A model of proliferating cell populations with inherited cycle length

A mathematical model of cell population growth introduced by J. L. Lebowitz and S. I. Rubinow is analyzed. Individual cells are distinguished by age and cell cycle length. The cell cycle length is viewed as an inherited property determined at birth. The density of the population satisfies a first order linear partial differential equation with initial and boundary conditions. The boundary condition models the process of cell division of mother cells and the inheritance of cycle length by daughter cells. The mathematical analysis of the model employs the theory of operator semigroups and the spectral theory of linear operators. It is proved that the solutions exhibit the property of asynchronous exponential growth.     

The relation between length of the cell cycle duration and RNA content in HeLa S3 cells

The cell cycle of HeLa S3 cells synchronized by hydroxyurea was investigated by flow cytometry. Metachromatic fluorochrome acridine orange was used to strain the DNA and RNA of the cells differentially. Periodic changes in the cellular DNA and RNA contents were observed through five cell cycles. The G1 and S phases of synchronized HeLa S3 cells that contained large amounts of RNA became shorter than those of cells that contained smaller amounts of RNA.     

Variation with age in the timing and duration of spawning in American plaice

Spawning time of female American plaice Hippoglossoides platessoides varied significantly with age. This effect, however, was not consistent across years. Generally, younger fish spawned earlier than older fish, but in the 1990s they spawned later than older fish. Spawning duration also varied with age, with younger fish generally having a longer spawning period than older fish. Changes in depth distribution were related to changes in both spawning time and duration. As depth increased, spawning time became later and duration became shorter. Fish <11 years old showed the largest change in both spawning time and depth distribution.     

Variation of cell cycle duration within suspension cultures ofDaucus carota and its consequence for the induction of ploidy changes with colchicine

Summary Continuous exposure to colchicine was used to estimate the variation in cell cycle time between cells within suspension cultures ofDaucus carota. Observations were made of the pattern of disappearance of cells of the initially predominant ploidy levels in diploid and tetraploid cultures having markedly different aggregation patterns. Both cultures showed a similar range of cycle times, normally distributed about the culture mean. Shorter colchicine treatments, followed by regrowth in colchicine-free medium, showed that spread of cycle times in the diploid culture prevented uniform induction of tetraploidy, and that the resulting mixoploid suspensions showed a gradual reversion to diploidy during subsequent subculture.     

A joint mixed effects dispersion model for menstrual cycle length and time-to-pregnancy

Menstrual cycle patterns are often used as indicators of female fecundity and are associated with hormonally dependent diseases such as breast cancer. A question of considerable interest is in identifying menstrual cycle patterns, and their association with fecundity. A source of data for addressing this question is prospective pregnancy studies that collect detailed information on reproductive aged women. However, methodological challenges exist in ascertaining the association between these two processes as the number of longitudinally measured menstrual cycles is relatively small and informatively censored by time to pregnancy (TTP), as well as the cycle length distribution being highly skewed. We propose a joint modeling approach with a mixed effects dispersion model for the menstrual cycle lengths and a discrete survival model for TTP to address this question. This allows us to assess the effect of important characteristics of menstrual cycle that are associated with fecundity. We are also able to assess the effect of fecundity predictors such as age at menarche, age, and parity on both these processes. An advantage of the proposed approach is the prediction of the TTP, thus allowing us to study the efficacy of menstrual cycle characteristics in predicting fecundity. We analyze two prospective pregnancy studies to illustrate our proposed method by building a model based on the Oxford Conception Study, and predicting for the New York State Angler Cohort Prospective Pregnancy Study. Our analysis has relevant findings for assessing fecundity.     

Variability of the duration of the cell cycle in pig embryo kidney cells in monolayer culture and correlation of the cycle duration in sister cells

The distribution of generation time of sister cells for the exponentially proliferating monolayer SPEV culture was obtained with time lapse cinemicrographic technique. The distribution is characterized by the average generation time equal to 24.3 hour, with the variation coefficient, asymmetry coefficient and correlation coefficient for sister pair cell being, respectively, 17%, 0.2 and 0.78. The results obtained are compared with the prediction of "a random transition" in the cell cycle.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes.

The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation.

In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola–Kirchhoff active stress tensor.

As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola-Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

Structural finite deformation model of the left ventricle during diastole and systole

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.     

Scaling of chew cycle duration in primates

The biomechanical determinants of the scaling of chew cycle duration are important components of models of primate feeding systems at all levels, from the neuromechanical to the ecological. Chew cycle durations were estimated in 35 species of primates and analyzed in conjunction with data on morphological variables of the feeding system estimating moment of inertia of the mandible and force production capacity of the chewing muscles. Data on scaling of primate chew cycle duration were compared with the predictions of simple pendulum and forced mass-spring system models of the feeding system. The gravity-driven pendulum model best predicts the observed cycle duration scaling but is rejected as biomechanically unrealistic. The forced mass-spring model predicts larger increases in chew cycle duration with size than observed, but provides reasonable predictions of cycle duration scaling. We hypothesize that intrinsic properties of the muscles predict spring-like behavior of the jaw elevator muscles during opening and fast close phases of the jaw cycle and that modulation of stiffness by the central nervous system leads to spring-like properties during the slow close/power stroke phase. Strepsirrhines show no predictable relationship between chew cycle duration and jaw length. Anthropoids have longer chew cycle durations than nonprimate mammals with similar mandible lengths, possibly due to their enlarged symphyses, which increase the moment of inertia of the mandible. Deviations from general scaling trends suggest that both scaling of the jaw muscles and the inertial properties of the mandible are important in determining the scaling of chew cycle duration in primates.     

Stem cell renewal and duration of spermatogonial cycle in the goldhamster

Summary The duration of the cycle of the seminiferous epithelium of the hamster is estimated to be 9.0 days. The duration of the stages was also determined.The stem cells were found to be daughter cells of the A₃ spermatogonia. This confirms the hypothesis that in general stem cells for the next spermatogonial cycle arise on the moment of morphological differentiation of the A spermatogonia.The author wishes to thank Prof. Dr. M. T. Jansen and Dr. M. F. Kramer for helpfull discussions and Mr. J. G. van Essen for technical assistance.     

Variation in cyanogenesis in plants with season and insect pressure

Cyanogenesis of 800 plant specimens (108 species) growing on a sandy tract of land between the sea and an inner lagoon 400 m distant was found to increase with insect density and, hence, with distance from the seashore and seasonal variation towards summer.     

Increasing pulse wave velocity in a realistic cardiovascular model does not increase pulse pressure with age

The mechanism of the well-documented increase in aortic pulse pressure (PP) with age is disputed. Investigators assuming a classical windkessel model believe that increases in PP arise from decreases in total arterial compliance (C(tot)) and increases in total peripheral resistance (R(tot)) with age. Investigators assuming a more sophisticated pulse transmission model believe PP rises because increases in pulse wave velocity (c(ph)) make the reflected pressure wave arrive earlier, augmenting systolic pressure. It has recently been shown, however, that increases in c(ph) do not have a commensurate effect on the timing of the reflected wave. We therefore used a validated, large-scale, human arterial system model that includes realistic pulse wave transmission to determine whether increases in c(ph) cause increased PP with age. First, we made the realistic arterial system model age dependent by altering cardiac output (CO), R(tot), C(tot), and c(ph) to mimic the reported changes in these parameters from age 30 to 70. Then, c(ph) was theoretically maintained constant, while C(tot), R(tot), and CO were altered. The predicted increase in PP with age was similar to the observed increase in PP. In a complementary approach, C(tot), R(tot), and CO were theoretically maintained constant, and c(ph) was increased. The predicted increase in PP was negligible. We found that increases in c(ph) have a limited effect on the timing of the reflected wave but cause the system to degenerate into a windkessel. Changes in PP can therefore be attributed to a decrease in C(tot).