Dynamics of Tumour Growth: Comparison of Growth Rates and Extrapolation of Growth Curve to One Cell

Laird, Anna Kane

doi:10.1038/bjc.1965.32

Cited by 341 publications

(246 citation statements)

References 7 publications

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“…This specific pattern is not observed in rats. Rather, skeletal growth of the rat proceeds continuously through the juvenile and prepubertal phases along an exponential trajectory evident at birth (Laird, 1965b;Kilborn et al, 2002), which later decays as a function of animal age and endocrine activity. In this study, we have observed that significant longitudinal growth enters a decay phase at approximately 64 days of age, lagging slightly behind the reported age at which sexual maturity is assumed by the appearance of mature spermatozoa in the vas deferens in male (45-55 days), or the first ovulation in female (35-40 days) rats (Ojeda and Urbanski, 1994).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Ontogeny of Skeletal Maturation in the Juvenile Rat

Horton

Bariteau

Loomis

et al. 2008

The Anatomical Record

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Systemic regulation of the cellular processes that produce endochondral elongation and endochondral mineralization during postnatal skeletal maturation are not completely understood. In particular, a mechanism coupling the decline of cellular activity in the bone microenvironment to the onset of sexual maturity remains elusive. The purpose of this study was to empirically integrate the dynamic progression of bone mineral accrual and endochondral elongation as a function of animal age in growing male and female Sprague-Dawley rats. We used serial dual-energy X-ray absorptiometry (DXA) and radiography to study the temporal progression of bone growth and mineral accrual from weaning to adulthood. We observed that skeletal maturation proceeds in a pattern adequately described by the Gompertz function. During this period of growth, we found that serum markers of osteoblastic bone formation declined with age, while osteoclastic bone resorption activity remained unchanged. We also report a slight lag in the age at inflection in the rate of bone mineral accrual relative to the rate of tibial elongation and that both endochondral processes eventually come to asymptotic equilibrium by approximately 20 weeks of age. In addition, we studied tibial growth plate histomorphometry at select time points through 1 year of age. We report that, despite the histologic persistence of physeal cartilage, very little proliferative or elongative activity was measured in this tissue beyond 20 weeks of age. Taken together, these data provide insight to the temporal coordination of postnatal endochondral growth processes.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Ontogeny of Skeletal Maturation in the Juvenile Rat

Horton

Bariteau

Loomis

et al. 2008

The Anatomical Record

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“…The SCs at 12 and 18 months (SC12 and SC18) were obtained from the nonlinear logistic function used by Nelder (1961). This was found to be the best out of six nonlinear curves for SC growth that were tried out in relation to the present database: Brody, Richards, Von Bertalanffy, Logistic, Gompertz and modified Logistic form, respectively, Brody (1945), Richards (1959), Von Bertalanffy (1957), Nelder (1961), Laird (1965) and Quirino et al (1999). The nonlinear logistic function was described as follows:…”

Section: Methodsmentioning

confidence: 99%

“…However, it is known that the growth of cattle is described by a sigmoid curve. Thus, it is expected that nonlinear models would describe their body growth better (Laird, 1965). For beef cattle, in particular Zebu breeds, the standard ages of 205, 365 and 550 days are used.…”

Section: Introductionmentioning

confidence: 99%

Heritability estimates and genetic correlations for body weight and scrotal circumference adjusted to 12 and 18 months of age for male Nellore cattle

Frizzas

Grossi

Buzanskas

et al. 2009

Animal

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Heritability estimates and genetic correlations were obtained for body weight and scrotal circumference, adjusted, respectively, to 12 (BW12 and SC12) and 18 (BW18 and SC18) months of age, for 10 742 male Nellore cattle. The adjustments to SC12 and SC18 were made using a nonlinear logistic function, while BW12 and BW18 were obtained by linear adjustment. The contemporary groups (CGs) were defined from animals born on the same farm, in the same year and birth season. The mean heritability estimates obtained using the restricted maximum likelihood method in bi-trait analysis were 0.25, 0.25, 0.29 and 0.42 for BW12, BW18, SC12 and SC18, respectively. The genetic correlations were 0.30 6 0.11, 0.21 6 0.13, 0.21 6 0.11, 20.08 6 0.15, 0.16 6 0.12 and 0.89 6 0.04 between the traits BW12 and BW18; BW12 and SC12; BW12 and SC18; BW18 and SC12; BW18 and SC18; and SC12 and SC18. The heritability for SC18 was considerably greater than for SC12, suggesting that this should be included as a selection criterion. The genetic correlation between BW18 and SC12 was close to zero, indicating that these traits did not influence each other. The contrary occurred between SC12 and SC18, indicating that selection using one of these could alter the other. Because of the mean magnitudes of heritabilities in the various measurements of weight and scrotal perimeter, it is suggested that the practice of individual selection for these traits is possible.

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“…Each of these implies different model-specific dynamics of tumour g2rowth (Mendelsohn. 1963: Laird. 1965: Steel and Lamerton.…”

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confidence: 99%

The growth law of primary breast cancer as inferred from mammography screening trials data

Hart

Shochat²,

Agur³

1998

Br J Cancer

154

111

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Summary 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 = 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 Flehinger. 1991 and Xu and Prorok. 1997 for theoretical discussions). Nex ertheless. the benefit of screening. especiall in youncer women (< 50 Xyears). still remains somew-hat controv-ersial (Fletcher et al. 1993: Tabar et al. 1995 In the present w-ork. we employed extensive clinical data from large mammogaraphv screening trials that should be representatiVe of the general population. Usinc mathematical tools. we extracted from these data useful information about breast cancer growth.

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Dynamics of Tumour Growth: Comparison of Growth Rates and Extrapolation of Growth Curve to One Cell

Cited by 341 publications

References 7 publications

Ontogeny of Skeletal Maturation in the Juvenile Rat

Ontogeny of Skeletal Maturation in the Juvenile Rat

Heritability estimates and genetic correlations for body weight and scrotal circumference adjusted to 12 and 18 months of age for male Nellore cattle

The growth law of primary breast cancer as inferred from mammography screening trials data

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