Observation of mammalian similarity through allometric scaling laws

Kokshenev, V. B.

doi:10.1016/s0378-4371(02)01923-4

Cited by 17 publications

(42 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4,5 Many different explanations have been put forward for the scaling laws, ranging from four-dimensional biology. 6 and quantum statistics 7 to long-bone allometry combined with muscular development, 8 but, as yet, the debate is far from being settled. In this letter we suggest that multicellular tumor spheroids (MTS) are excellent experimental model systems to test the validity of the proposed mechanisms.…”

mentioning

confidence: 99%

Growth model for multicellular tumor spheroids

Delsanto

Guiot

Degiorgis

et al. 2004

Applied Physics Letters

View full text Add to dashboard Cite

Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m. Although this relation is generally recognized to be of the form B͑m͒ = m p , the specific value of the exponent p is the object of an ongoing debate, with many mechanisms being postulated to support different predictions. We propose that multicellular tumor spheroids provide an ideal experimental model system for testing these allometric growth theories, especially under controlled conditions of malnourishment and applied mechanical It was recently proposed 1 that tumors may follow the general model of ontogenetic growth for all living organisms (from mammals to mollusks to plants) developed by West, Brown and Enquist (WBE). 2 The beauty of the WBE model is that it is entirely based on energy conservation and other general physical arguments, i.e., scaling. The authors start with the assumption that the energy intake, supplied by ingested nutrients, is spent partly to support the metabolic functions of the organism's existing cells and partly for cell replication, i.e., to reproduce new cells. Based on this key assumption, a universal growth curve is derived, which the authors conjectured to be applicable to all living organisms. Their conjecture, based on a fractal-like distribution model, is supported by data encompassing many different species. 2 Although they assumed B ϰ m p with p =3/4, their value of p is not universally accepted. Indeed there is strong evidence that growth may be consistent with a 2 / 3 law in the case of birds and small mammals. 3 Due to its implications for tumor metastasis, cell turnover rates, angiogenesis, and invasion, the proposal of Ref. 1 has immediately contributed to an ongoing debate. 4,5 Many different explanations have been put forward for the scaling laws, ranging from four-dimensional biology. 6 and quantum statistics 7 to long-bone allometry combined with muscular development, 8 but, as yet, the debate is far from being settled. In this letter we suggest that multicellular tumor spheroids (MTS) are excellent experimental model systems to test the validity of the proposed mechanisms. MTS are spherical aggregations of malignant cells, 9,10 which can be grown in vitro under strictly controlled nutritional and mechanical conditions. Although cells appear to preserve the evolutionary self-organization rules governing the growth of the original tumor line, they also evolve according to the environmental conditions of the particular experimental setting. Here we show that MTS indeed grow following a scaling law and obtain their expected properties under conditions of malnourishment and rising mechanical stress-conditions that often apply to tumors in vivo.Following WBE, we assume, for simplicity, that metabolism and growth are the same for all MTS cells. Let B be the resting metabolic energy expenditure. Then, at any time t and for any discrete sho...

show abstract

mentioning

confidence: 99%

Growth model for multicellular tumor spheroids

Delsanto

Guiot

Degiorgis

et al. 2004

Applied Physics Letters

View full text Add to dashboard Cite

show abstract

“…Experimental studies of the peak stress measured in the midshaft of long bones in fast walking, moderately running (or trotting) animals, and fast running (or galloping) animals with smoothly changing speed, resulted in that σ (max) bone (M, V) is a linear piecewise function of speed, which domains are limited by the gait-dependent "speed-equivalent" points V (max) trans , as suggested by Biewener & Taylor (1986). When the allometric data from individual bones in running mammals are generalized to effective limb bone (e.g., Kokshenev, 2003), the corresponding peak functional stress is suggested here in the form…”

Section: Dynamic Strain and Stress Similaritiesmentioning

confidence: 99%

“…It has been in particular demonstrated that the consistency between the elastic strain similarity by Rubin & Lanyon (1982, 1984 and the elastic static stress similarity by McMahon (1975a) exists, since both are underlaid by the same patterns of elastic forces emerging in solids, that can be revealed if the external gravitational forces are substituted by predominating functional muscular forces (Kokshenev, 2003;Kokshenev et al, 2003). In this chapter, we try to establish a link between the mechanical elastic similarity in limb bones of different-sized animals (McMahon, 1973(McMahon, , 1975aRubin & Lanyon, 1982, 1984Kokshenev, 2003Kokshenev, , 2007 and the seminal dynamic similarity in locomotion of animals (Alexander, 1976(Alexander, , 1989Alexander & Jayes, 1983), arising in turn from the more general mechanical similarity of uniform classical systems (Kokshenev, 2011a, b). Following Schmidt-Neielsen (1984), it has been widely recognized that body mass is often a major locomotory factor scaling muscle force output establishing limits for body ability in animals (Alexander, 1985b;Hutchinson & Garcia, 2002;Biewener, 2005, Hutchinson et al, 2005Marden, 2005), through their maximal speed (Garland, 1983;Jones & Lindstedt, 1993;Sellers & Manning, 2007) and maximal size (Hokkanen, 1986a;Biewener, 1989;Kokshenev, 2007).…”

Section: Introductionmentioning

confidence: 98%

“…However, the problem as to which specific mechanical characteristics are most relevant remains open (e.g., Rubin & Lanyon, 1984;Fritton et al, 2000;Biewener, 2000Biewener, , 2005. Aiming to establish correlations between structural proportions and posture of mammalian limbs coping with body's locomotory functions, including support of mass in the gravitational field, scaling studies of limb long bones in terrestrial mammals have been subject to long standing debate and controversy (Biewener, 1982(Biewener, , 1983(Biewener, , 1989(Biewener, , 1990(Biewener, , 2000(Biewener, , 2005Biewener et al, 1983;Biewener & Taylor, 1986;Selker & Carter, 1989;Bertram & Biewener, 1990Christiansen, 1997Christiansen, , 1998Christiansen, , 1999Christiansen, , 2002aChristiansen, , b, 2007Fariña et al, 1997;Carrano, 1998Carrano, , 1999Carrano, , 2001Currey, 2003;Kokshenev, 2003;Kokshenev et al, 2003). The exploration of basic concepts of stability of ideal and non-ideal solid cylinders loaded in non-critical, transient and near critical mechanical regimes, mapped to arbitrary loaded curved limb long bones, resulted in a number of mechanical patterns of similarity in long bones adjusted to their design (Kokshenev, 2007).…”

Section: Introductionmentioning

confidence: 99%

“…Instead, a new kind of dynamic strain similarity (physically equivalent to dynamic stress similarity) observed in limb bones of walking, trotting, and galloping animals experimentally established by many researchers (Rubin & Lanyon, 1982, 1984Rubin & Lanyon, 1982;Biewener et al, 1983;Biewener & Taylor, 1986) has been only recently understood in light of more general mechanical elastic similarity (Kokshenev, 2007). It has been in particular demonstrated that the consistency between the elastic strain similarity by Rubin & Lanyon (1982, 1984 and the elastic static stress similarity by McMahon (1975a) exists, since both are underlaid by the same patterns of elastic forces emerging in solids, that can be revealed if the external gravitational forces are substituted by predominating functional muscular forces (Kokshenev, 2003;Kokshenev et al, 2003). In this chapter, we try to establish a link between the mechanical elastic similarity in limb bones of different-sized animals (McMahon, 1973(McMahon, , 1975aRubin & Lanyon, 1982, 1984Kokshenev, 2003Kokshenev, , 2007 and the seminal dynamic similarity in locomotion of animals (Alexander, 1976(Alexander, , 1989Alexander & Jayes, 1983), arising in turn from the more general mechanical similarity of uniform classical systems (Kokshenev, 2011a, b).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evolution of Locomotor Trends in Extinct Terrestrial Giants Affected by Body Mass

Kokshenev¹,

Christiansen²

2011

Theoretical Biomechanics

View full text Add to dashboard Cite

Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Sittert

Skinner

Mitchell

2014

Journal of Morphology

View full text Add to dashboard Cite

Giraffes have remarkably long and slender limb bones, but it is unknown how they grow with regard to body mass, sex and neck length. In this study we measured the length, medio-lateral diameter (ML), cranio-caudal diameter (CC) and circumference of the humerus, radius, metacarpus, femur, tibia and metatarsus in 10 fetuses, 21 females and 23 males of known body masses. Allometric exponents were determined and compared. We found the average bone length increased from 340±50mm at birth to 700±120mm at maturity, while average diameters increased from 30±3mm to 70±11mm. Fetal bones increased with positive allometry in length (relative to body mass) and in diameter (relative to body mass and length). In postnatal giraffes bone lengths and diameters increased iso-or negatively allometric relative to increases in body mass, except for the humerus CC diameter which increased with positive allometry. Humerus circumference also increased with positive allometry, that of the radius and tibia isometrically and the femur and metapodials with negative allometry. Van Sittert Page 2 of 43Relative to increases in bone length, both the humerus and femur widened with positive allometry. In the distal limb bones ML diameters increased isometrically (radius, metacarpus) or positively allometric (tibia, metatarsus) while the corresponding CC widths increased with negative allometry and isometrically respectively. Except for the humerus and femur, exponents were not significantly different between corresponding front and hind limb segments.We concluded that the patterns of bone growth in males and females are identical. In fetuses the growth of the appendicular skeleton is faster than it is after birth which is a pattern opposite to that reported for the neck. Allometric exponents seemed unremarkable compared to the few species described previously, and pointed to the importance of neck elongation rather than leg elongation during evolution.Nevertheless, the front limb bones and especially the humerus may show adaptation to behaviors such as drinking posture.

show abstract

Observation of mammalian similarity through allometric scaling laws

Cited by 17 publications

References 23 publications

Growth model for multicellular tumor spheroids

Growth model for multicellular tumor spheroids

Evolution of Locomotor Trends in Extinct Terrestrial Giants Affected by Body Mass

Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Contact Info

Product

Resources

About