Search

Gompertzian tumor growth can be reproduced by mitosis, related to nutrient supply, with local spatial cell correlations. The global energy constraint alone does not reproduce in vivo data by the observed values of the nutrient expenditure for the cell activities. The depletion of the exponential growth, described by the Gompertz law, is obtained by mean field spatial correlations or by a small word network among cells. The well-known interdependence between the two parameters of the Gompertz growth naturally emerges and depends on the cell volume and on the tumor density.

The exponential increase with age in mortality rate, the Gompertz law, indicates that the decrease in vitality and viability linked to aging depends on phenomena with exponential or logarithmic dynamics. Gompertz slope (alpha) is assumed to be a measure of aging rate, provided the studied cohort is homogeneous and in a supporting environment. The law provides no clue about the cause of aging, but may be formally correlated with various physical or mathematical functions. A possible correlation between the Ogston-Laurent exclusion equation and human aging is examined. An increase with age of an inert cross-linked insoluble protein network is assumed to result in a logarithmic decrease in water volume available to colloidal macromolecules. In this model, alpha is assumed to be a measure of the rate of accumulation of the polypeptide network.

A square lattice is introduced into the Penna model for biological aging in order to study the evolution of diploid sexual populations under certain conditions when one single locus in the individual's genome is considered as identifier of species. The simulation results show, after several generations, the flourishing and coexistence of two separate species in the same environment, i.e., one original species splits up into two on the same territory (sympatric speciation). As well, the mortalities obtained are in a good agreement with the Gompertz law of exponential increase of mortality with age., 5 pages including 3 encapsulated postscript (*.eps) figures; To appear in European Physical Journal B

The Gompertz transform of the distribution function for the age at death expresses mortality in a form R = R0ealpha t where R0 is themortality at time zero and α is the rate of increase ofmortality, frequently taken as the rate of ageing. The slope ofthe line α is frequently used as a measure of the rate of ageing.It is argued that it is incorrect to use α in this way. Tosupport this contention, a paradox is produced whereby selectionfor longevity increases α, which could lead to the absurdconclusion that selection for longevity increases the rate ofageing.

Despite considerable progress in understanding tumour development, the law of growth for human tumours is still a matter of some dispute. In this study, we used large-scale mammography screening trial data to deduce the growth law of primary breast cancer. We compared the empirical tumour population size distributions of primary breast cancer inferred from these data to the distributions that correspond to various possible theoretical growth functions. From this, we showed that the data are inconsistent with the exponential, logistic and Gompertz laws, but support power law growth (exponent approximately 0.5). This law indicates unbounded growth but with slowing mass-specific growth rate and doubling time. In the clinical size ranges, it implies a greater decline in the mass-specific growth rate than would be predicted by the Gompertz law using the accepted parameters. This suggests that large tumours would be less sensitive to cycle-specific therapies, and be better treated first by non-cell cycle-specific agents. We discussed the use of our study to estimate the sensitivity of mammography for the detection of small tumours. For example, we estimated that mammography is about 30% less sensitive in the detection of tumours in the 1 to 1.5-cm range than it is in detecting larger tumours.

The Gompertz law of dependence of human mortality rate on age is derived from a simple model of death as a result of an exponentially rare escape of abnormal cells from immunological response.

Increased mortality rates of a constant proportion or corresponding to a constant increase in age produce increasing excess mortality by comparison with rates allowing for a constant addition to the rates and under quite general conditions (monotony or convexity of qx). The comparison of the effect of an age increase with that of a constant proportionate increase in the rates leads, however, to different results if one starts from different mortality formulae. The age increase produces proportionally constant (by Gompertz) or increasing (by de Moivre, Makeham, Lazarus) or decreasing (by Dormoy II) excess mortality; by Dormoy I it represents no excess mortality at all.

Mortality kinetics of various animal species and failure kinetics of industrial components and materials are in variance with Gompertz’s law or law of exponentially increasing force of mortality. A pair of straight lines is in general obtained on a semilogarithmic plot, one for the first part of the cumulative mortality curve, up to its inflection point, the other, for the second part of the survivorship curve, after its inflection point. It is concluded that after a certain species-characteristic age, force of mortality and probability of death cease to increase exponentially with age, with the exception of certain human populations, and remain constant at a high level on the average for the remainder of the life span.