow of tears into the tear film. It incorporates a tear drainage model and a model that relates the tear film thickness to the meniscus radius of curvature. To predict the solute concentrations, the tear balance is coupled with the solute balance. The differential equations for the unsteady balances are solved numerically. RESULTS: The model predicts that the tear film thickness depends on a number of physiological factors, such as rates of tear production and evaporation, geometry and modulus of the canaliculi, and surface tension and viscosity of tears, and varies from about 3 to 15 microm. The model also predicts that the drainage time for an instilled volume of 15 microl is 1283 s. Additionally, the time required for the tracer concentration to decay to 1% of the value immediately after instillation of a drug-laden 40 microl drop is about 2480 s. Similarly, the time for intensity decay for a radioactive tracer after 25 microl instillation is about 1566 s. Also, the model predicts that the fraction of the instilled drug that reaches the cornea is about 1.3% for topical application of timolol. CONCLUSIONS: The predicted results agree reasonably with the reported experimental results, at least qualitatively. The model developed here can serve as a useful tool to develop a more precise understanding of various issues related to tears and also evaluate the effect of various parameters on the tear volume.

Eye↗
PubMedDate not supplied

A mathematical model of mandibular movement on the Hanau articulator and computerized simulation system of dynamic occlusion for complete denture.

This study is concerned with the construction of a mathematical model of mandibular movement on the Hanau articulator and a complete denture occlusion simulation system (CDOSS) in the field of dental restoration. On the basis of the theory of spatial mechanisms, degrees of freedom in the kinematic chain of the Hanau articulator are analysed, and a hypothesis of constraints is presented to obtain constrained motion. Then, a series of mathematical expressions are derived to describe the three dimensional mandibular movement on the Hanau articulator. By adopting techniques and tools such as laser scanning, computer graphics, and computer databases, a 3D digitized model of complete denture is reconstructed, and a CDOSS is developed. With the aid of this software, the visualization and diagnosis of mandibular movement can be easily realized. One edentulous case discussed in this study shows that CDOSS provides a useful tool to deal with the functional aspects of occlusal morphology in a diagnostic and therapeutic sense.

Aged↗
PubMedDate not supplied

Mathematical model of chloride concentration in human blood.

This paper deals with mathematical modelling of blood chloride concentration. The main features of the model are that it reveals mathematically the physiological relationship between blood chloride and other electrolytes and serves as an accurate indirect method for chloride measurements with accuracy fulfilling clinical requirements. The main advantages of the method based on this model are that it is more comfortable than traditional methods and clinically less harmful for the patient under study. Experimental verification of the developed model ensures that the results of chloride measurements obtained using this model are significantly correlated with the results for the blood samples obtained from standard chloride analysers.

Algorithms↗
PubMed2003

Estimation of polishing and leaching behaviour of antifouling paints using mathematical modelling: a literature review.

The development of chemically active antifouling paints has traditionally been based on an empirical approach. Optimisation and evaluation of novel and existing products are frequently conducted by means of, for example, systematic paint rotary tests in the laboratory or at sea sites. In this review, the usefulness of combining rotary experiments with the development of detailed mathematical models of paint behaviour will be discussed with reference to the relevant literature. Mathematical models can generally be used in the design of suitable release systems for various active components such as proteins or biocides, as well as for the estimation of release rates from different compositions of paints under various seawater conditions. Insoluble matrix, soluble matrix and self-polishing paints will be considered. Simulations from recent publications that show the effects of dynamic changes in seawater on paint behaviour will be presented. Examples of potential uses of paint models for accelerated polishing and leaching tests and screening of novel paint components will also be discussed. Directions of future modelling work are suggested.

Materials Testing↗