Computing and Information A MATHEMATICAL INVESTIGATION OF THE ROLE OF INTRACRANIAL PRESSURE PULSATIONS AND SMALL GRADIENTS IN THE PATHOGENESIS OF HYDROCEPHALUS

Abstract. Cerebrospinal fluid (CSF) pulsations have been proposed as a possible causative mechanism for the ventricular enlargement that characterizes the neurological condition known as hydrocephalus. This paper summarizes recent work by the authors to anaylze the effect of CSF pulsations on brain tissue to determine if they are mechanically capable of enlarging the cerebral ventricles. First a poroelastic model is presented to analyze the interactions that occur between the fluid and porous solid constituents of brain tissue due to CSF pulsations. A viscoelastic model is then presented to analyze the effects of the fluid pulsations on the solid brain tissue. The combined results indicate that CSF pulsations in a healthy brain are incapable of causing tissue damage and thus the ventricular enlargement observed in hydrocephalus. Therefore they cannot be the primary cause of this condition. Finally, a hyper-viscoelastic model is presented and used to demonstrate that small long-term transmantle pressure gradients may be a possible cause of communicating hydrocephalus in infants

Tumour Control Probability in Cancer Stem Cells Hypothesis

<div><p>The tumour control probability (TCP) is a formalism derived to compare various treatment regimens of radiation therapy, defined as the probability that given a prescribed dose of radiation, a tumour has been eradicated or controlled. In the traditional view of cancer, all cells share the ability to divide without limit and thus have the potential to generate a malignant tumour. However, an emerging notion is that only a sub-population of cells, the so-called cancer stem cells (CSCs), are responsible for the initiation and maintenance of the tumour. A key implication of the CSC hypothesis is that these cells must be eradicated to achieve cures, thus we define TCP_S as the probability of eradicating CSCs for a given dose of radiation. A cell surface protein expression profile, such as CD44high/CD24low for breast cancer or CD133 for glioma, is often used as a biomarker to monitor CSCs enrichment. However, it is increasingly recognized that not all cells bearing this expression profile are necessarily CSCs, and in particular early generations of progenitor cells may share the same phenotype. Thus, due to the lack of a perfect biomarker for CSCs, we also define a novel measurable TCP_CD+, that is the probability of eliminating or controlling biomarker positive cells. Based on these definitions, we use stochastic methods and numerical simulations parameterized for the case of gliomas, to compare the theoretical TCP_S and the measurable TCP_CD+. We also use the measurable TCP to compare the effect of various radiation protocols.</p></div

The images, adapted from [20], show that CD133+ tumor cells can proliferate in culture as non-adherent spheres, whereas CD133− tumor cells are not able to proliferate and form spheres.

<p>We assume that CSCs and early progenitors (from non-CSC compartment) share the CD133 biomarker. Here , (), and denote stem, progenitors and mature cells, respectively.</p

A panel showing a comparison for the measurable TCP curves when <i>k</i> = 3, for scheme 1 (conventional therapy), scheme 2 (hyper-fractionated therapy), and scheme 3 (accelerated hyper-fractionated therapy), noting that there is qualitative agreement with the theoretical TCP curves.

<p>The left graph is for TCP as a function of time in days, and the right is a for TCP as a function of dose of radiaton administered.</p

A panel showing a comparison for the measurable and theoretical TCP curves for <i>k</i> = 0,1,2,3, for the conventional therapy (scheme 1), noting that as <i>k</i> is increased, a slight shift occurs in the TCP curve.

<p>The left graph is for TCP as a function of time in days, and the right is a for TCP as a function of dose of radiaton administered.</p

A graph showing a comparison of the survival fraction, as a function of a single dose for biomarker-positive and biomarker-negative cells, assuming a three-fold increase in the radio-sensitivity parameters <i>α</i> and <i>β</i> for biomarker-negative cells as compared to positive cells.

<p>A graph showing a comparison of the survival fraction, as a function of a single dose for biomarker-positive and biomarker-negative cells, assuming a three-fold increase in the radio-sensitivity parameters <i>α</i> and <i>β</i> for biomarker-negative cells as compared to positive cells.</p

The fixation probability of mutants in the absence of plasticity.

<p>We assume <i>N</i>_S = <i>N</i>_D = 10, , and <i>η</i>₁ = <i>η</i>₂ = 0 in simulations (points) and exact calculations (solid lines) for an initial mutant in the SC compartment. Each error bar shown at each point is the standard error of the mean. In (a) changing parameters <i>u</i>₁, <i>u</i>₂, that are the differentiation rates of normal and tumor SCs respectively, the trends for the fixation probability of mutants is given as a function of relative fitness of mutants, referred to as . In (b) and (c) the fixation probability variation is given in terms of asymmetric differentiation rates <i>u</i>₁ = <i>u</i>₂ = <i>u</i> and various values of <i>r</i> and the ratio of the differentiation rates of normal SCs <i>ϵ</i> = <i>u</i>₂/<i>u</i>₁. In (b) <i>ϵ</i> = 0.5 and in (c) <i>ϵ</i> = 1.5.</p