Understanding cyclical thrombocytopenia: a mathematical modeling approach

Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in the platelet count. Although first reported in 1936, the pathogenesis and an effective therapy remain to be identified. Since besides fluctuations in platelet levels the patients hematological profile have been consistently normal, a destabilization of a peripheral control mechanism might play an important role in the genesis of this disorder. In this paper, we investigate through computer simulations the mechanisms underlying the platelet oscillations observed in CT. First, we collected the data published in the last 40 years and quantified the significance of the platelet fluctuations using Lomb-Scargle periodograms. Our analysis reveals that the incidence of the statistically significant periodic data is equally distributed in men and women. The mathematical model proposed in this paper captures the essential features of hematopoiesis and successfully duplicates the characteristics of CT. With the same parameter changes, the model is able to fit the platelet counts and to qualitatively reproduce the TPO oscillations (when data is available). Our results indicate that a variation in the megakaryocyte maturity, a slower relative growth rate of megakaryocytes, as well as an increased random destruction of platelets are the critical elements generating the platelet oscillations in CT.     

Chancroid transmission dynamics: a mathematical modeling approach

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.     

Characterization of brain cancer stem cells: a mathematical approach

Objective:  In recent years, support has increased for the notion that a subpopulation of brain tumour cells in possession of properties typically characteristic of stem cells is responsible for initiating and maintaining the tumour. Unravelling details of the brain tumour stem cell (BTSC) hierarchy, as well as interactions of these cells with various therapies, will be essential in the design of optimal treatment strategies.
Materials and methods:  Motivated by this, we have developed a mathematical model of the BTSC hypothesis that may aid in characterization of brain tumours, as well as in prediction of effective therapeutic strategies, which can be further validated in experimental and clinical studies. At the level of a small number of cells, the model developed herein is stochastic. For larger populations of cancer cells, the model is handled from a deterministic approach.
Results and conclusions:  In the stochastic regime, importance of a relationship between the likelihoods of two distinct types of symmetric BTSC divisions in determining BTSC survival rates becomes apparent, consequently emphasizing the need for a set of biomarkers that are able to better characterize the BTSC hierarchy. At the large scale, we predict the importance of the aforementioned symmetric division rates in dictating brain tumour composition. Furthermore, we demonstrate possible therapeutic benefits of considering combination treatments of radiotherapy and putative BTSC inhibitors, such as bone morphogenetic proteins, while reinforcing the importance of developing novel treatment strategies that specifically target the BTSC subpopulation.     

Quantitative analysis of electrophoretograms: A mathematical approach to super-resolution

A mathematical method is presented for the quantitative analysis of overlapping spots or bands taken from digitized gel patterns. The procedure is applied to both one- and two-dimensional gel electrophoretic separations.     

A mathematical approach to cytoskeletal assembly

The cytoskeleton is a fundamental and important part of cell's structure, and is known to play a large role in controlling the shape, function, division, and motility of the cell. In recent years, the traditional biological and biophysical experimental work on the cytoskeleton has been enhanced by a variety of theoretical, physical and mathematical approaches. Many of these approaches have been developed in the traditional frameworks of physico-chemical and statistical mechanics or equilibrium thermodynamic principles. An alternative is to use kinetic modelling and couch the analysis in terms of differential equations which describe mean field properties of cytoskeletal networks or assemblies. This paper describes two such recent efforts. In the first part of the paper, a summary of work on the kinetics of polymerization, fragmentation, and dynamics of actin and polymers in the presence of gelsolin (which nulceates, fragments, and caps the filaments) is given. In the second part, some of the kinetic models aimed at elucidating the spatio-angular density distribution of actin filaments interacting via crosslinks is described. This model given insight into effects that govern the formation of clusters and bundles of actin filaments, and their spatial distribution. Received: 7 January 1998 / Revised version: 4 March 1998 / Accepted: 7 March 1998     

Mechanism and mathematical modeling of electro-enzymatic denitrification

In this study, a novel nitrate reduction method using an electro-enzymatic system was investigated to treat an aqueous solution containing high concentrations of nitrate. This system was comprised of working electrodes and their counter electrodes, where enzymes for nitrate removal were located inside the microorganisms. A nitrate reduction mechanism for the electro-enzymatic system was proposed and a mathematical model was developed. The modeling results were compared to the experimental results and all the experimental results fit well with the model; thus, the derived mathematical model can be used for reactor control and effluent prediction.     

Outline of a mathematical approach to history

A mathematical model for the development of human society, beginning with the earliest stages of urban cultures, is outlined. In the early stages of history, behavior was characterized largely by adherence to a number of beliefs and prejudices of diffeirent kinds, which were accepted on faith and not subject to critical rational analysis. Due to psychobiological variability a very small number of individuals spontaneously appear at all times who challenge the accepted beliefs and prejudices and do not follow the accepted patterns of social behavior. The effect of these individuals upon the rest of the society, especially upon the younger generation, depends on the facilities with which information spreads in society. In earliest societies, when modern methods of mass communication were unknown, the channels of communication were practically identical with the channels of economic transport. The latter in its turn depended on the nature of the roads, and especially on the presence of waterway, which facilitated transportation. The sizes of the earliest cities and the distances between them were largely determined by relative ease of transporation. Expressions are derived for the average size of the earliest cities and for the average distance between them. The calculated average populations of the earliest cities are of the order of 10³; the distance of the order of 10² km. Both are in agreement with some archaeological findings. An expression for the time spaon required for the development from the earliest stages of urban cultures to the present time is derived and shown to depend on the specific shoreline of the country, that is, the length of the shorline divided by the area of the country. It is pointed out that western Europe's specific shoreline, including land bordering both seas and rivers, is ten times as large as the shoreline area of other parts of the world. It is shown that this greater specific shoreline may account quantitatively for the faster social and technological development of western Europe in the last few centuries. The calculated total span of time of development from earliest urban cultures to our days is found to be of the order of magnitude of ten thousand years. It is shown that the model accounts for the existence at the present time of primitive cultures. A number of suggestions is made in regard to other possible applications of mathematics to history.     

Mapping baroreceptor function to genome: a mathematical modeling approach

To gain information about the genetic basis of a complex disease such as hypertension, blood pressure averages are often obtained and used as phenotypes in genetic mapping studies. In contrast, direct measurements of physiological regulatory mechanisms are not often obtained, due in large part to the time and expense required. As a result, little information about the genetic basis of physiological controlling mechanisms is available. Such information is important for disease diagnosis and treatment. In this article, we use a mathematical model of blood pressure to derive phenotypes related to the baroreceptor reflex, a short-term controller of blood pressure. The phenotypes are then used in a quantitative trait loci (QTL) mapping study to identify a potential genetic basis of this controller.     

Dry-heat destruction of lipopolysaccharide: mathematical approach to process evaluation.

A mathematical model was developed to estimate the number of logarithmic cycles (LDec) of lipopolysaccharide concentration destroyed by a dry-heat sterilization process. The LDec values calculated from the mathematical model agreed well with those obtained from the destruction of lipopolysaccharide by a dry-heat treatment. A discussion of how the mathematical model may be used to evaluate a dry-heat sterilization cycle is presented. This mathematical model and the dry-heat destruction curves indicated existence of a maximum LDec value at each temperature. The implications of this finding are discussed.     

Dry-heat destruction of lipopolysaccharide: mathematical approach to process evaluation.

A mathematical model was developed to estimate the number of logarithmic cycles (LDec) of lipopolysaccharide concentration destroyed by a dry-heat sterilization process. The LDec values calculated from the mathematical model agreed well with those obtained from the destruction of lipopolysaccharide by a dry-heat treatment. A discussion of how the mathematical model may be used to evaluate a dry-heat sterilization cycle is presented. This mathematical model and the dry-heat destruction curves indicated existence of a maximum LDec value at each temperature. The implications of this finding are discussed.     

Effects of bone-conducted music on swimming performance

Music has been shown to be a useful adjunct for many forms of exercise and has been observed to improve athletic performance in some settings. Nonetheless, because of the limited availability of practical applications of sound conduction in water, there are few studies of the effects of music on swimming athletes. The SwiMP3 is a novel device that uses bone conduction as a method to circumvent the obstacles to transmitting high fidelity sound in an aquatic environment. Thus, we studied the influence of music on swimming performance and enjoyment using the SwiMP3. Twenty-four competitive swimmers participated in a randomized crossover design study in which they completed timed swimming trials with and without the use of music delivered via bone conduction with the SwiMP3. Each participant swam four 50-m trials and one 800-m trial and then completed a physical enjoyment survey. Statistically significant improvements in swimming performance times were found in both the 50-m (0.32 seconds; p = 0.013) and 800-m (6.5 seconds; p = 0.031) trials with music using the SwiMP3. There was no significant improvement in physical enjoyment with the device as measured by a validated assessment tool. Bone-conducted music appears to have a salutary influence on swimming performance in a practice environment among competitive adult swimmers.     

A mathematical approach to multiple genetic relationships

A fundamental concept in the treatment of genetic relationships is that of gene identity which first was introduced by Cotterman (1940). Based on this notion several measures of relationship evolved such as the inbreeding coefficient, the coefficient of kinship, and the identity coefficients; by means of these quantities joint and conditional phenotype probabilities could be derived. This paper is an attempt at a general mathematical treatment of genetic relationships: Identity states are defined for any number of individuals, a method is given for the calculation of the corresponding identity coefficients by means of generalized coefficients of kinship, and applications are emphasized.     

On immunotherapies and cancer vaccination protocols: A mathematical modelling approach

In this paper we develop a new mathematical model of immunotherapy and cancer vaccination, focusing on the role of antigen presentation and co-stimulatory signaling pathways in cancer immunology. We investigate the effect of different cancer vaccination protocols on the well-documented phenomena of cancer dormancy and recurrence, and we provide a possible explanation of why adoptive (i.e. passive) immunotherapy protocols can sometimes actually promote tumour growth instead of inhibiting it (a phenomenon called immunostimulation), as opposed to active vaccination protocols based on tumour-antigen pulsed dendritic cells. Significantly, the results of our computational simulations suggest that elevated numbers of professional antigen presenting cells correlate well with prolonged time periods of cancer dormancy.     

Dynamic coordinate data for describing muscle-tendon paths: a mathematical approach

When modelling the musculoskeletal system over a range of joint angles the use of fixed points to describe muscle-tendon paths has inherent limitations. These result in fewer deflection points and the use of effective insertions to accommodate both relative marker movement and avoid muscle paths contacting bony structures. Model performance is dependent on the joint angle relative to the anatomical position where the muscle-tendon paths were defined. The present study proposes a scheme for the implementation of dynamic coordinates for describing muscle-tendon paths. For each muscle-tendon element a plane is defined in which the muscle-tendon complex acts when crossing a given joint. The muscle-tendon plane is dependent on 3D segment orientations and describes one degree of freedom, while the remaining two degrees of freedom are described by polar coordinates and locate the dynamic point in the muscle-tendon plane. The dynamic approach is implemented on four muscles of the lower limb in modelled and simulated joint movements and offers a significant improvement on previous approaches based on fixed deflection points. The scheme accommodates compound 3D rotations about joint axes, is not computationally difficult or require large data sets, and does not impose limitations on the number of points that may be defined along a muscle-tendon path.     

Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach

Atherosclerosis is a chronic disease which involves the build up of cholesterol and fatty deposits within the arterial wall. This results in the narrowing of the vessel lumen, which eventually restricts blood flow to vital organs such as the heart and lungs. These events may culminate in a heart attack or stroke, the commonest causes of death in the U.K. population. In this paper we study the early stages of atherosclerosis which include the build up of cholesterol within subendothelial cells to form what is known as a fatty streak, the earliest identifiable evidence of atherosclerosis. The deposition of cholesterol is believed to be a consequence of oxidation of circulating cholesterol-rich lipoproteins, in particular low density lipoproteins (LDLs). Via a mathematical model we investigate this process of oxidation within the context of an in vitro framework. We first recreate existing experimental results and then extend the model to investigate phenomenon not studied by current experimental protocols. We find that the model displays hysteresis which reveals some interesting insights into possible in vivo events. Mathematical analysis of this behaviour predicts that vitamin E supplementation is not as beneficial as high density lipoproteins (HDLs) and vitamin C. Furthermore, the scavenging of oxidants by HDL can provide an important first line of defence against LDL oxidation.     

Role of environmental persistence in pathogen transmission: a mathematical modeling approach

Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.     

Mechanism of arsenic carcinogenesis: an integrated approach

Epidemiological evidence shows an association between inorganic arsenic in drinking water and increased risk of skin, lung and bladder cancers. The lack of animal models has hindered mechanistic studies of arsenic carcinogenesis in the past, but some promising new models for these cancers are now available. The various forms of arsenic to which humans are exposed, either directly or via metabolism of inorganic arsenic to various methylated forms, further complicate the issue of mechanism, since these compounds can have different effects, both genotoxic and non-genotoxic. This review will try to integrate all of these issues, with a strong bias toward effects that are produced by environmentally relevant arsenic concentrations.