A general model for the origin of allometric scaling laws in biology

Aerosol deposition modeling using ACSL

An aerosol deposition model has been written for inclusion into physiologically based pharmacokinetic (PBPK) models, allowing PBPK model based risk assessments to be performed for aerosolized materials. Previously, PBPK models could only treat inhaled gases and vapors. The deposition model employs a semi-empirical equation to describe extrathoracic deposition and employs data concerning the geometry of the thoracic conducting airways as well as that of the gas exchange regions of the lung to compute the deposited aerosol mass based on aerosol diffusion, sedimentation, and impaction. Provisions are made to allow calculations for polydisperse aerosols whose size distribution and mass vary with time. Variations in the model subject's respiration can be accommodated through selection of respiratory parameters at model startup as well as through consideration of carbon dioxide stimulation of respiration. The model is compared with other similar calculations and experimental data to validate the calculations. An example model application is presented in the form of a comparison of two inhalation atmospheres, one from an inhalation toxicity study and one from a similar atmosphere produced for fire extinguishing agent testing.

A three-dimensional model for arterial tree representation, generated by constrained constructive optimization

The computational method of constrained constructive optimization (CCO) has been generalized in two important respects: (1) arterial model trees are now grown within a convex, three-dimensional piece of tissue and (2) terminal flow variability has been incorporated into the model to account for the heterogeneity of blood flow observed in real vascular beds. Although no direct information from topographic anatomy enters the model, computer-generated CCO trees closely resemble corrosion casts of real arterial trees, both on a visual basis and with regard to morphometric parameters. Terminal flow variability was found to induce transitions in the connective structure early in the trees' development. The present generalization of CCO offers--for the first time--the possibility to generate optimized arterial model trees in three dimensions, representing a realistic geometrical substrate for hemodynamic simulation studies. With the implementation of terminal flow variability the model is ready to simulate processes such as the adaptation of arterial diameters to changes in blood flow rate or the formation of different patterns of angiogenesis induced by changing needs of blood supply.

Analyte-Receptor Binding Kinetics for Biosensor Applications: A Single-Fractal and a Dual-Fractal Analysis of the Influence of the Fractal Dimension on the Binding Rate Coefficient

The diffusion-limited binding kinetics of antigen (analyte) in solution to antibody (receptor) immobilized on a biosensor surface is analyzed within a fractal framework. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot ("Scientific Graphing Procedure, User's Manual," Jandel Scientific, San Rafael, CA, 1993). A couple of examples of a dual-fractal analysis are also presented. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for the analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis and for the binding of cell surface proteins from Helicobacter pylori strain in solution to sialyl-(alpha-2,3)-lactose-conjugated (20 mol%) polyacrylamide immobilized on a resonant mirror biosensor (S. Hirmo et al., Anal. Biochem. 257, 63, 1998), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, was 14.15. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient(s) expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface and further emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance. Copyright 1998 Academic Press.

Architectural patterns in branching morphogenesis in the kidney

During kidney development, several discrete steps generate its three-dimensional pattern including specific branch types, regional differential growth of stems, the specific axes of growth and temporal progression of the pattern. The ureteric bud undergoes three different types of branching. In the first, terminal bifid type, a lateral branch arises and immediately bifurcates to form two terminal branches whose tips induce the formation of nephrons. After 15 such divisions (in humans) of this specifically renal type of branching, several nephrons are induced whose connecting tubules fuse and elongate to form the arcades. Finally, the last generations undergo strictly lateral branching to form the cortical system. The stems of these branches elongate in a highly regulated pattern. The molecular basis of these processes is unknown and we briefly review their potential mediators. Differential growth in three different axes of the kidney (cortico-medullary, dorsoventral and rostro-caudal) generate the characteristic shape of the kidney. Rapid advances in molecular genetics highlight the need for development of specific assays for each of these discrete steps, a prerequisite for identification of the involved pathways. The identification of molecules that control branching (the ultimate determinant of the number of nephrons) has acquired new urgency with the recent suggestion that a reduced nephron number predisposes humans to hypertension and to progression of renal failure.

An analysis of analyte-receptor binding kinetics for biosensor applications: influence of the fractal dimension on the binding rate coefficient

The diffusion-limited binding kinetics of analyte in solution to receptor immobilized on a biosensor surface is analysed within a fractal framework. Both a single- as well as a dual-fractal analysis are utilized. Antigen-antibody and analyte-receptor systems are analysed. For the antigen-antibody and analyte-receptor systems where a single- or a dual-fractal analysis was used, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction. The binding rate coefficient expressions obtained as a function of the fractal dimension indicate the high sensitivity of the binding rate coefficient with respect to the fractal dimension. For example, for a single-fractal analysis and for the binding of (a) 1 microM BSA in solution to the anti-BSA-protein fused to a biosensor surface, and for (b) the binding of m-xylene-saturated STE buffer solution to the microorganism immobilized to the fiber-optic end and covered with a polycarbonate membrane, the orders of dependence of the binding rate coefficient on the fractal dimension were 5.535 and 3.314, respectively. This emphasizes the importance of the degree of heterogeneity on the biosensor surface and its impact on the binding rate coefficient, k. This high sensitivity is also indicated for a dual-fractal analysis, at least for the binding rate coefficient, k2. For example, during regeneration runs and for the binding of polymerase chain-reaction amplified DNA in solution to DNA capture protein immobilized on a fiber-optic biosensor, the order of dependence of k2 on Df2 was 3.399. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient expressions developed as a function of the fractal dimension for both single-fractal analysis and dual-fractal analysis systems are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface. Also, the importance of the nature of the surface on biosensor performance is emphasized in a quantitative sense.

Fractal dimension of the bone marrow in metastatic lesions

We previously reported that the distribution of the cells in normal bone marrow is fractal and self-similar. The purpose of this study was to determine whether the same is true in metastatic tumors. Thirty-two bone marrow biopsy sections (3 to 5 microm thick) of 28 patients were used to measure the fractal dimensions of the metastatic tumor cells' distribution. Microscopic images were obtained and were used for the fractal measurements. In the two-dimensional images, the fractal dimensions were 1.98 +/- 0.02 (95% +/- 5% cellularity), suggesting a compact nonfractal structure. The dimensions, however, were 1.72 +/- 0.1 (56% +/- 11% cellularity) for the normal components, with a P-value of <.0001 that is in agreement with our previous study. These results suggest that loss of the fractal structure in the metastatic lesions may be attributable to loss or suppression of the regulatory mechanisms maintaining the fractal morphogenesis of the bone marrow. This report provides a novel objective approach in the study of pathophysiology of the bone marrow disorders.

Epigenetic stratification: the role of individual change in the biological aging process

Aging is a complex process. It consists of a diverse assortment of seemingly random manifestations that occur in the individual, the mutual relationship and impact on mortality of which is frequently obscure. We derive a simple equation to model the aging process based on scale invariant and increasing change. The solution to this equation indicates that this change itself, irrespective of its quality, is the cause and not simply the effect of aging. This model establishes loss of homeostasis as a fundamental feature of aging. The model is deterministic, but it supports the stochastic nature of age changes. Paradoxically, this model states that a sufficient augmentation of aging processes results in a lack of aging. Experimental evidence in support of this model is presented that spans the levels of population mortality rates, cellular spatial organization, and gene dysregulation.

Imaging the structure of the striatum: a fractal approach to SPECT image interpretation

The spatial pattern of striatal dopamine transporter density in the living human brain was tested by duplicate SPECT scans with [123I]PE2I, [123I]beta-CIT or [123I]beta-CIT-FP and striatal phantom measurements. The resolution-dependent spatial variation was calculated by the fractal analysis of SPECT images. This variation, which depends on the size of the region of interest, was described by the spatial dispersion i.e. the standard deviation of the count densities divided by the mean density. In each sub-region, the observed and methodological dispersions were computed, and the resulting spatial dispersion was calculated. The methodological dispersion is caused by the imaging resolution, flood field non-uniformity, count density, scatter, reconstruction errors and partial volume effects, whereas the spatial dispersion is based on the cerebral heterogeneity of the dopamine transporter density. Recognition of the normal variation in heterogeneity is important in evaluation of the striatal dopamine transporter density between controls and patients suffering from various neuropsychiatric disorders.

Mortality invariants and their genetic implications

Old noninbred fly mortality decreases according to the inverse linear law and reduces to a single suborder-specific age. Relative child mortality (the mortality at a given age related to the mortality at 10 years) from 1 mo to 11 years is the same with 8% mean accuracy for all humans, independent of race, country, sex, and birth year (from 1780 to 1995), in contrast to birth mortality, which in developed countries changed fiftyfold during the last century. The concept of invariants, which is very powerful in physics, is applied to mortality of species as remote as humans and flies. It provides quantitative estimates for the selection of hereditary Methuselahs, who live, e.g., over six-mean lifespans and who may be relatively young biologically. It also demonstrates that old fly and relative child mortality are determined genetically and that the former is related to genetic heterogeneity.

Host cell allometry and regulation of the symbiosis between pea aphids, Acyrthosiphon pisum, and bacteria, Buchnera

The symbiotic bacteria Buchnera in aphids are borne in cells, called bacteriocytes, in the insect haemocoel. The number and median volume of bacteriocytes in pre-reproductive adult insects varied significantly among 14 parthenogenetic clones of the pea aphid Acyrthosiphon pisum. After logarithmic transformation of the data, the relationship of both number and median volume of bacteriocytes with aphid weight for the clones could be described by common regression lines with slopes significantly greater than zero. The allometric slope for median bacteriocyte volume was calculated as 1.06, by model I regression and 1.94 by model II regression; and the equivalent values of the allometric slope for total volume of bacteriocytes were 1.51 and 2.50, suggesting that the total volume of bacteriocytes increases disproportionately with aphid body weight. The partial correlation coefficient between the number and median volume of bacteriocytes was +0.07, with body weight held constant. It is proposed that the regulation of number and size of bacteriocytes is not linked and that bacteriocytes may not exhibit compensatory changes in size, in response to alteration in number. Experimental manipulation of the rates of bacteriocyte differentiation and division could therefore perturb the total volume of the symbiosis, on which aphid pests depend for normal growth and reproduction.

Fractal analysis--a new approach in brain receptor imaging

Improvements in detector technology and the development of radioligands for brain receptor imaging have introduced exiting new insights into the pathophysiology of various neuropsychiatric disorders and have improved the possibilities of optimizing the treatment for patients suffering from them. Positron emission tomography (PET) and single-photon emission tomography (SPET) with tailored radiopharmaceuticals provide information on the topographic physiological chemistry of the living human brain. The different patterns of brain receptor densities and distribution can be imaged and modelled with PET and SPET. The normal receptor distribution in the brain is broadly heterogeneous with different cortical layers, which show receptor densities varying from very low to high. Further exploration of the data shows that human neurophysiology and neural architectures possess fractal properties that may be altered during activation and in different neuropsychiatric disorders. This review highlights recent findings in SPET receptor imaging and the use of fractal analysis in the interpretation of images representing various neuropsychiatric disorders.

Analyte-receptor binding kinetics for biosensor applications. An analysis of the influence of the fractal dimension on the binding rate coefficient

The diffusion-limited binding kinetics of antigen (analyte), in solution with antibody (receptor) immobilized on a biosensor surface, is analyzed within a fractal framework. Most of the data presented is adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot. A single example of a dual-fractal analysis is also presented. It is of interest to note that the binding-rate coefficient (k) and the fractal dimension (Df) both exhibit changes in the same and in the reverse direction for the antigen-antibody systems analyzed. Binding-rate coefficient expressions, as a function of the Df developed for the antigen-antibody binding systems, indicate the high sensitivity of the k on the Df when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis, and for the binding of antibody Mab 0.5 beta in solution to gp120 peptide immobilized on a BIAcore biosensor, the order of dependence on the Df was 4.0926. For a dual-fractal analysis, and for the binding of 25-100 ng/mL TRITC-LPS (lipopolysaccharide) in solution with polymyxin B immobilized on a fiberoptic biosensor, the order of dependence of the binding-rate coefficients, k1 and k2, on the fractal dimensions, Df1 and Df2, were 7.6335 and -11.55, respectively. The fractional order of dependence of the k(s) on the Df(s) further reinforces the fractal nature of the system. The k(s) expressions developed as a function of the Df(s) are of particular value, since they provide a means to better control biosensor performance, by linking it to the heterogeneity on the surface, and further emphasize, in a quantitative sense, the importance of the nature of the surface in biosensor performance.

Standardized structure and modular design of a pharmacokinetic database

BACKGROUND

The accumulated knowledge on drugs can be used for an individual drug dosage adjustment if it is placed at our disposal in an informatically structured form.

THEORY AND METHODS

We have started building up a pharmacokinetic database aimed at adjusting drug dosages, in exemplary form, to patients with renal impairment. Parameters needed for the three dosage adjustment rules (Dettli, Kunin, Holford) and the most general concept of pharmacokinetics constituted the theoretical basis.

TWO PROCESSES PERTAIN TO ALL DRUGS

Distribution and elimination. Total drug clearance and at least two parameters representing distribution and elimination processes are closely interdependent in mathematical terms (clearance = volume of distribution*rate of elimination). This relation yields the unifying concept that serves as a prerequisite for a structured recording of 30 assigned pharmacokinetic and pharmacodynamic parameters within an informatic database.

SOLUTIONS AND RESULTS

The information is retrieved and referenced from 2383 original publications by means of a standardized input module. The complete database at present contains 15,397 records for 1573 drugs. A programmed meta-analytic algorithm is used to calculate the statistical measures for the central value and variance--as available--from the pooled values of primary records. The statistically standardized parameters are extracted for 6601 pharmacokinetic parameters, and placed at the users disposal with the output module.

PRACTICAL UTILITY

Following meta-analysis, published pharmacokinetics can be used as statistical estimates of population parameters. The statistical estimates with variances permit an individual drug dosage adjustment by applying the Bayesian approach or neural networks.

Myocardial blood flow heterogeneity in shock and small-volume resuscitation in pigs with coronary stenosis

Myocardial blood flow heterogeneity in shock and small-volume resuscitation in pigs with coronary stenosis. J. Appl. Physiol. 83(6): 1832-1841, 1997.-We analyzed the effects of shock and small-volume resuscitation in the presence of coronary stenosis on fractal dimension (D) and spatial correlation (SC) of regional myocardial perfusion. Hemorrhagic shock was induced and maintained for 1 h. Pigs were resuscitated with hypertonic saline-dextran 60 [HSDex, 10% of shed blood volume (SBV)] or normal saline (NS; 80% of SBV). Therapy was continued after 30 min with dextran (10% SBV). At baseline, D was 1.39 +/- 0.06 (mean +/- SE; HSDex group) and 1.34 +/- 0.04 (NS group). SC was 0.26 +/- 0.07 (HSDex) and 0.26 +/- 0.04 (NS). Left anterior descending coronary artery stenosis changed neither D nor SC. Shock significantly reduced D (i.e., homogenized perfusion): 1.26 +/- 0.06 (HSDex) and 1.23 +/- 0.05 (NS). SC was increased: 0.41 +/- 0.1 (HSDex) and 0.48 +/- 0.07 (NS). Fluid therapy with HSDex further decreased D to 1.22 +/- 0.05, whereas NS did not change D. SC was increased by both HSDex (0.56 +/- 0.1) and NS (0.53 +/- 0.06). At 1 h after resuscitation, SC was constant in both groups, and D was reduced only in the NS group (1.18 +/- 0.02). We conclude that hemorrhagic shock homogenized regional myocardial perfusion in coronary stenosis and that fluid therapy failed to restore this.