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PubMed1998

Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues.

We analyse the limits of the diffusion approximation to the time-independent equation of radiative transfer for homogeneous and heterogeneous biological media. Analytical calculations and finite-difference simulations based on diffusion theory are compared with discrete-ordinate, finite-difference transport calculations. The influence of the ratio of absorption and transport scattering coefficient (mu(a)/mu'(s)) on the accuracy of the diffusion approximation are quantified and different definitions for the diffusion coefficient, D, are discussed. We also address effects caused by void-like heterogeneities in which absorption and scattering are very small compared with the surrounding medium. Based on results for simple homogeneous and heterogeneous systems, we analyse diffusion and transport calculation of light propagation in the human brain. For these simulations we convert density maps obtained from magnetic resonance imaging (MRI) to optical-parameter maps (mu(a) and mu'(s)) of the brain. We show that diffusion theory fails to describe accurately light propagation in highly absorbing regions, such as haematoma, and void-like spaces, such as the ventricles and the subarachnoid space.

Absorption↗
PubMed1995

Thermal relaxation of port-wine stain vessels probed in vivo: the need for 1-10-millisecond laser pulse treatment.

Although thermal relaxation times of cutaneous port-wine stain microvessels have been calculated and used to formulate laser selective photothermolysis, they have never been measured. A scheme to do so was devised by measuring the skin response to pairs of 585-nm dye laser pulses (250-360 microseconds each) as a function of the time interval between the two pulses, in five volunteers with port-wine stains. After a pump pulse delivering 80% of the fluence necessary for causing purpura, the fluence of a second probe pulse necessary to cause purpura was determined and was found to increase with the interval between the two pulses, in a manner consistent with thermal diffusion theory. Biopsy specimens were obtained from four of the five subjects to examine the nature and extent of vessel damage and to measure the port-wine stain vessel diameters. Using diffusion theory, the thermal relaxation time was calculated based on the measured vessel diameters. These calculated values are consistent with the increase in radiant exposure (fluence) of the probe pulse necessary to induce purpura for longer time delays. Two simple models for thermal relaxation of port-wine stain vessels are presented and compared with the data. The data and histologic assessment of the vessel injury strongly suggest that pulse durations for ideal laser treatment are in the 1-10-millisecond region and depend on vessel diameter. No dermatologic lasers presently used for port-wine stain treatment operate in this pulse width domain.

Adult↗
PubMedDate not supplied

Relationship between two different functions derived from diffusion-based decompression theory.

Hempleman's diffusion-based decompression theory yields two different functions; one is expressed by a simple root function and the other by a complex series function. Although both functions predict the same rate of gas uptake for relatively short exposure times, no clear mathematical explanation has been published that describes the relationship between the two functions. We clarified that (1) the root function is the solution of the one-dimensional diffusion equation for a semi-infinite slab, (2) the series function is an applicable solution for a finite slab thickness, (3) the parameter values of the root function can be used to determine the parameter values of the series function, and (4) the predictions of gas kinetics from both functions agree until an adequate amount of diffusing inert gas reaches the boundary at the opposite end of the finite slab. The last point allows the use of the simpler root function for predicting short no-stop decompression limits. Experience dictates that the inert gas accumulation for a 22 min at 100 feet of seawater (fsw) dive is considered safe for no-stop decompression. Although the constraint, Depth square root of Bottom Time = 100 square root of 22, has been applied as an index to determine either the safe depth or bottom time (given the other) for no-stop decompression, it should not be applied more broadly to dives requiring decompression stops.

Atmospheric Pressure↗
PubMed1991

Ozone absorption into excised porcine and sheep tracheae by a bolus-response method.

The absorption of ozone (O3) into excised porcine and sheep tracheae was characterized by a bolus-response experiment in which a bolus with a peak O3 concentration of 1 ppm was rapidly injected into a steadily flowing airstream entering the trachea. Using a fast-responding chemiluminescent analyzer of our design, the O3 concentration curves at the proximal end (i.e., the bolus input) and at the distal end (i.e., the response) of the trachea were monitored. Each concentration curve was numerically integrated, and the fraction of O3 absorbed in the trachea was obtained by subtracting from unity the ratio of the response integral to the bolus input integral. Average values of ozone-absorbed fraction decreased from about 0.50 to 0.15 at increasing airflows from 50 to 200 ml/sec. A diffusion theory that includes the effects of bulk convection, axial dispersion, and first-order absorption was developed to relate the fractional absorption to an overall mass transfer coefficient (K). The results indicate that K is independent of airflow, suggesting that the diffusion resistance in mucus is much greater than that in the gas phase. The time-weighted integrals of the concentration curves were also computed, allowing the mean residence time of O3 in the trachea (delta tau) to be determined. As predicted by the diffusion theory, delta tau was inversely related to the rate of O3 absorption.

Absorption↗
PubMed1998

Investigation of a Monte Carlo model for chemical reactions.

Monte Carlo computer simulations are in use at a number of laboratories for calculating time-dependent yields, which can be compared with experiments in the radiolysis of water. We report here on calculations to investigate the validity and consistency of the procedures used for simulating chemical reactions in our code, RADLYS. Model calculations were performed of the rate constants themselves. The rates thus determined showed an expected rapid decline over the first few hundred ps and a very gradual decline thereafter out to the termination of the calculations at 4.5 ns. Results are reported for different initial concentrations and numbers of reactive species. Generally, the calculated rate constants are smallest when the initial concentrations of the reactants are largest. It is found that inhomogeneities that quickly develop in the initial random spatial distribution of reactants persist in time as a result of subsequent chemical reactions, and thus conditions may poorly approximate those assumed from diffusion theory. We also investigated the reaction of a single species of one type placed among a large number of randomly distributed species of another type with which it could react. The distribution of survival times of the single species was calculated by using three different combinations of the diffusion constants for the two species, as is sometimes discussed in diffusion theory. The three methods gave virtually identical results.

Computer Simulation↗
PubMed1999

Mechanistic aspects of iontophoresis in human epidermal membrane.

A large number of factors are involved in the movement of ions and molecules across human epidermal membrane (HEM) under the influence of an electric field. These factors and their interplay need to be understood if our knowledge of iontophoretic transport of drugs across HEM is to reach a point where physical models and strategies may be employed for useful quantitative predictions. In a typical in vitro experiment, the fully hydrated HEM is positioned between aqueous compartments of a two-chamber diffusion cell. When a low electric field is applied across the HEM under these conditions, the transport enhancement of ions in the pre-existing pores of the stratum corneum is the result of, (a) the direct interaction of the electric field with the charge of the ion in question, and (b) convective solvent flow (electroosmosis); in the case where the permeant is non-ionic under these circumstances, transport enhancement is by convective solvent flow only. At moderate-to-high voltage iontophoresis (> or = around 1.0 V applied across a single HEM), in addition to the direct field effect and convective solvent flow in the pre-existing pores, there can generally be a significant (e.g. 10- to 100-fold enhancement) contribution to transport enhancement arising from new pore induction (electroporation). Much of the recent work in our laboratory has been devoted to defining and quantifying HEM electroporation, and an especially difficult aspect has been that of dealing with the large HEM membrane-to-membrane variabilities with regard to, (a) the extent of new pore induction, and (b) the characteristics of the newly induced pores. Recently we discovered that the extent of relevant (i.e. permeant accessible) pore induction may be correlated to the change in HEM electrical conductance (and quantifiable) if an appropriate matching background electrolyte can be selected having ion sizes comparable to that of the permeant. For example, employing tetraethylammonium (TEA) pivalate (PIV) for which the ion sizes are approximately 3.5 A, but not KCl (ion sizes approximately 1.9 A), as the background electrolyte for TEA (as the permeant) gave very good results; in this example, the sizable contribution of pore induction to iontophoresis was quantitatively factored out from the total iontophoretic enhancement. Experiments with a large number of HEM samples gave good agreement with the Nernst-Planck (N-P) predictions of the direct field effect when TEA-PIV was used as the background electrolyte for TEA transport, but large variations (up to 300%) between N-P predictions and experimental results were observed with KCl as the background electrolyte. Another area of recent effort has been HEM pore size determinations, both at low voltages (i.e. for pre-existing pores) and at voltages where the newly induced pores dominate HEM permeability. The sizes of pre-existing pores of HEM have been determined with the hindered diffusion theory (using experimental fluxes of several probe permeants of different known molecular sizes) to be generally in the range, 10-20 A, by a number of investigators in our laboratory for a large number HEM samples. Deducing pore sizes of electric field induced pores under steady electroporation conditions has been a more challenging task. We succeeded recently in developing a novel method for 'passively' determining pore sizes (i.e. by passive diffusion with hindered diffusion theory) under steady electroporation conditions: by using low frequency (12.5 Hz) a.c. at 2-5 V. We have been able to sustain electroporation at a nearly constant state of electroporation long enough to carry out a set of 'passive' diffusion experiments with relatively good precision to obtain the sizes of the newly induced pores. Studies to date have revealed that the sizes of pores induced with 2-5 V are of the same order of magnitude as those of the pre-existing pores (i.e. 10-20 A). Finally, another research question of interest has been that of pore charge

Biological Transport↗
PubMed2000

Population outbreaks in a discrete world.

We present and analyze a simple three-patch host-parasitoid model where population growth is discrete. The model gives solutions that are qualitatively similar to the stable large-amplitude patterns in space found in reaction-diffusion theory. In the context of host-parasitoid interactions, the large-amplitude portions of the solution can be thought of as spatially localized host population outbreaks. Here, we show that the biological requirements for localized population outbreaks in a discrete world are identical to those found in reaction- diffusion theory. Furthermore, the model conveniently allows investigation into the robustness of these population outbreaks under the influence of density-dependent dispersal behavior. We find that localized population outbreaks in space can still occur with modest amounts of pursuit and aggregative behavior by parasitoids. We end by showing that evidence from a real host-parasitoid system is consistent with the predictions of the model.

Animals↗
PubMed1989

Toward absolute reflectance oximetry: I. Theoretical consideration for noninvasive tissue reflectance oximetry.

The photon diffusion theory can yield quantitative estimation of tissue hemoglobin saturation, provided that the medium is homogeneous and that one calibration data is available. The error in detection of tissue OS of the gut mucosa ranged from 5 to 10% in oxygen saturation. In application to skin, the two-layer tissue model suggests that by properly designing the optical sensor and by appropriately selecting the illumination wavelengths, it is possible to capture mainly the light returning from the specific depth in tissue. Since the skin layer thickness is roughly in the order of 1 mm, the source and detector separation distance of approximately 3 mm or larger would ensure that the measured reflectance is truly returning from the deeper layer. When such reflectances are normalized to the blood-free reflectance obtained by squeezing the blood out of the tissue, the normalized reflectance truly represents the deeper layer characteristics. In application to head, since the skin and skull thickness is considerable large, separation distance of 40 mm or greater is required to ensure the reflectance is actually returning from the brain. Closely spaced optical sensor would measure the scattering and absorption characteristics of the skin and skull of the head. As for directional changes in optical propagation due to tissue inhomogeneities, multiple light sources at the equi-distance around the detector can be placed to average out the effect. The resultant reflectance can be analyzed based on the similar mathematical treatment as presented in this study. However, since the absolute reflectance level calculated by the theory and the actual reflectance for a given transducer geometry have some deviation, again one point calibration is required to close the gap between them. This can be accomplished through arterialization of the tissue and ventilating with pure oxygen to yield reflectance from tissue containing 100% saturated blood. As for hemoglobin content, isosbestic reflectance, for example at 805 nm, can be utilized to estimate tissue hemoglobin content. Once one point calibration is accomplished, reflectance changes thereafter due to changes in HbT and OST can be fairly accurately predicted by the photon diffusion theory in combination with linear analysis. Concerning separation of arterial and venous blood in tissue, the diastolic and systolic phases of the optical plethysmographic signal can be assumed to relate to venous or DC level, and to arterial or AC component. Since the four components, arterial and venous OS and Hb, are unknowns in the system, four equations or four wavelength measurements are required to sort out each effect.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed2006

Polyelectrolyte adsorption layers studied by streaming potential and particle deposition.

Adsorption of a cationic polyelectrolyte, polyallylamine hydrochloride (PAH), having a molecular weight of 70,000 on mica was characterized by the streaming potential method and by deposition of negative polystyrene latex particles. Formation of PAH layers was followed by determining the apparent zeta potential of surface zeta as function of bulk PAH concentration. The zeta potential was calculated from the streaming potential measured in the parallel-plate channel formed by two mica plates precovered by the polyelectrolyte. The experimental data were expressed as the dependence of the reduced zeta potential zeta/zeta0 on the PAH coverage Theta(PAH), calculated using the convective diffusion theory. It was found that for the ionic strength of 10(-2) M, the dependence of zeta/zeta0 on Theta(PAH) can be reflected by the theoretical model formulated previously for surfaces covered by colloid particles. The electrokinetic measurements were complemented by particle deposition experiments on PAH-covered mica surfaces. A direct correlation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For ThetaPAH > 0.3 the initial deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. The initial deposition rates for surfaces modified by PAH were compared with previous experimental and theoretical results obtained for heterogeneous surfaces formed by preadsorption of colloid particles. It was revealed that negative latex deposition occurred at surfaces exhibiting negative apparent zeta potential, which explained the anomalous deposition of particles observed in previous works. It was suggested that the combined electrokinetic and particle deposition methods can be used for detecting adsorbed polyelectrolytes at surfaces for coverage range of a percent. This enables one to measure bulk polyelectrolyte concentrations at the level of 0.05 ppm.

Journal Article↗
PubMedDate not supplied

Measurement of fibrous cap thickness in atherosclerotic plaques by spatiotemporal analysis of laser speckle images.

Necrotic-core fibroatheromas (NCFA) with thin, mechanically weak fibrous caps overlying lipid cores comprise the majority of plaques that rupture and cause acute myocardial infarction. Laser speckle imaging (LSI) has been recently demonstrated to enable atherosclerotic plaque characterization with high accuracy. We investigate spatio-temporal analysis of LSI data, in conjunction with diffusion theory and Monte Carlo modeling of light transport, to estimate fibrous cap thickness in NCFAs. Time-varying laser speckle images of 20 NCFAs are selected for analysis. Spatio-temporal intensity fluctuations are analyzed by exponential fitting of the windowed normalized cross-correlation of sequential laser speckle patterns to obtain the speckle decorrelation time constant, tau(rho), as a function of distance rho from the source entry location. The distance, rho', at which tau(rho) dropped to 65% of its maximum value is recorded. Diffusion theory and Monte Carlo models are utilized to estimate the maximum photon penetration depth, zmax(rho'), for a distance equal to rho', measured from LSI. Measurements of zmax(rho') correlate well with histological measurements of fibrous cap thickness (R=0.78, p<0.0001), and paired t-tests show no significant difference between the groups (p=0.4). These results demonstrate that spatio-temporal LSI may allow the estimation of fibrous cap thickness in NCFAs, which is an important predictor of plaque stability.

Algorithms↗
PubMedDate not supplied

Investigation of light propagation models to determine the optical properties of tissue from interstitial frequency domain fluence measurements.

Four models, standard diffusion approximation (SDA), single Monte Carlo (SMC), delta-P1, and isotropic similarity (ISM), are developed and evaluated as forward calculation tools in the estimation of tissue optical properties. The inverse calculation uses the ratio of the fluences and phase difference at two locations close to an intensity modulated isotropic source to recover the reduced scattering coefficient mus' and the absorption coefficient mua. Diffusion theory allows recovery of optical properties (OPs) within 5% for media with mus'mua>10. The performance of the delta-P1 model is similar to SDA, with limited enhanced accuracy. The collimation approximation may limit the use of the delta-P1 model for spherical geometry, and/or the fluence may not be accurately calculated by this model. The SMC model is the best, recovering OPs within 10% regardless of the albedo. However, the necessary restriction of the searched OPs space is inconvenient. The performance of ISM is similar to that of diffusion theory for media with mus'mua>10, and better for 1 5.

Algorithms↗
PubMed2005

Kokua Mau: a statewide effort to improve end-of-life care.

BACKGROUND: Many Americans die in pain, without hospice, and without regard to advance directives, suggesting a need to improve end-of-life (EOL) awareness and services. OBJECTIVE: This paper describes Kokua Mau, a community-state partnership to improve EOL in Hawaii funded by The Robert Wood Johnson Foundation (RWJF). Coalition activities were guided by innovation-diffusion theory, targeting "innovators" and "change agents" within communities and organizations willing to learn about and facilitate improvements to EOL care. DESIGN: Evaluation of a community-wide intervention to improve EOL care. SETTING/SUBJECTS: Honolulu, Hawaii. MEASUREMENTS: We tracked dissemination of campaign messages by counting numbers of coalition members (including innovators and change agents to carry on the work), individuals reached through awareness and educational offerings, and new EOL projects initiated during and after the initial 3-year RWJF funding. To measure change, we counted the number of legislative policies that were modified by the coalition as well as indicators of hospice utilization, advance directive (AD) completion, support for physician-assisted death, and place of death. RESULTS: In the first 3 years of the project: coalition membership grew to 350 members; EOL care curricula were developed and offered to various target audiences; 17,000 individuals attended educational events; policy changes were facilitated; decreases were seen in proportions of residents supporting physician-assisted suicide; and increases were seen in advance directive completion rates and hospice utilization. Most importantly, after the grant period, coalition members went on to develop and implement new programs to improve care to the dying. CONCLUSIONS: Although it will take several years to effect comprehensive and sustained changes in the way death is perceived and the dying process is facilitated, findings suggest that programs based on innovation-diffusion theory can increase EOL awareness and help develop the change agents and role models needed to affect community-wide change over the long term.

Adolescent↗
PubMed2003

Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence.

Steady-state diffusion theory models of fluorescence in tissue have been investigated for recovering fluorophore concentrations and fluorescence quantum yield. Spatially resolved fluorescence, excitation and emission reflectance Carlo simulations, and measured using a multi-fibre probe on tissue-simulating phantoms containing either aluminium phthalocyanine tetrasulfonate (AlPcS4), Photofrin meso-tetra-(4-sulfonatophenyl)-porphine dihydrochloride The accuracy of the fluorophore concentration and fluorescence quantum yield recovered by three different models of spatially resolved fluorescence were compared. The models were based on: (a) weighted difference of the excitation and emission reflectance, (b) fluorescence due to a point excitation source or (c) fluorescence due to a pencil beam excitation source. When literature values for the fluorescence quantum yield were used for each of the fluorophores, the fluorophore absorption coefficient (and hence concentration) at the excitation wavelength (mu(a,x,f)) was recovered with a root-mean-square accuracy of 11.4% using the point source model of fluorescence and 8.0% using the more complicated pencil beam excitation model. The accuracy was calculated over a broad range of optical properties and fluorophore concentrations. The weighted difference of reflectance model performed poorly, with a root-mean-square error in concentration of about 50%. Monte Carlo simulations suggest that there are some situations where the weighted difference of reflectance is as accurate as the other two models, although this was not confirmed experimentally. Estimates of the fluorescence quantum yield in multiple scattering media were also made by determining mu(a,x,f) independently from the fitted absorption spectrum and applying the various diffusion theory models. The fluorescence quantum yields for AlPcS4 and TPPS4 were calculated to be 0.59 +/- 0.03 and 0.121 +/- 0.001 respectively using the point source model, and 0.63 +/- 0.03 and 0.129 +/- 0.002 using the pencil beam excitation model. These results are consistent with published values.

Algorithms↗
PubMed1972

Computer simulation of radial immunodiffusion. I. Selection of an algorithm for the diffusion process.

Theories of diffusion with chemical reaction are reviewed as to their contributions toward developing an algorithm needed for computer simulation of immunodiffusion. The Spiers-Augustin moving sink and the Engelberg stationary sink theories show how the antibody-antigen reaction can be incorporated into boundary conditions of the free diffusion differential equations. For this, a stoichiometric precipitate was assumed and the location of precipitin lines could be predicted. The Hill simultaneous linear adsorption theory provides a mathematical device for including another special type of antibody-antigen reaction in antigen excess regions of the gel. It permits an explanation for the lowered antigen diffusion coefficient, observed in the Oudin arrangement of single linear diffusion, but does not enable prediction of the location of precipitin lines. The most promising mathematical approach for a general solution is implied in the Augustin alternating cycle theory. This assumes the immunodiffusion process can be evaluated by alternating computation cycles: free diffusion without chemical reaction and chemical reaction without diffusion. The algorithm for the free diffusion update cycle, extended to both linear and radial geometries, is given in detail since it was based on gross flow rather than more conventional expressions in terms of net flow. Limitations on the numerical integration process using this algorithm are illustrated for free diffusion from a cylindrical well.

Antigen-Antibody Reactions↗
PubMedDate not supplied

Antecedents of clinical information technology sophistication in hospitals.

Grounded in the resource-based theory and the innovation diffusion theory, this article develops and tests a research model for assessing the antecedents of hospital innovativeness with regard to clinical information technology (IT) applications. A cross-sectional survey was conducted in a sample of U.S. hospitals (n = 74) to assess three dimensions of clinical IT sophistication. Secondary data were used to measure the antecedents, namely, four groups of organizational capacity variables. Bivariate and regression analyses were conducted to identify significant associations. A significant percentage (45-61%) of the variance in clinical IT sophistication was explained, mostly by leadership and knowledge sharing capacities. In particular, IT tenure and technical knowledge resources were significantly related to clinical IT sophistication. Surprisingly, managerial tenure and hospital's belonging to a network showed significant negative associations with two dimensions of the clinical IT sophistication construct. To address the challenges they face, hospitals should consider encouraging career development for current individuals in charge of IT activities, and attracting professionals with an IT background who have the knowledge and ability to trigger new ideas and favor the adoption and use of clinical IT applications in these settings.

Cross-Sectional Studies↗
PubMed1990

Experimental support for the theory of diffusion limitation of maximum oxygen uptake.

The four experiments summarized above demonstrate that there is a strong relationship between both measured muscle venous PO2 and calculated mean muscle capillary PO2 and VO2max. This is true for whole body or exercising muscle VO2max, and is seen both in isolated canine gastrocnemius and intact man. This behavior is exactly what would be expected if the diffusing properties for oxygen in skeletal muscle play a constraining role in setting maximum VO2. These data therefore support the hypothesis we advanced (Wagner, 1988a; Wagner, 1988b), that it is a quantitative integrative relationship between convective and diffusive phenomena that combine to set maximum VO2. A specific prediction of this integrative hypothesis (i.e., the non-uniqueness of VO2max as a function of convective oxygen delivery) was confirmed (Experiment 3). While at this point in time phenomena such as perfusion heterogeneity and muscle shunts cannot be quantitatively taken into account in such analyses, the remarkable concurrence between expectations of the hypothesis and experimental data continue to lend support to the basic idea that maximum VO2 is not limited by any single step of the oxygen transport pathway from atmosphere to mitochondria, but rather by the way in which each and every step combines with every other step to determine oxygen supply.

Animals↗
PubMed1961

Theory of diffusion in gels.

It has been shown that when concentration of solute is expressed as amount per unit volume of gel-solvent-solute system, Fick's laws for diffusion in a gel take the same form as for diffusion in solvent alone, except that the usual coefficient must be replaced by a new coefficient, D', equal to D(1 - alphaphi)/(1 - phi), where phi is the effective volume fraction of the gel substance and alpha is a coefficient of obstruction equal to 5/3 if the gel substance can be considered to be made up of randomly oriented rods. An equation was derived for the total amount of solute entering the gel, which is analogous to but not identical with the equation for the total amount of solute crossing the initial boundary in free diffusion. The effect of slice thickness was investigated by a mathematical procedure involving the solutions of approximate differential equations. It was shown that even for slices so thick that 95 per cent of the solute in the gel is contained in the first two, a correction factor equal to the square of the slice thickness divided by 48D't permits one to obtain accurate measurement of D' from the mean concentration and the position of the midplane of the slice.

Diffusion↗