A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth

During the past two decades computerized tomography (CT) and magnetic resonance imaging (MRI) have permitted the detection of tumours at much earlier stages in their development than was previously possible. In spite of this earlier diagnosis the effects of earlier and more extensive treatments have been difficult to document. This failure has led to an increasing awareness of the importance of infiltration of glioma cells into surrounding grossly normal brain tissue such that recurrence still occurs. In this paper a simple mathematical model for the proliferation and infiltration of such tumours is introduced, based in part on quantitative image analysis of histological sections of a human brain glioma and especially on cross-sectional area/volume measurements of serial CT images while the patient was undergoing chemotherapy. The model parameters were estimated using optimization techniques to give the best fit of the simulated tumour area to the CT scan data. Numerical solution of the model on a two-dimensional domain, which took into account the geometry of the brain and its natural barriers to diffusion, was used to determine the effect of chemotherapy on the spatiotemporal growth of the tumour.     

Skeletal changes associated with vascular malformations

Five hundred and eighty birthmarks were reviewed; 356 were hemangiomas and 224 were malformations. Bony alterations occurred in association with only 1 percent of hemangiomas, in contrast with 34 percent of patients with vascular malformations. These alterations in bone development were classified according to size, shape, and density changes. Hypertrophy and distortion were typical of lymphatic malformations. Hypoplasia and demineralization were characteristic findings in the extremity venous malformations. Destructive and intraosseous changes were more commonly noted in the arterial or high-flow lesions. Possible mechanisms of altered skeletal growth include mechanical, physiological, and developmental processes.     

Characteristics of patients found not to have multiple sclerosis.

Of 400 consecutive patients referred to Dalhousie University''s multiple sclerosis research unit 52 (13%) were found not to have multiple sclerosis. Forty-one (79%) of the patients were female and 11 (21%) were male. About half of the patients had raised the suspicion of multiple sclerosis, and about half had either a medical background or a close association with a patient with the disease. Although in many cases a diagnosis was made at the initial visit, in difficult cases the most effective diagnostic technique was repeated assessment of the patient over a long period. It is important to keep an open mind when assessing patients suspected of having multiple sclerosis and to apply the recognized criteria for diagnosis of the disease.     

Anaphylactic reaction to aprotinin despite negative ocular sensitivity tests.

A man with a history of pancreatitis was given aprotinin intravenously just before endoscopic retrograde pancreatography. Despite negative sensitivity tests with aprotinin eye drops he developed a profound anaphylactic reaction on intravenous administration of the drug. Ocular sensitivity tests may not predict severe anaphylactic reactions to intravenous aprotinin.     

The adverse effect of iron repletion on the course of certain infections.

The incidence of infections was studied in 137 iron-deficient Somali nomads, 67 of whom were treated with placebo and 71 with iron. Seven episodes of infection occurred in the placebo group and 36 in the group treated with iron; these 36 episodes included activation of pre-existing malaria, brucellosis, and tuberculosis. This difference suggested that host defence against these infections was better during iron deficiency than during iron repletion. Iron deficiency among Somali nomads may be part of an ecological compromise, permitting optimum co-survival of host and infecting agent.     

The ecological interdependence of diet and disease in tribal societies.

Observations among nomads suggest there is a strong ecological interdependence of diet and disease in tribal societies which favors survival of man. This relationship may be disrupted by changes in diet to conform to the highly productive technology of the West. Such changes may result in intensification of indigenous disease and in the transfer of disease characteristics of Western societies. To prevent these consequences, relief feeding and long-term attempts to upgrade nutrition should be carried out with traditional foods wherever possible.     

Non-specific induction of increased resistance in mice to Trypanosoma congolense and Trypanosoma brucei by immunostimulants.

Administration of the immunostimulants Corynebacterium parvum, Bacillus Calmette-Guérin (BCG) or Bordetella pertussis prior to, or at the same time as, challenge with Trypanosoma congolense significantly increased survival times in mice, both of trypano-susceptible (A/J) and trypano-resistant (C57Bl) strains. The increased survival time was associated with significant alterations in parasitaemia, which included lengthening of the pre-patent period, a delay in the time taken to reach the first peak of parasitaemia and a reduction in the level of parasitaemia. Similar results were obtained when these strains of mice were challenged with Trypanosoma brucei following pre-treatment with C. parvum. Thus, by the use of immunostimulants it was possible to reduce the susceptibility of mice to trypanosomiasis and the hope is that this can also be achieved with domestic livestock.     

A generalized diffusion model for growth and dispersal in a population

A reaction-diffusion model is presented in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species. The approach is based on a Landau-Ginzburg free energy model. A problem involving simple logistic kinetics is fully analyzed, and a nonlinear stability analysis based on a multi-scale perturbation method shows bifurcation to non-uniform states.Part of this work was done while at the Mathematical Institute, Oxford University as a Senior Visiting Fellow supported by the Science Research Council of Great Britain under grant GR/B31378