Complex enameloid microstructure of †Ischyrhiza mira rostral denticles

Serving in a foraging or self-defense capacity, pristiophorids, pristids, and the extinct sclerorhynchoids independently evolved an elongated rostrum lined with modified dermal denticles called rostral denticles. Isolated rostral denticles of the sclerorhynchoid Ischyrhiza mira are commonly recovered from Late Cretaceous North American marine deposits. Although the external morphology has been thoroughly presented in the literature, very little is known about the histological composition and organization of these curious structures. Using acid-etching techniques and scanning electron microscopy, we show that the microstructure of I. mira rostral denticles are considerably more complex than that of previously described dermal denticles situated elsewhere on the body. The apical cap consists of outer single crystallite enameloid (SCE) and inner bundled crystallite enameloid (BCE) overlying a region of orthodentine. The BCE has distinct parallel bundled enameloid (PBE), tangled bundled enameloid (TBE), and radial bundled enameloid (RBE) components. Additionally, the cutting edge of the rostral denticle is produced by a superficial layer of SCE and a deeper ridges/cutting edge layer (RCEL) of the BCE. The highly organized enameloid observed in the rostral denticles of this batomorph resembles that of the multifaceted tissue architecture observed in the oral teeth of selachimorphs and demonstrates that dermal scales have the capacity to evolve histologically similar complex tooth-like structures both inside and outside the oropharyngeal cavity.

An open-source solution for shape modeling and analysis of objects of challenging topologies

Shape analysis is an important and powerful tool in a wide variety of medical applications. Many shape analysis techniques require shape representations which are in correspondence. Unfortunately, popular techniques for generating shape representations do not handle objects with complex geometry or topology well, and those that do are not typically readily available for non-expert users. We describe a method for generating correspondences across a population of objects using a given template. We also describe its implementation and distribution via SlicerSALT, an open-source platform for making powerful shape analysis techniques more widely available and usable. Finally, we show results of this implementation on mouse femur data.

Advanced statistical analysis to classify high dimensionality textural probability-distribution matrices

Temporomandibular Joint (TMJ) Osteoarthritis (OA) is associated with significant pain and disability. It is really hard to diagnose TMJ OA during early stages of the disease. Subchondral bone texture has been observed to change in the TMJ early during TMJ OA progression. We believe that raw probability-distribution matrices describing image texture encode important information that might aid diagnosing TMJ OA. In this paper we present novel statistical methods for High Dimensionality Low Sample Size Data (HDLSSD) to test the discriminatory power of probability-distribution matrices in computed from TMJ OA medical scans. Our results, and comparison with previous results obtained from the summary features obtained from them indicate that probability-distribution matrices are an important piece of information provided by texture analysis methods and should not be down sampled for analysis.

Methods for quantitative characterization of bone injury from computed-tomography images

Computed tomography (CT) images can potentially provide insights into bone structure for diagnosis of disorders and diseases. However, evaluation of trabecular bone structure and whole bone shape is often qualitative or semi-quantitative. This limits inter-study comparisons and the ability to detect subtle bone quality variations during early disease onset or in response to new treatments. In this work, we enable quantitative characterization of bone diseases through bone morphometry, texture analysis, and shape analysis methods. The potential of our analysis methods to identify the impact of hemophilia is validated in a mouse femur wound model. In our results, shape localizes and characterizes the formation of spurious bone, and our texture and bone morphometry analysis results provide extra information about the composition of that bone. Some of our one-dimensional (1D) textural features were able to significantly differentiate our injured femurs from our healthy femurs, even with this small sample size demonstrating the potential of the proposed analysis framework. While trabecular bone morphometrics have been a pillar in 3D microCT bone research for decades, the proposed analysis framework augments how we define and understand phenotypical presentation of bone disease. The contributed open source software is exposed to the medical image analysis community through 3D Slicer extensions to ensure both robustness and reproducibility.

Detection of bone loss via subchondral bone analysis

To date, there is no single sign, symptom, or test that can clearly diagnose early stages of Temporomandibular Joint Osteoarthritis (TMJ OA). However, it has been observed that changes in the bone occur in early stages of this disease, involving structural changes both in the texture and morphometry of the bone marrow and the subchondral cortical plate. In this paper we present a tool to detect and highlight subtle variations in subchondral bone structure obtained from high resolution Cone Beam Computed Tomography (hr-CBCT) in order to help with detecting early TMJ OA. The proposed tool was developed in ITK and 3DSlicer and it has been disseminated as open-source software tools. We have validated both our texture analysis and morphometry analysis biomarkers for detection of TMJ OA comparing hr-CBCT to μCT. Our initial statistical results using the multidimensional features computed with our tool indicate that it is possible to classify areas of demonstrated loss of trabecular bone in both μCT and hr-CBCT. This paper describes the first steps to alleviate the current inability of radiological changes to diagnose TMJ OA before morphological changes are too advanced by quantifying subchondral bone biomarkers. This paper indicates that texture based and morphometry based biomarkers have the potential to identify OA patients at risk for further bone destruction.

Small brain, large brain -- a quest for nature's scale-up rules

A scaling model of the gyrencephalic mammalian brain, invoking identical repeating cortical units, whose number and size both increase with increasing brain size, was described previously (Prothero, 1997a,b). Each repeating unit, of microscopic dimensions, is viewed as extending from the pial membrane to the underlying white matter. The model predicts discrete scaling exponents, all integral multiples of 1/9, as a function of brain size, as follows: cortical thickness (1/9), outer cortical surface area (6/9), total (folded) cortical surface area (8/9), cortical volume (9/9), white matter volume (9/9), neuron line-count (0/9) and neuron volume density (-3/9). In the present paper extensions to the model give discrete exponents for the scaling of the cross-sectional area of the corpus callosum (6/9), for mean foliar and gyral width (each 1/9), for foliar number (2/9), for mean foliar length (3/9), for mean foliar and gyral perimeter (each 3/9) and for total foliar and total gyral length (each 5/9). The predicted scaling exponent for cross-sectional area of the corpus callosum is in reasonable agreement with the empirical observations. Needed are more precise and more extensive data on cortical folding to stringently test the model predictions relating to cortical folding. On the whole, the model is in good agreement with a diverse body of empirical data bearing on the scaling of the gyrencephalic mammalian brain.

Scaling of cortical neuron density and white matter volume in mammals

A prior scaling model, based on repeating cortical units, whose number and size increase with brain size, gave discrete exponents for cortical thickness (1/9), outer (visible) surface area (2/3), folded cortical surface area (8/9) and cortical volume (1), each as a function of brain volume. These exponents are in reasonable agreement with a diversity of empirical data (Prothero, 1997). Rockel et al. (1980) reported that neuron number, assayed in a narrow column across cortex (pia to white matter) is invariant over several differing brain regions and species. Since cortical thickness scales, empirically, as about the 1/9 power of brain volume, their data imply that neuron line density (across cortex) scales with an exponent of about -1/9. Rockel et al. (1980) also urged that cortical neuron surface density is invariant. This extrapolation implies that neuron volume density scales, like line density, as the -1/9 power of brain volume, in marked disparity with the data of Haug (1987) and Tower (1954). The present model assumes an invariant number of neurons per repeating unit. Thus neuron number, assayed across cortical thickness, is independent of brain size, in accord with Rockel et al. (1980). The model predicts that neuron line density (in any direction) scales as the -1/9 power of brain volume. Now neuron volume density scales as the -1/3 power of brain volume, in reasonable agreement with the results of Haug (1987) and Tower (1954). For white matter, I assume that mean axon length scales with brain diameter (exponent of 1/3). The number of white matter axons scales in proportion to the number of repeating units (exponent of 2/3). Given an invariant size distribution of white matter axons, white matter volume thus scales with an exponent of one, in reasonable accord with Haug (1970).

Visualization-based mapping of language function in the brain

Cortical language maps, obtained through intraoperative electrical stimulation studies, provide a rich source of information for research on language organization. Previous studies have shown interesting correlations between the distribution of essential language sites and such behavioral indicators as verbal IQ and have provided suggestive evidence for regarding human language cortex as an organization of multiple distributed systems. Noninvasive studies using ECoG, PET, and functional MR lend support to this model; however, there as yet are no studies that integrate these two forms of information. In this paper we describe a method for mapping the stimulation data onto a 3-D MRI-based neuroanatomic model of the individual patient. The mapping is done by comparing an intraoperative photograph of the exposed cortical surface with a computer-based MR visualization of the surface, interactively indicating corresponding stimulation sites, and recording 3-D MR machine coordinates of the indicated sites. Repeatability studies were performed to validate the accuracy of the mapping technique. Six observers-a neurosurgeon, a radiologist, and four computer scientists, independently mapped 218 stimulation sites from 12 patients. The mean distance of a mapping from the mean location of each site was 2.07 mm, with a standard deviation of 1.5 mm, or within 5.07 mm with 95% confidence. Since the surgical sites are accurate within approximately 1 cm, these results show that the visualization-based approach is accurate within the limits of the stimulation maps. When incorporated within the kind of information system envisioned by the Human Brain Project, this anatomically based method will not only provide a key link between noninvasive and invasive approaches to understanding language organization, but will also provide the basis for studying the relationship between language function and anatomical variability.

Cortical scaling in mammals: a repeating units model

A simple scaling model germane to the gyrencephalic mammalian cortex is proposed. The model aims to account for the empirical scaling of morphometric variables such as cortical thickness, surface area and volume, as a function of brain size. Several assumptions are made. Gyrencephalic cortices are assumed to be modular in construction, comprised of identical repeating units. Both the number and size of cortical units are assumed to increase with increasing brain size. The shape of the brain and of the repeating units are assumed not to vary systematically with brain size. The surface-density of repeating units is taken to be invariant. The model exponents for cortical thickness, folded surface area and volume, each as a function of cerebral volume, are one-ninth, eight-ninths and one, respectively. These discrete model exponents, and others, are in reasonable agreement with a diverse body of scaling data, both phylogenetic and ontogenetic. One interpretation is that phylogenetic scaling simply reflects ontogenetic scaling, extended over a wide range of adult brain sizes. The model is confined to ontogenetic/phylogenetic scaling. It is suggested that the model exponents are not adaptive, in the usual sense of that term.

Scaling of organ subunits in adult mammals and birds: a model

Members of one class of organs--including kidney and lung--consist chiefly of repeating units, or subunits, similar in size and shape. Across species, both the number and size of repeating units may increase with increasing organ size. A simple model is proposed, relating the scaling of unit-size and unit-number to that of organ volume. The model makes three structural assumptions, the crucial one, biologically speaking, being that the numerical density of repeating units scales as does organ surface-to-volume ratio. Data were collected from the literature bearing on the number, diameter, total surface area and total volume of such repeating units (i.e., alveoli, air capillaries, renal tubules and glomeruli), for avian and mammalian lung and for mammalian kidney, each as a function of organ size. These data, after log-log transformation, were submitted to standard linear least squares regression analysis. The resultant slopes for nine different regression lines are in good agreement with the model predictions. This finding suggests, surprisingly, that organ scale-up, at least for selected organs, expressed in terms of repeating units, as a function of organ volume, in mammals and birds, and conceivably in other phyla, may be based on a small number of elementary structural principles.

Visualization and mapping of neurosurgical functional brain data onto a 3-D MR-based model of the brain surface

The Human Brain Project was initiated with the goal of developing methods for managing and sharing information about the brain. As a prototype Human Brain Project application we are developing a system for organizing, visualizing, integrating and sharing information about human language function. The goal of the brain mapping component of our work, described in this article, is to generate the 3D location and extent of cortical language sites with respect to a uniform, 3D patient coordinate system. The language sites of individual patients can then be combined with or related to other patient data in terms of a Talairach, surface-based, or other deformable coordinate systems. Language site mapping is done by visually comparing an intraoperative photograph with the rendered image (from MRI data). The techniques outlined in this article have been utilized to map cortical language sites of six patients. Preliminary results point to the adequacy of our volume visualizations for language mapping. The strength of the visualization scheme lies in the combination of interactive segmentation with volume and surface visualization. We are now in the process of acquiring more patient data to further validate the usefulness of our method.

Bone and fat as a function of body weight in adult mammals

Three independent data sets, for both bone and fat weight, in adult mammals, expressed as a function of body weight, were submitted to linear regression analysis of the log-log transformed data. For land mammals generally, weighing up to 6.6 metric tons, the slope of the best-fit regression line for skeletal weight is 1.073 +/- 0.021. This regression line underestimates skeletal weight in the elephant by about 40%. For cetaceans, varying in body weight from about 0.1 to over 100 metric tons, the slope of the best-fit regression line for skeletal weight is 1.133 +/- 0.044. Since the slopes for these two groups of mammals are not statistically different, and since cetaceans are normally shielded from gravity, due to buoyancy, it is suggested that the slope (1.073) in land mammals may not be an adaption to gravity. After pooling the data from the three data sets for fat, the resultant regression has a slope of 1.146 +/- 0.026. It is argued, on theoretical grounds, that slopes greater than 1.2-1.3 will not be found for the log-log regression of any major tissue on body weight, taken over the whole mammalian weight range.

A resource guide to VR in medicine

This guide provides a bibliography of many of the most noteworthy contributions to the emerging literature about virtual reality in medicine, along with listings of the most relevant conferences and resources for researchers. This is an abridged version of a continuously updated comprehensive document which is available on-line to the research community.

Adult life span as a function of age at maturity

A regression analysis was made of age at first reproduction in female mammals, as a function of body weight, using the data of Wootton. Data on maximal life span, also expressed as a function of body weight, were used to calculate "adult" life span, wherever possible, by subtracting the cognate value for age at first reproduction. Then a regression analysis of adult life span as a function of age at first reproduction was made. In both cases global regression lines (i.e., for whole data sets) were computed by standard least squares and by a robust method, as well as local regression lines for subgroups classified by taxonomic and ecological criteria. The slopes of the various regression lines were found to vary widely as a function of the method of classification. This result argues against the notion that the ratio of life history variables is a constant, or that one life history variable is likely to be a simple function of another. The results for bats are anomalous, in that age at first reproduction appears to be independent of body weight (over about two orders of magnitude). It is concluded that a full understanding of life history variables, such as maximal life span and age at maturity, is likely to depend on combined physiological, ecological, and evolutionary insights.

Determination of relative fiber orientation in heart muscle: methodological problems

Knowledge of the muscle pattern in the heart is important to understanding cardiac contraction and propagation of the electrical stimulus. Most work on this pattern has been carried out by blunt gross dissection, whereby fiber bundles are easily visible on the peeled heart wall. However, it has never been shown, to our knowledge, that the orientation of macroscopic fiber bundles seen in a peeled heart corresponds to that of the constituent myofibers (muscle cells). For this purpose, one needs to carry out a three-dimensional microscopic reconstruction within a documented macroscopic reference frame. To draw valid conclusions in such a coordinated macroscopic and microscopic study, one must estimate the (slice) angle between the long axis of a muscle cell and the plane of section. Otherwise any alleged differences between the macroscopic and microscopic orientations may be just an artifact of sectioning. In this study we have shown that, provided the images of the myofibers meet simple criteria, one can be reasonably confident that the potential error incurred by sectioning is small. On this basis, we demonstrated that while there is a general correspondence between the macroscopic fiber and the microscopic myofiber orientations, there are significant differences in detail.

Scaling of bodily proportions in adult terrestrial mammals

To model body shape, a data base was constructed for body, forelimb, and hindlimb length, surface area, and girth, each as a function of body weight, in a diversity of mammals. These data were submitted to linear least-squares regression analysis. In addition, data on the partitioning of weight and surface area among the body segments (head-trunk, forelimbs, and hindlimbs) were collected. These data imply a relatively constant partitioning of body weight and surface area among the body segments. The regression parameters and the body segment data were used to build and test a model of bodily proportions. The model consists of three classes of cylinders, each specified by a length and a diameter, representing the three classes of body segments. The parameters of the model were constrained to enforce geometric similarity (constant shape). The model was found to agree reasonably well with an independent subset of the data. It is concluded that adult land mammals do exhibit geometric similarity over a substantial weight range.

Myofiber orientation in the weanling mouse heart

This study provides a quantitative description at the cellular level of myofiber orientation throughout the ventricles of the mouse heart. We employed computer-based methods of three-dimensional reconstruction from 3 microns plastic-embedded serial sections. Registration marks were introduced by drilling minute holes into each plastic block. Subfields of selected sections were photographed at 20 x magnification, using a computer-controlled microscope. The 35-mm film frames were projected onto a digitizer tablet and the epi- and endocardial boundaries were digitized manually. The "heads" and "tails" of linear segments of a representative myofiber sample present in each projected image were digitized in point mode. The many x-, y-, z-coordinate tables generated by digitization were reassembled automatically, giving a numerical description of the myofiber pattern. This pattern was studied interactively on a high-performance graphics workstation. We find that the heart wall is, to a first approximation, a "sandwich," in which the myofibers in the middle layer run mainly circumferentially, whereas those in the inner and outer layers run parallel or oblique to the apical-basal axis, a variant of the classical model of the myofiber pattern. We observed a "sleeve" in the interventricular septum, formed by longitudinal and oblique myofibers, a feature which apparently has not been described previously. Myofibers not running parallel to the transverse or longitudinal planes were not resolved in this study. We conclude that three-dimensional reconstruction of the cardiac myofiber pattern at the light-microscopic level, while laborious, is technically feasible and scientifically worthwhile.

Lifetime energy budgets in mammals and birds

1. Two data sets for standard energy metabolism (351 and 320 species, respectively) and one for maximal lifespan (494 species) in mammals have been assembled from the literature. 2. In addition smaller data sets of active (field) energy metabolism in mammals (36 species) and in birds (25 species) have been drawn on. 3. The products of the respective regression parameters as well as the products of energy metabolism and maximal lifespan in individual species have been computed in order to estimate lifetime energy metabolism in mammals generally and in various mammalian orders. 4. It is found that lifetime energy budgets in mammals generally, whether standard or active, very systematically with body mass with slopes between 0.87 and 0.93, significantly different from unity (P less than 0.001 or P less than 0.01). 5. In birds, lifetime energy budgets, whether standard or active, vary with slopes of 0.94 +/- 0.05 and 0.88 +/- 0.09, which are not significantly different from unity (P greater than 0.1). 6. In carnivores, artiodactyls, primates and bats the slopes for lifetime standard as well as lifetime active energy budgets are not significantly different from one in any of the investigated data sets. 7. In rodents the lifetime standard energy budgets have slope significantly different from one; in marsupials one data set for lifetime standard and the one for lifetime active energy budget lead to slopes significantly different from one. 8. It is concluded from this analysis that current data do not support the hypothesis that lifetime energy budgets, whether standard or active, vary as the first power of body mass in mammals generally.(ABSTRACT TRUNCATED AT 250 WORDS)

Independent evidence for a commitment model of clonal attenuation

We previously reported a model of clonal attenuation which assumes three classes of cells: small highly replicative cells; intermediate size cells of limited replicative potential and large non-diving cells. Computer simulations carried out with the model lead to predictions of how the relative proportion of each cell type varies throughout the in vitro replicative life span of a mass population. These predictions appear to be broadly confirmed by independent data recently reported by another laboratory.

Cell enlargement: one possible mechanism underlying cellular senescence

We previously demonstrated an inverse relationship between the G1 volume of human diploid fibroblast-like (HDFL) cells obtained from foreskin tissue and clonal replicative potential. On the basis of these results, we suggested that one process underlying in vitro senescence is a progressive increase in the mean cell volume of successive progeny within clonal lineages. We now report that the size of HDFL cells, as well as of chick embryo fibroblasts, can be increased in the virtual absence of cell division by culturing at low density and at low serum concentration (0.1-1.0%). Consequent to an increase in cell size, the replicative potential of the cells is reduced to the level of later-passage cells of similar size. By clonal analysis, the populations of enlarged cells contain up to three times as many nondividing cells as do controls. In the enlarged populations, the proportion of cells producing attenuated clones (four or fewer progeny) increases by about 30%, whereas the proportion of cells yielding greater than 32 cells declines by a similar percentage. These observations lead us to propose that replicative potential may be limited by cell size, which in turn may be regulated by a kinetic relationship between cellular growth and cell division cycles.

Three-dimensional reconstruction of the myofiber pattern in the fetal and neonatal mouse heart

A methodology for three-dimensional reconstruction from serial sections and interactive computer graphics is described briefly. This methodology was applied to study the morphogenesis of the cardiac myofiber pattern in the fetal and neonatal mouse heart (ventricles). Few organized in-plane myofibers were found in the myocardial wall before 12 days postconception, but many fibers were observed in the very numerous trabeculae at all times up to birth. However, beginning at about 12 days, the number of fibers in the myocardial wall increases rapidly: these are seen predominantly in the transverse plane. The neonatal mouse heart, especially the left ventricle, resembles a small adult muscular artery. But the global myofiber pattern in the mouse heart at these stages appears to be more complex than might be inferred from earlier studies of the local myofiber pattern at a few sites in the ventricles of a few species of adult mammals. In particular, the pattern in and adjacent to the interventricular septum appears quite complex.

Coordinated three-dimensional reconstruction from serial sections at macroscopic and microscopic levels of resolution: the human heart

This report describes procedures we have developed for obtaining correlated quantitative structural information at two very different levels of resolution. Accurate reconstructions of entire organs and samples of tissue within organs were produced in correct scalar and topographical relationship using computer-assisted techniques. A specially designed sectioning apparatus, a macrovibratome, was used to section serially the ventricles of the human heart macroscopically. Photographs were taken of every slice. A tissue block excised from a slice at a specified locus in the left ventricular wall was embedded in plastic; serial-3 micron sections were cut in each of two orthogonal orientations. Photomicrographs were taken by semi-automated microscopy. Images of both macroscopic and microscopic sections were projected onto a bitpad and manually digitized. The resulting tables of x-, y-, and z-coordinates were reassembled on a VAX 11/750 computer, then transferred to a high-performance graphics workstation and displayed as three-dimensional images. Microscopic images were shown in the correct reference frame with respect to the macroscopic (parent) structure.

Proliferative potential of human fibroblasts: an inverse dependence on cell size

Human foreskin fibroblast-like cells were separated on the basis of DNA content and cell size by fluorescence-activated cell sorting. Subpopulations of "large" or "small" cells with the same (G1) DNA content were clonally expanded and found to contain predominantly nondividing or highly proliferative cells, respectively. From the rate of clonal growth, we deduce that small cells divide faster than large cells. Intermediate-sized cells were found to yield primarily smaller ("attenuated") clones. The clonal data can be incorporated into a previously reported kinetic model of clonal attenuation. This version of the model postulates that small "stem" cells yield larger daughters which have only a limited proliferative potential. We also postulate that a progressive increase in cell size can account for the decreasing concentration of DNA polymerase alpha, which has been reported in older cultures.

Scaling of maximal lifespan in bats

1. Values for maximal lifespan in heterothermic and homeothermic bats as a function of body weight, brain weight and lifetime basal energy consumption were submitted to linear (log-log) and multiple regression analysis. 2. The results of the regression analyses of maximal lifespan in bats were compared with those reported for non-flying mammals based on both narrow and wide weight ranges. 3. It was found that the regression lines (linear or multiple) for maximal lifespan in bats (heterothermic or homeothermic) lie well above the regression lines for non-flying mammals. 4. Predictions of maximal lifespan in heterothermic bats based on estimated lifetime basal energy consumption and body weight are in reasonable agreement with observed values when torpor and hibernation behaviour are taken into account. 5. But observed values of maximal lifespan in homeothermic bats were found to lie substantially above the regression lines derived for non-flying mammals. 6. It was concluded that existing hypotheses do not account for the long lifespan observed in bats generally.

Methodological aspects of scaling in biology

Interest in the scaling approach to problems of biological design has increased dramatically in the past few years. But thus far no systematic attempt has been made to review the possible pitfalls attendant upon this approach. As a beginning, the problems which can arise from rounding exponents, or taking standard errors at face value, or expressing dependent variables in ratio form are discussed. There follows a discussion of fitting specific functions to scaling data, of the special needs for documentation and of the potential value to be derived from suitable computer programs in scaling studies. Finally, the possible difficulties of demonstrating global optimization in biological systems, the risks of dimensional analysis and the value and nature of scaling models are discussed.

Scaling of energy metabolism in unicellular organisms: a re-analysis

The database used by Hemmingsen (1960) to compute energy metabolism in unicellular organisms was reassembled and submitted to linear (log-log) analysis. As Hemmingsen noted, this data set includes marine zygotes, which are not unicellular organisms. If no temperature correction factors are applied to the data the best-fit regression line has a slope of 0.698 +/- 0.024. Application of the temperature correction factors assumed to have been used by Hemmingsen gave a slope of 0.756 +/- 0.021, identical to the value he reported. The correlation coefficient is 0.97. The mean scatter about the regression line exceeds 100%. A revised set of temperature correction factors gave a slope of 0.730 +/- 0.021, suggesting that the value of almost exactly three-quarters obtained by Hemmingsen was probably fortuitous. The slope of the best-fit regression line is very sensitive to the inclusion of bacteria and flagellates. When the data points for these organisms are omitted from the calculation the slope decreases to 0.645 +/- 0.045. When the data points for bacteria, flagellates and marine zygotes are omitted, the slope drops to 0.608 +/- 0.025. The correlation coefficient (0.97), compared to the best-fit line reported by Hemmingsen, is unaffected; the mean deviation about the regression line drops to 40% and the points are evenly distributed about the regression line. Because of the small number of species for which measurements have been made, the existing database relating energy metabolism to cell size is not representative of unicellular organisms generally. It is concluded that the case for a three-quarters power rule expressing energy metabolism as a function of size in unicellular organisms generally is not at all persuasive.

Scaling of standard energy metabolism in mammals: I. Neglect of circadian rhythms

The original data employed to derive the three-quarters power rule relating standard or basal energy metabolism in mammals to adult body weight are examined. It is shown that the data may contain a systematic bias due to an (apparent) neglect of circadian rhythms. Correction for this bias would tend to decrease the slope of the regression line, bringing it into better conformity with the value of about two-thirds obtained in a recent study of a larger sample by Bartels (1982).

Organ scaling in mammals: the kidneys

Values of kidney weight in adult male and female mammals, both terrestrial and aquatic, as well as values for renal blood flow and glomerular number and diameter, were submitted to linear (log-log) regression analysis. The slope of the regression line for kidney weight in 63 species of adult terrestrial mammals was 0.85 %/- 0.01. No statistically significant difference was found between the slopes of the regression lines for male and female terrestrial mammals. The slope of regression line for kidney weight in eight species of adult aquatic mammals was 0.92 +/- 0.01. Again, no statistically significant difference was found between the slopes for males and females. However, the slope (0.92) of the regression line for aquatic mammals was significantly different from the slope (0.85) for terrestrial mammals (P much less than 0.001). The slope of the regression of renal blood flow on body weight was 0.82 +/- 0.01. This value is consistent with the hypothesis that renal blood flow represents a constant fraction of cardiac output (over about 3.4 orders of magnitude in body weight). The slopes of the regression lines for glomerular number (per kidney) and mean glomerular diameter were 0.59 +/- 0.02 and 0.11 +/- 0.01, respectively. A schematic model representing the scaling of energy-partitioning in mammals is introduced.

A model of clonal attenuation

Two formal models of clonal attenuation [Kirkwood, T. B. L. & Holliday, R. (1975) J. Theor. Biol. 53, 481-496; Shall, S. & Stein, W. D. (1979) J. Theor. Biol. 76, 219-231] are considered in the light of recent data on the changing distribution of replicative potential among individual cultured fibroblasts on subcloning. The experimental data [Smith, J. R., Pereira-Smith, O. & Good, P. I. (1977) Mech. Ageing Dev. 6, 283-286] are shown to contradict both models. A new model, compatible with the subcloning data, is proposed. This model involves a gradual increase in the probability of commitment during cell growth in culture and a small number (about seven) of divisions following commitment. The gradual increase in commitment probability is shown to be compatible with the gradual accumulation of a gene product subject to autogenous regulation.

Heart weight as a function of body weight in mammals

Linear regression analysis was carried out on logarithmically transformed heart weight and body weight data in 104 mammalian species. It was shown that heart weight varies as the 0.98 power of body weight over essentially the whole mammalian weight range. The coefficient of correlation between heart weight and body weight is 0.99. Student's test was employed to compare the slopes of the several regression lines as between male and female animals, and as between terrestrial and aquatic mammals. In neither case were the differences in slope found to be statistically significant (df greater than 177, p less than 0.5).

Cell kinetics in the erythroid compartment of guinea pig bone marrow: a model based on 3H-TdR studies

A model of steady-state erythropoiesis in the guinea pig is described. The model incorporates an unidentified progenitor compartment, as well as compartments representing proerythroblasts, basophilic, polychromatic and orthochromatic cells. A computer representation of the model permits a simulation of the labeling curves obtained in pulse and intermittent labeling regimes. It was found that a reasonable fit to the data can be achieved when the parameters for the various compartments are essentially identical. The results of a preliminary sensitivity analysis, carried out by perturbing the duration of S phase from the best fit value, are reported. The fit achieved to the data supports the hypothesis underlying the model that each compartment corresponds to one generation and that the flux within and between compartments is sequential.