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Fractals in biology and medicine

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

Review↗

Possible effects of protracted exposure on the additivity of risks from space radiations

Conventional radiation risk assessments are presently based on the additivity assumption. This assumption states that risks from individual components of a complex radiation field involving many different types of radiation can be added to yield the total risk of the complex radiation field. If the assumption is not correct, the summations and integrations performed to obtain the presently quoted risk estimates are not appropriate. This problem is particularly important in the area of space radiation risk evaluation because of the many different types of high- and low-LET radiation present in the galactic cosmic ray environment. For both low- and high-LET radiations at low enough dose rates, the present convention is that the addivity assumption holds. Mathematically, the total risk, Rtot is assumed to be Rtot = summation (i) Ri where the summation runs over the different types of radiation present. If the total dose (or fluence) from each component is such that the interaction between biological lesions caused by separate single track traversals is negligible within a given cell, it is presently considered to be reasonable to accept the additivity assumption. However, when the exposure is protracted over many cell doubling times (as will be the case for extended missions to the moon or Mars), the possibility exists that radiation effects that depend on multiple cellular events over a long time period, such as is probably the case in radiation-induced carcinogenesis, may not be additive in the above sense and the exposure interval may have to be included in the evaluation procedure. It is shown, however, that "inverse" dose-rate effects are not expected from intermediate LET radiations arising from the galactic cosmic ray environment due to the "sensitive-window-in-the-cell-cycle" hypothesis.

NASA Discipline Number 45-10↗

Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series

The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state [Physiol. Rev. 9, 399-431 (1929)]. However, recent studies [Phys. Rev. Lett. 70, 1343-1346 (1993); Fractals in Biology and Medicine (Birkhauser-Verlag, Basel, 1994), pp. 55-65] reveal that under normal conditions, beat-to-beat fluctuations in heart rate display the kind of long-range correlations typically exhibited by dynamical systems far from equilibrium [Phys. Rev. Lett. 59, 381-384 (1987)]. In contrast, heart rate time series from patients with severe congestive heart failure show a breakdown of this long-range correlation behavior. We describe a new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series. Application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. This method may be of use in distinguishing healthy from pathologic data sets based on differences in these scaling properties.

NASA Discipline Number 14-10↗

Space proton transport in one dimension

An approximate evaluation procedure is derived for a second-order theory of coupled nucleon transport in one dimension. An analytical solution with a simplified interaction model is used to determine quadrature parameters to minimize truncation error. Effects of the improved method on transport solutions with the BRYNTRN data base are evaluated. Comparisons with Monte Carlo benchmarks are given. Using different shield materials, the computational procedure is used to study the physics of space protons. A transition effect occurs in tissue near the shield interface and is most important in shields of high atomic number.

NASA Discipline Number 45-10↗

Comparison of mode estimation methods and application in molecular clock analysis

BACKGROUND: Distributions of time estimates in molecular clock studies are sometimes skewed or contain outliers. In those cases, the mode is a better estimator of the overall time of divergence than the mean or median. However, different methods are available for estimating the mode. We compared these methods in simulations to determine their strengths and weaknesses and further assessed their performance when applied to real data sets from a molecular clock study. RESULTS: We found that the half-range mode and robust parametric mode methods have a lower bias than other mode methods under a diversity of conditions. However, the half-range mode suffers from a relatively high variance and the robust parametric mode is more susceptible to bias by outliers. We determined that bootstrapping reduces the variance of both mode estimators. Application of the different methods to real data sets yielded results that were concordant with the simulations. CONCLUSION: Because the half-range mode is a simple and fast method, and produced less bias overall in our simulations, we recommend the bootstrapped version of it as a general-purpose mode estimator and suggest a bootstrap method for obtaining the standard error and 95% confidence interval of the mode.

Evolution, Molecular↗

The high-energy proton fluxes in the SAA observed with REM aboard the MIR orbital station

During two years, from November 1994 to 1996, the particle detector REM measured the highly energetic electron and proton environment at the outside of the MIR orbital station. Using mission averaged data we investigate various aspects of the proton fluxes in the SAA. Comparison with the radiation belt model AP8 reveal important differences. c2002 Elsevier Science Ltd. All rights reserved.

long duration↗

Dipole potentials indicate restructuring of the membrane interface induced by gadolinium and beryllium ions

The dipole component of the membrane boundary potential, phi(d), is an integral parameter that may report on the conformational state of the lipid headgroups and their hydration. In this work, we describe an experimental approach to measurements of the dipole potential changes, Deltaphi(d), and apply it in studies of Be(2+) and Gd(3+) interactions with membranes composed of phosphatidylserine (PS), phosphatidylcholine (PC), and their mixtures. Deltaphi(d) is determined as the difference between the changes of the total boundary potential, phi(b), measured by the IFC method in planar lipid membranes and the surface potential, phi(s), determined from the electrophoretic mobility of liposomes. The Gouy-Chapman-Stern formalism, combined with the condition of mass balance, well describes the ion equilibria for these high-affinity cations. For the adsorption of Be(2+) and Gd(3+) to PC membranes, and of Mg(2+) to PS membranes, the values of Deltaphi(b) and Deltaphi(s) are the same, indicative of no change of phi(d). Binding of Gd(3+) to PS-containing membranes induces changes of phi(d) of opposite signs depending on the density of ionized PS headgroups in the bilayer. At low density, the induced Deltaphi(d) is negative (-30 mV), consistent with the effect of dehydration of the surface. At maximal density (pure PS, neutral pH), adsorption of Be(2+) or Gd(3+) induces an increase of phi(d) of 35 or 140 mV, respectively. The onset of the strong positive dipole effect on PS membranes with Gd(3+) is observed near the zero charge point and correlates with a six-fold increase of membrane tension. The observed phenomena may reflect concerted reorientation of dipole moments of PS headgroups as a result of ion adsorption and lipid condensation. Their possible implications to in-vivo effects of these high-affinity ions are discussed.

Non-NASA Center↗

Numerical experiments with model monophyletic and paraphyletic taxa

The problem of how accurately paraphyletic taxa versus monophyletic (i.e., holophyletic) groups (clades) capture underlying species patterns of diversity and extinction is explored with Monte Carlo simulations. Phylogenies are modeled as stochastic trees. Paraphyletic taxa are defined in an arbitrary manner by randomly choosing progenitors and clustering all descendants not belonging to other taxa. These taxa are then examined to determine which are clades, and the remaining paraphyletic groups are dissected to discover monophyletic subgroups. Comparisons of diversity patterns and extinction rates between modeled taxa and lineages indicate that paraphyletic groups can adequately capture lineage information under a variety of conditions of diversification and mass extinction. This suggests that these groups constitute more than mere "taxonomic noise" in this context. But, strictly monophyletic groups perform somewhat better, especially with regard to mass extinctions. However, when low levels of paleontologic sampling are simulated, the veracity of clades deteriorates, especially with respect to diversity, and modeled paraphyletic taxa often capture more information about underlying lineages. Thus, for studies of diversity and taxic evolution in the fossil record, traditional paleontologic genera and families need not be rejected in favor of cladistically-defined taxa.

Non-NASA Center↗

Limits to randomness in paleobiologic models: the case of Phanerozoic species diversity

The question of how random, or unconstrained, paleobiologic models should be is examined with a case study: Signor's (1982, 1985) inverse calculation of levels of marine species diversity through the Phanerozoic. His calculation involved an ingenious model that estimated species numbers and species abundances in the world oceans of the past by correcting known numbers of fossil species for variations in sedimentary rocks available for sampling and in effort paleontologists might devote to sampling. The model proves robust to changes in possible shapes of species-abundance distributions, but it is sensitive to alterations in the assumption that paleontologists collect fossils at random. If it is assumed that ease of collecting varies with age of sediment (with the Cenozoic offering easy sampling) or that paleontologists tend to seek out rarer fossils, results of the inverse calculation change. In particular, the magnitude of the calculated Cenozoic diversity increase always declines from the factor of about seven as originally reported to something considerably smaller. This leaves open the problem of the magnitude of Cenozoic increase in marine species diversity, awaiting better empirical data and, perhaps, more exacting models, random or otherwise.

Non-NASA Center↗

A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation

DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.

DNA/radiation effects↗

Applications of amorphous track models in radiation biology

The average or amorphous track model uses the response of a system to gamma-rays and the radial distribution of dose about an ion's path to describe survival and other cellular endpoints from proton, heavy ion, and neutron irradiation. This model has been used for over 30 years to successfully fit many radiobiology data sets. We review several extensions of this approach that address objections to the original model, and consider applications of interest in radiobiology and space radiation risk assessment. In the light of present views of important cellular targets, the role of target size as manifested through the relative contributions from ion-kill (intra-track) and gamma-kill (inter-track) remains a critical question in understanding the success of the amorphous track model. Several variations of the amorphous model are discussed, including ones that consider the radial distribution of event-sizes rather than average electron dose, damage clusters rather than multiple targets, and a role for repair or damage processing.

NASA Discipline Radiation Health↗

Implication of microdosimetry in estimation of radiation quality in space environment

Errors introduced using a tissue equivalent proportional counter to estimate radiation quality of an arbitrary ion field as related to space radiations are examined. This is accomplished by using a generalized analytic model to calculate the effect of energy loss straggling, track structure, and pathlength distribution on the microdosimetric distribution. The error can be as large as a factor of two, but no systematic trend could be found.

NASA Discipline Radiation Health↗

Calculations of hadronic dissociation of 28Si projectiles at 14.6A GeV by nucleon emission

An optical potential abrasion-ablation collision model is used to calculate hadronic dissociation cross sections for one, two, and three nucleon removal for the first time for a 14.6A GeV 28Si beam fragmenting in aluminum, tin, and lead targets. These estimates are compared with recent semi-inclusive measurements. Significant differences between some calculated and measured semi-inclusive cross sections exist which cannot be resolved without measurements of the exclusive channel hadronic cross sections. Calculations for each exclusive reaction channel contributing to the semi-inclusive cross sections are presented and discussed.

NASA Program Radiation Health↗

Self-reported coping behavior in health and disease: assessment with a card sort game

The authors tested the hypothesis that individuals with a variety of severe chronic illnesses and the healthy elderly exhibit a loss of flexibility in their response to a variety of stressors, compared with healthy adults. A card sort game designed to assess self-reported coping behavior under different stressful life situations was used to compare healthy adults with individuals with multiple sclerosis, rheumatoid arthritis, systemic lupus erythematosus, and the elderly. The healthy adults were found to exhibit more variability than any of the illness groups or the elderly. Healthy function is marked by a complex type of variability.

Non-NASA Center↗

Prediction of human gait parameters from temporal measures of foot-ground contact

Investigation of the influence of human physical activity on bone functional adaptation requires long-term histories of gait-related ground reaction force (GRF). Towards a simpler portable GRF measurement, we hypothesized that: 1) the reciprocal of foot-ground contact time (1/tc); or 2) the reciprocal of stride-period-normalized contact time (T/tc) predict peak vertical and horizontal GRF, loading rates, and horizontal speed during gait. GRF data were collected from 24 subjects while they walked and ran at a variety of speeds. Linear regression and ANCOVA determined the dependence of gait parameters on 1/tc and T/tc, and prediction SE. All parameters were significantly correlated to 1/tc and T/tc. The closest pooled relationship existed between peak running vertical GRF and T/tc (r2 = 0.896; SE = 3.6%) and improved with subject-specific regression (r2 = 0.970; SE = 2.2%). We conclude that temporal measures can predict force parameters of gait and may represent an alternative to direct GRF measurements for determining daily histories of habitual lower limb loading quantities necessary to quantify a bone remodeling stimulus.

NASA Center ARC↗

A system for the accurate measurement of pointing responses

We present an accurate, yet relatively inexpensive, system for measuring the direction of pointing responses. This system utilizes off-the-shelf business presentation components in a novel way to help detect and quantify the pointing measurements. The system configuration, measurement features, and procedures to enhance measurement accuracy are described.

NASA Center JSC↗

Initiation-promotion model of tumor prevalence in mice from space radiation exposures

Exposures in space consist of low-level background components from galactic cosmic rays (GCR), occasional intense-energetic solar-particle events, periodic passes through geomagnetic-trapped radiation, and exposure from possible onboard nuclear-propulsion engines. Risk models for astronaut exposure from such diverse components and modalities must be developed to assure adequate protection in future NASA missions. The low-level background exposures (GCR), including relativistic heavy ions (HZE), will be the ultimate limiting factor for astronaut career exposure. We consider herein a two-mutation, initiation-promotion, radiation-carcinogenesis model in mice in which the initiation stage is represented by a linear kinetics model of cellular repair/misrepair, including the track-structure model for heavy ion action cross-sections. The model is validated by comparison with the harderian gland tumor experiments of Alpen et al. for various ion beams. We apply the initiation-promotion model to exposures from galactic cosmic rays, using models of the cosmic-ray environment and heavy ion transport, and consider the effects of the age of the mice prior to and after the exposure and of the length of time in space on predictions of relative risk. Our results indicate that biophysical models of age-dependent radiation hazard will provide a better understanding of GCR risk than models that rely strictly on estimates of the initial slopes of these radiations.

NASA Discipline Radiation Health↗

Risk cross sections and their application to risk estimation in the galactic cosmic-ray environment

Radiation risk cross sections (i.e. risks per particle fluence) are discussed in the context of estimating the risk of radiation-induced cancer on long-term space flights from the galactic cosmic radiation outside the confines of the earth's magnetic field. Such quantities are useful for handling effects not seen after low-LET radiation. Since appropriate cross-section functions for cancer induction for each particle species are not yet available, the conventional quality factor is used as an approximation to obtain numerical results for risks of excess cancer mortality. Risks are obtained for seven of the most radiosensitive organs as determined by the ICRP [stomach, colon, lung, bone marrow (BFO), bladder, esophagus and breast], beneath 10 g/cm2 aluminum shielding at solar minimum. Spectra are obtained for excess relative risk for each cancer per LET interval by calculating the average fluence-LET spectrum for the organ and converting to risk by multiplying by a factor proportional to R gamma L Q(L) before integrating over L, the unrestricted LET. Here R gamma is the risk coefficient for low-LET radiation (excess relative mortality per Sv) for the particular organ in question. The total risks of excess cancer mortality obtained are 1.3 and 1.1% to female and male crew, respectively, for a 1-year exposure at solar minimum. Uncertainties in these values are estimated to range between factors of 4 and 15 and are dominated by the biological uncertainties in the risk coefficients for low-LET radiation and in the LET (or energy) dependence of the risk cross sections (as approximated by the quality factor). The direct substitution of appropriate risk cross sections will eventually circumvent entirely the need to calculate, measure or use absorbed dose, equivalent dose and quality factor for such a high-energy charged-particle environment.

NASA Discipline Radiation Health↗