Biomedical subjects

Kjell Hausken

Publications and source records attributed to Kjell Hausken.

6 recordsLinked to original sources

PubMed2006

A mathematical model for the proliferation of bacteria in the urinary bladder due to enlarged prostate.

Urinary retention due to enlargement of the prostate (prostate hypertrophy) leads to increased proliferation of bacteria in the bladder. This in turn increases the infection rate. The reason is that the enlarged prostate presses on the urine channel and tends to close it. Thus the out flux of the bladder consists of repeatedly small amounts of fluid during a day. A mathematical dynamic model with differential equations is developed for the proliferation of bacteria in the urinary bladder (vesica urinary). The model accounts for how this proliferation is associated with varying amounts of mass of urine within the bladder. Parameters are estimated from published data and analytical and numerical results are presented. The relationships between the proliferation of bacteria within the bladder and the type of urinal out flux from the bladder are examined. The proliferation is shown to depend on the amount of mass of urine and the out flux of urine from the bladder. In the normal situation the bladder is drained successfully which also drains the bacteria. In the abnormal situation the bladder drains only partly. Despite frequent urination, substantial urine mass in the bladder on the average allows bacteria to proliferate and increase in number through time. The simulations depend on the numerical values of the parameters which again depend on the prostate condition of each male adult under scrutiny. By determining the parameters for each male, the dynamic model can be used as a powerful tool by which the proliferation of bacteria in the bladder can be studied and controlled by different means. Three clinical advices are provided. First, try to achieve that the proliferation rate of bacteria in the bladder is as small as possible, e.g. through altering the pH or chemical composition within the bladder. Second, try to achieve that the out flux of urine from the bladder is substantial, through sufficient drinking. Third, try to achieve that the mass of urine in the bladder is as small as possible, through sufficient urination. The intrinsic parameters for each male can be used to pinpoint the actual out flux during a day necessary to keep the number of bacteria in the bladder low. Suggestions for how to test the model are briefly presented.

Bacteria↗

PubMed2004

The truthful signalling hypothesis: an explicit general equilibrium model.

In mating competition, the truthful signalling hypothesis (TSH), sometimes known as the handicap principle, asserts that higher-quality males signal while lower-quality males do not (or else emit smaller signals). Also, the signals are "believed", that is, females mate preferentially with higher-signalling males. Our analysis employs specific functional forms to generate analytic solutions and numerical simulations that illuminate the conditions needed to validate the TSH. Analytic innovations include: (1) A Mating Success Function indicates how female mating choices respond to higher and lower signalling levels. (2) A congestion function rules out corner solutions in which females would mate exclusively with higher-quality males. (3) A Malthusian condition determines equilibrium population size as related to per-capita resource availability. Equilibria validating the TSH are achieved over a wide range of parameters, though not universally. For TSH equilibria it is not strictly necessary that the high-quality males have an advantage in terms of lower per-unit signalling costs, but a cost difference in favor of the low-quality males cannot be too great if a TSH equilibrium is to persist. And although the literature has paid less attention to these points, TSH equilibria may also fail if: the quality disparity among males is too great, or the proportion of high-quality males in the population is too large, or if the congestion effect is too weak. Signalling being unprofitable in aggregate, it can take off from a no-signalling equilibrium only if the trait used for signalling is not initially a handicap, but instead is functionally useful at low levels. Selection for this trait sets in motion a bandwagon, whereby the initially useful indicator is pushed by male-male competition into the domain where it does indeed become a handicap.

Animal Communication↗

PubMed2004

The dynamics of cell proliferation.

The article provides a mathematical description based on the theory of differential equations, for the proliferation of malignant cells (cancer). A model is developed which enables us to describe and predict the dynamics of cell proliferation much better than by using ordinary curve fitting procedures. By using differential equations the ability to foresee the dynamics of cell proliferation is in general much better than by using polynomial extrapolations. Complex time relations can be revealed. The mass of each living cell and the number of living cells are described as functions of time, accounting for each living cell's age since cell-birth. The linkage between micro-dynamics and the population dynamics is furnished by coupling the mass increase of each living cell up against the mitosis rate. A comparison is made by in vitro experiments with cancer cells exposed to digitoxin, a new promising anti-cancer drug. Theoretical results for the total number of cells (living or dead) is found to be in good agreement with experiments for the cell line considered, assuming different concentrations of digitoxin. It is shown that for the chosen cell line, the proliferation is halted by an increased time from birth to mitosis of the cells. The delay is probably connected with changes in the Ca concentration inside the cell. The enhanced time between the birth and mitosis of a cell leads effectively to smaller mitosis rates and thereby smaller proliferation rates. This mechanism is different from the earlier results on digitoxin for different cell lines where an increased rate of apoptosis was reported. But we find it reasonable that cell lines can react differently to digitoxin. A development from enhanced time between birth and mitosis to apoptosis can be furnished, dependent of the sensitivity of the cell lines. This mechanism is in general very different from the mechanism appealed to by standard chemotherapy and radiotherapy where the death ratios of the cells are mainly affected. Thus the analysis supports the view that a quite different mechanism is invoked when using digitoxin. This is important, since by appealing to different types of mechanism in parallel during cancer treatment, more selectivity in the targeting of benign versus malignant cells can be invoked. This increases the probability of successful treatment. The critical digitoxin level concentration, i.e. the concentration level where the number of living cells is not increasing, is approximately 50 ng/ml for the cell line we investigated in this article. Therapeutic plasma concentration of digitoxin when treating cardiac congestion is about 15-33 ng/ml, but individual tolerances are large. The effect of digitoxin during cancer treatment is therefore very promising. The dynamic model constitutes a new powerful tool, supported by empirics, describing the mechanism or process by which the number of malignant cells during anti-cancer treatment can be studied and reduced.

Animals↗

PubMed2003

Predicting the concentration level of an anti-cancer drug during treatment of a living organism.

For many drugs used in chemotherapy the difference between the therapeutic concentration and the toxic concentration is small. During treatment of a living organism from cancer by using chemotherapy, it is therefore important to foresee the therapeutic concentration in the organism as a function of the injected therapeutic drug dose. This article provides a mathematical dynamic description of the interaction between the organism and the drug, and analyses the dynamics by using ordinary differential equations. The model is tested in a clinical situation where digitoxin is used as the therapeutic drug. The agreement with this experiment is good.

Antineoplastic Agents↗

PubMed2002

Probabilistic risk analysis and game theory.

The behavioral dimension matters in Probabilistic Risk Analysis (PRA) since players throughout a system incur costs to increase system reliability interpreted as a public good. Individual strategies at the subsystem level generally conflict with collective desires at the system level. Game theory, the natural tool to analyze individual-collective conflicts that affect risk, is integrated into PRA. Conflicts arise in series, parallel, and summation systems over which player(s) prefer(s) to incur the cost of risk reduction. Frequently, the series, parallel, and summation systems correspond to the four most common games in game theory, i.e., the coordination game, the battle of the sexes and the chicken game, and prisoner's dilemma, respectively.

Journal Article↗

PubMed2001

Behaviorist stochastic modeling of instrumental learning.

A mathematical model is presented descriptive of instrumental learning, i.e. operant conditioning. An agent learns to commit a certain number of acts per time unit, distributed as a non-stationary Poisson process. The derivative of the agent's expected utility per time unit, where utility is expected benefit minus expected cost, is interpreted as his drive to reach a local maximum of his expected utility. This drive multiplied with his act intensity are proportional to the change of the agent's act intensity per time unit, which is an ordinary first order differential equation for instrumental learning.

Journal Article↗