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Results for “Deterministic Measurement”

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PubMedDate not supplied

Demonstration of three-dimensional deterministic radiation transport theory dose distribution analysis for boron neutron capture therapy.

The Monte Carlo stochastic simulation technique has traditionally been the only well-recognized method for computing three-dimensional radiation dose distributions in connection with boron neutron capture therapy (BNCT) research. A deterministic approach to this problem would offer some advantages over the Monte Carlo method. This paper describes an application of a deterministic method to analytically simulate BNCT treatment of a canine head phantom using the epithermal neutron beam at the Brookhaven medical research reactor (BMRR). Calculations were performed with the TORT code from Oak Ridge National Laboratory (ORNL), an implementation of the discrete ordinates, or Sn method. Calculations were from first principles and used no empirical correction factors. The phantom surface was modeled by flat facets of approximately 1 cm2. The phantom interior was homogeneous. Energy-dependent neutron and photon scalar fluxes were calculated on a 32 x 16 x 22 mesh structure with 96 discrete directions in angular phase space. The calculation took 670 min on an Apollo DN10000 workstation. The results were subsequently integrated over energy to obtain full three-dimensional dose distributions. Isodose contours and depth-dose curves were plotted for several separate dose components of interest. Phantom measurements were made by measuring neutron activation (and therefore neutron flux) as a function of depth in copper-gold alloy wires that were inserted through catheters placed in holes drilled in the phantom. Measurements agreed with calculations to within about 15%. The calculations took about an order of magnitude longer than comparable Monte Carlo calculations but provided various conveniences, as well as a useful check.

Animals↗

PubMed1996

A simulation of microbial competition in the human colonic ecosystem.

Many investigations of the interactions of microbial competitors in the gastrointestinal tract used continuous-flow anaerobic cultures. The simulation reported here was a deterministic 11-compartment model coded by using the C programming language and based on parameters from published in vitro studies and assumptions were data were unavailable. The resource compartments were glucose, lactose and sucrose, starch, sorbose, and serine. Six microbial competitors included indigenous nonpathogenic colonizers of the human gastrointestinal tract (Escherichia coli, Enterobacter aerogenes, Bacteroids ovatus, Fusobacterium varium, and Enterococcus faecalis) and the potential human enteropathogen Salmonella typhimurium. Flows of carbon from the resources to the microbes were modified by resource and space controls. Partitioning of resources to the competitors that could utilize them was calculated at each iteration on the basis of availability of all resources by feeding preference functions. Resources did not accumulate during iterations of the model. The results of the computer simulation of microbial competition model and for various modifications of the model. The results were based on few measured parameters but may be useful in the design of user-friendly software to aid researchers in defining and manipulating the microbial ecology of colonic ecosystems as relates to food-borne disease.

Carbohydrates↗

PubMed2005

A record linkage protocol for a diabetes registry at ethnically diverse community health centers.

Community health centers serve ethnically diverse populations that may pose challenges for record linkage based on name and date of birth. The objective was to identify an optimal deterministic algorithm to link patient encounters and laboratory results for hemoglobin A1c testing and examine its variability by health center site, patient ethnicity, and other variables. Based on data elements of last name, first name, date of birth, gender, and health center site, matches with >/=50% to < 100% of a maximum score were manually reviewed for true matches. Match keys based on combinations of name substrings, date of birth, gender, and health center were used to link encounter and laboratory files. The optimal match key was the first two letters of the last name and date of birth, which had a sensitivity of 92.7% and a positive predictive value of 99.5%. Sensitivity marginally varied by health center, age, gender, but not by ethnicity. An algorithm that was inexpensive, accurate, and easy to implement was found to be well suited for population-based measurement of clinical quality.

Adult↗

PubMed1987

Periodic rotational crosses. III. Sire-breed rotations with overlapping generations among dams.

Sire-breed rotations are defined as the changing of sire breeds ignoring the sire-breed pedigree of dams from overlapping generations. The limiting theoretical proportion of maximum potential heterozygosity maintained at equilibrium when there is no culling of dams was found to be equal to that of a composite population with the same breed composition. Heterozygosity was simulated with a deterministic model that assumed 20% of reproducing females in each age group were culled each mating period. Maximum age of reproducing females was varied from 3 to 10 mating periods (years for cattle and sheep, half-years for swine). Consecutive use of each sire breed in a sire-breed sequence from two to four mating periods maintained more heterozygosity than predicted by the limiting theoretical formula, which did not take the culling of females into account. Compared with complete sire and dam rotations, sire-breed rotations with the same breed sequence resulted in reductions of .03 to .13 of potential heterosis. Among two-breed, periodic rotations, the difference ranged from .03 to .08. The smaller differences were generally associated with younger maximum reproducing females ages and the larger differences with older maximum ages. Heterozygosity difference times heterosis is a measure of the expected returns for the more intensive management often needed for complete rotations. Scaled breed difference ranges over which one periodic rotation of sire breeds exceeds another are shifted by overlapping generations among the females. Breed utilization is unchanged by overlapping generations, but relative differences in heterosis utilization are altered.

Animal Husbandry↗

PubMed1995

Application of the correlation integral to respiratory data of infants during REM sleep.

Non-linear time sequence analysis has been performed on infant sleep measurement data in order to obtain more information about the respiratory processes. As a first step, respiration data during REM sleep were analysed with methods from non-linear dynamics, especially, the correlation integral and the slope of its log-log plot, representing the correlation dimension. Before calculation of the correlation integral, a special kind of filtering has to be applied to the data. This filtering algorithm is a state space and singular value decomposition-based noise reduction method, and it is used to separate the noise and signal subspaces. The dynamics of a signal (in our case data from the respiratory process) and its degrees of freedom can be characterised by the correlation integral and by the correlation dimension, respectively. The main result of this study is that the highly irregular-looking breathing patterns during REM sleep could be described by a deterministic system, and finally the physiological significance of this finding is discussed.

Electroencephalography↗

PubMed2006

The transcriptional regulator CBP has defined spatial associations within interphase nuclei.

It is becoming increasingly clear that nuclear macromolecules and macromolecular complexes are compartmentalized through binding interactions into an apparent three-dimensionally ordered structure. This ordering, however, does not appear to be deterministic to the extent that chromatin and nonchromatin structures maintain a strict 3-D arrangement. Rather, spatial ordering within the cell nucleus appears to conform to stochastic rather than deterministic spatial relationships. The stochastic nature of organization becomes particularly problematic when any attempt is made to describe the spatial relationship between proteins involved in the regulation of the genome. The CREB-binding protein (CBP) is one such transcriptional regulator that, when visualised by confocal microscopy, reveals a highly punctate staining pattern comprising several hundred individual foci distributed within the nuclear volume. Markers for euchromatic sequences have similar patterns. Surprisingly, in most cases, the predicted one-to-one relationship between transcription factor and chromatin sequence is not observed. Consequently, to understand whether spatial relationships that are not coincident are nonrandom and potentially biologically important, it is necessary to develop statistical approaches. In this study, we report on the development of such an approach and apply it to understanding the role of CBP in mediating chromatin modification and transcriptional regulation. We have used nearest-neighbor distance measurements and probability analyses to study the spatial relationship between CBP and other nuclear subcompartments enriched in transcription factors, chromatin, and splicing factors. Our results demonstrate that CBP has an order of spatial association with other nuclear subcompartments. We observe closer associations between CBP and RNA polymerase II-enriched foci and SC35 speckles than nascent RNA or specific acetylated histones. Furthermore, we find that CBP has a significantly higher probability of being close to its known in vivo substrate histone H4 lysine 5 compared with the closely related H4 lysine 12. This study demonstrates that complex relationships not described by colocalization exist in the interphase nucleus and can be characterized and quantified. The subnuclear distribution of CBP is difficult to reconcile with a model where chromatin organization is the sole determinant of the nuclear organization of proteins that regulate transcription but is consistent with a close link between spatial associations and nuclear functions.

Acetylation↗

PubMed1996

[Vienna version for clinical application of the Multiple Choice Vocabulary Intelligence Test].

A deterministic reliability analysis of the Mehrfachwahl-Wortschatz-Intelligenztest, Lehrl (MWT-A, MWT-B), a very economical device for the assessment of crystallized intelligence and the most frequently administered intelligence test by physicians in Germany, was performed on the test data of n = 300 in- and outpatients (University Clinic for Psychiatry, Vienna). Numerical outcomes showed a substantial lack of satisfying test properties, which are further also discussed under non-numerical aspects. For the clinical application of the MWT in Eastern Austria three alternative versions of the MWT (each consisting of 37 items and having better scale characteristics in the analysed sample than the original scales) were developed from the original item pool and presented as MWT-PIRIT, MWT-RIT, and MWT-PI. All five MWT scales were standardized for the present with the patient sample for clinical application. Correlational analyses with a measure for fluid intelligence (Standard Progressive Matrices) suggested only moderate associations between crystallized and fluid intelligence, as well as a differential validity for the MWT in our sample.

Adolescent↗

PubMed2006

Variability in isometric force and moment generating capacity of glenohumeral external rotator muscles.

BACKGROUND: Muscles which cause glenohumeral external rotation possess varying ability for generating force and moment due to differences in muscle architecture, moment arm, and the interaction of these two factors. This study's purpose was to determine a complete dataset of muscle-tendon parameters for predicting the moment generating capacity and force-length dependence for external rotation of infraspinatus, supraspinatus and teres minor muscles. METHODS: Muscle fascicle length, sarcomere length, pennation angle, and muscle volume were measured for sub-regions of infraspinatus and supraspinatus, and teres minor from 10 glenohumeral specimens. Tendon excursion was measured for glenohumeral rotation. From these parameter measurements, optimal fascicle length, physiological cross-sectional area, muscle force-length dependence, and maximum isometric moment generating capacity were calculated. FINDINGS: Substantial differences were found for optimal muscle length, physiologic cross-sectional area, and tendon length for the 10 specimens of this study. Muscle sub-region had a significant effect on the force-length relationship for infraspinatus (P<0.001), but was not significant for supraspinatus (P=0.49). For infraspinatus and supraspinatus, maximum isometric rotation moment capacity was greater at 10 degrees versus 60 degrees abduction (P<0.001). Maximum isometric rotation moment capacity for the teres minor was greater at 10 degrees versus 60 degrees abduction (P<0.01). Sub-regions demonstrated significant differences in isometric moment capacity (P<0.001). INTERPRETATION: Functional capabilities of these muscles depend on muscle architecture and moment arm as well as their combined effects. The results allow for development of stochastic and deterministic models of glenohumeral external rotation strength which can be used for prediction of muscle forces and joint moments.

Anatomy, Cross-Sectional↗

PubMed2000

Biodistribution and dosimetry of an aqueous solution containing sodium 3-(125I)iodo-4-hydroxybenzenesulfonate (Iotrex) for brachytherapy of resected malignant brain tumors.

UNLABELLED: Iotrex is an aqueous radiotherapy solution containing sodium 3-(125I)iodo-4-hydroxybenzenesulfonate (125I-HBS), which is used as the radiation source for the brachytherapy of resected of brain tumor cavity margins with the GliaSite catheter. During routine clinical use of this brachytherapy applicator and radiation source, approximately 0.1% of the afterloaded Iotrex will diffuse through the GliaSite balloon. Our purpose was to assess the radiation doses to normal organs under routine clinical use of the GliaSite. METHODS: Five groups of rats received intracerebral injections of an 131I-HBS solution (131I used as a surrogate for 125I in the synthesis of 125I-HBS) with one group sacrificed at 15 minutes, 30 minutes, 1 hour, 2 hours and 4 hours post-administration. Urine was collected and activity retention in numerous organs was measured. The biodistribution data were used to estimate radiation doses to normal organs of the Reference Adult Male and Female phantoms. RESULTS: Radioactivity was rapidly and completely cleared from the brain (98% cleared by 2 hours) and total body (urinary clearance; 93%@2 hours). No organ retained > 0.7% of the radioactivity at 4 hours. For 100% loss of the radiotherapy solution from the balloon catheter (device failure), all organs would receive less than 100 mGy (10 rad), except the bladder wall (2800 mGy, 280 rad), uterus (130 mGy, 13 rad) and distal colon (270 mGy, 27 rad). Under normal conditions, all organ doses are 1000-fold lower (< 3 mGy or 0.3 rad). CONCLUSIONS: Under routine clinical conditions, the radiation doses to normal organs are inconsequential. Should the maximum clinical load of Iotrex (16.7 GBq of 125I) be released intracerebrally, the radiation doses to all organs would be below the thresholds for deterministic effects.

Animals↗

PubMedDate not supplied

[Evaluation of patient doses in interventional radiology].

PURPOSE: To verify the suitability of indicative quantities to evaluate the risk related to patient exposure, in abdominal and vascular interventional radiology, by the study of correlations between dosimetric quantities and other indicators. MATERIAL AND METHODS: We performed in vivo measurements of entrance skin dose (ESD) and dose area product (DAP) during 48 procedures to evaluate the correlation among dosimetric quantities, and an estimation of spatial distribution of exposure and effective dose (E). To measure DAP we used a transmission ionization chamber and to evaluate ESD and its spatial distribution we used radiographic film packed in a single envelope and placed near the patient's skin. E was estimated by a calculation software using data from film digitalisation. RESULTS: From the data derived for measurements in 27 interventional procedures on 48 patients we obtained a DAP to E conversion factor of 0.15 mSv / Gy cm2, with an excellent correlation (r=.99). We also found a good correlation between DAP and exposure parameters such as fluoroscopy time and number of images. The greatest effective dose was evaluated for a multiple procedure in the hepatic region, with a DAP value of 425 Gy cm2. The greatest ESD was about 550 mGy. For groups of patients undergoing similar interventional procedures the correlation between ESD and DAP had conversion factors from 6 to 12 mGy Gy-1 cm-2. CONCLUSION: The evaluation of ESD and E by slow films represents a valid method for patient dosimetry in interventional radiology. The good correlation between DAP and fluoroscopy time and number of images confirm the suitability of these indicators as basic dosimetric information. All the ESD values found are lower than threshold doses for deterministic effects.

Fluoroscopy↗

PubMed1996

[Radiation exposure in interventional radiology as exemplified by the chemoembolization of hepatocellular carcinoma and laser angioplasty of the pelvic arteries].

PURPOSE: Estimation of radiogenic risks for patient and radiologist in chemoembolisation of hepatocellular carcinoma (HCC) and laser angioplasty of the pelvic arteries. METHODS: In 5 chemoembolisations of HCC (4 males, one female) and 6 laser angioplasties of the pelvic arteries (5 males, one female) the surface doses received by patient and operator were measured using thermoluminescent dosimeters in standardised positions. The organ doses of the patient were derived by conversion factors employed on the measured surface doses. Effective dose was determined according to the recommendations of ICRP 60. RESULTS: The risk of lethal malignant disease and genetic disorder derived from the doses in the patient was found to be of the magnitude of 10(-4)-10(-5). The thresholds for transient erythema of the skin and depression of hematopoiesis can be reached after high expositions. A theoretical maximum of 700 laser angioplasties of the pelvic arteries allowable in one year was calculated based on the dose to the operator's left hand. For chemoembolisation of HCC, the dose to the left eye lens would reach the yearly maximum after approximately 1000 procedures. Remarkable risks for malignant disease of skin and thyroid as well as detectable opacities of the eye lens can occur after frequent interventions for many years. CONCLUSIONS: Because of the lower life expectancy the patient's risk for stochastic effect can be seen as minimal. No clinically relevant deterministic effects will occur. In the case of frequent interventions, the dose absorbed by the radiologist is likely to exceed the prescribed dose limit and to cause remarkable risk for stochastic and non-stochastic effects after many years.

Aged↗

PubMed2004

Linearity of cortical receptive fields measured with natural sounds.

How do cortical neurons represent the acoustic environment? This question is often addressed by probing with simple stimuli such as clicks or tone pips. Such stimuli have the advantage of yielding easily interpreted answers, but have the disadvantage that they may fail to uncover complex or higher-order neuronal response properties. Here, we adopt an alternative approach, probing neuronal responses with complex acoustic stimuli, including animal vocalizations. We used in vivo whole-cell methods in the rat auditory cortex to record subthreshold membrane potential fluctuations elicited by these stimuli. Most neurons responded robustly and reliably to the complex stimuli in our ensemble. Using regularization techniques, we estimated the linear component, the spectrotemporal receptive field (STRF), of the transformation from the sound (as represented by its time-varying spectrogram) to the membrane potential of the neuron. We find that the STRF has a rich dynamical structure, including excitatory regions positioned in general accord with the prediction of the classical tuning curve. However, whereas the STRF successfully predicts the responses to some of the natural stimuli, it surprisingly fails completely to predict the responses to others; on average, only 11% of the response power could be predicted by the STRF. Therefore, most of the response of the neuron cannot be predicted by the linear component, although the response is deterministically related to the stimulus. Analysis of the systematic errors of the STRF model shows that this failure cannot be attributed to simple nonlinearities such as adaptation to mean intensity, rectification, or saturation. Rather, the highly nonlinear response properties of auditory cortical neurons must be attributable to nonlinear interactions between sound frequencies and time-varying properties of the neural encoder.

Acoustic Stimulation↗

PubMed2003

Absence of multiple local minima effects in intensity modulated optimization with dose-volume constraints.

This paper reports on the analysis of intensity modulated radiation treatment optimization problems in the presence of non-convex feasible parameter spaces caused by the specification of dose-volume constraints for the organs-at-risk (OARs). The main aim was to determine whether the presence of those non-convex spaces affects the optimization of clinical cases in any significant way. This was done in two phases: (1) Using a carefully designed two-dimensional mathematical phantom that exhibits two controllable minima and with randomly initialized beamlet weights, we developed a methodology for exploring the nature of the convergence characteristics of quadratic cost function optimizations (deterministic or stochastic). The methodology is based on observing the statistical behaviour of the residual cost at the end of optimizations in which the stopping criterion is progressively more demanding and carrying out those optimizations to very small error changes per iteration. (2) Seven clinical cases were then analysed with dose-volume constraints that are stronger than originally used in the clinic. The clinical cases are two prostate cases differently posed, a meningioma case, two head-and-neck cases, a spleen case and a spine case. Of the 14 different sets of optimizations (with and without the specification of maximum doses allowed for the OARs), 12 fail to show any effect due to the existence of non-convex feasible spaces. The remaining two sets of optimizations show evidence of multiple minima in the solutions, but those minima are very close to each other in cost and the resulting treatment plans are practically identical, as measured by the quality of the dose-volume histograms (DVHs). We discuss the differences between fluence maps resulting from those similar treatment plans. We provide a possible reason for the observed results and conclude that, although the study is necessarily limited, the annealing characteristics of a simulated annealing method may not be justified in clinical optimization in the presence of dose-volume constraints. The results of optimizations by the Newton gradient (NG) method with a quadratic cost function are reported in detail. An adaptive simulated annealing method, optimizing the same function, and the dynamically penalized likelihood method, optimizing a log likelihood function, have also been used in the study. The results of the latter two methods have only been discussed briefly, as they yielded the same conclusions as the NG method.

Algorithms↗

PubMed2006

Dynamic swallowing study and radiation dose to patients.

PURPOSE: The purpose of this study was to define an optimal radiological procedure to evaluate the results of rehabilitation therapy for swallowing disorders and to calculate both the effective and organ dose to the patient to provide a measure of the radiation risk associated with the procedure. MATERIALS AND METHODS: In order to define the optimal radiological procedure, kerma-area product (KAP) measurements and evaluations of image quality in fluoroscopy and fluorography mode were made using dedicated phantoms. Twenty-two patients were included in the study, and the values of KAP, screening time and average voltage selected were individually recorded. The recorded KAP values were used to estimate radiation risk with the use of dedicated calculation software. RESULTS: Median, first and third quartiles of the KAP distribution were, respectively, 2.1, 1.5 and 2.7 Gy cm2, with a corresponding effective dose of 0.35, 0.26 and 0.46 mSv. A good correlation between KAP and exposure time was also found (R2=0.85). Exposure of the thyroid, which is inside the radiation field, accounts for the greatest share to the effective dose, with a calculated median dose of 6 mGy. CONCLUSIONS: With the defined radiological procedure, the obtained KAP values are lower than recorded doses in interventional radiology, and the corresponding values of entrance skin dose are lower than the threshold dose for deterministic effects. Considering the effective dose at the median KAP value, the probability for stochastic effects is shown to be low, at approximately 1 in 39,000.

Adult↗

PubMed2004

Mathematical modelling and the control of lymphatic filariasis.

The current global initiative to eliminate lymphatic filariasis represents one of the largest mass drug administration programmes ever conceived for the control of a parasitic disease. Yet, it is still not known whether the WHO-recommended primary strategy of applying annual single-dose mass chemotherapy with a combination of two drugs for 4-6 years will effectively break parasite transmission from all endemic communities. Here we review recent work on the development and application of a deterministic mathematical model of filariasis transmission, to show how models of parasite transmission will help resolve the key currently debated questions regarding the ultimate effectiveness of the global strategy to control filariasis. These critical questions include the required duration of mass treatment in different endemic areas, the optimal drug coverage required to meet control targets within prescribed timeframes, the impact and importance of adding vector control to mass chemotherapy regimens, and the likelihood of the development of drug resistance by treated worm populations. The results demonstrate the vital role that integrating these models into control programming can have in providing effective decision-support frameworks for undertaking the optimal design and monitoring of regional and global filariasis-control programmes. Operationally, the models show that the effectiveness of the strategy to achieve filariasis control will be determined by successfully addressing two key factors: the need to maintain high community treatment coverages, and the need to include vector control measures especially in areas of high endemicity.

Animals↗

PubMed2004

A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability.

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

Adult↗

PubMed1998

Ascitic interleukin-12 is an independent prognostic factor in ovarian cancer.

PURPOSE: The clinical impact of endogenous cytokines supplied with deterministic properties in the generation of either T helper (Th)1 -type or Th2-type immune response was investigated in patients with ovarian cancer. Whereas interleukin (IL)- 12 initiates the differentiation of naive Th0 cells toward Th1 phenotype, IL-4 and IL-10 mediate the development of Th2-type immunity. PATIENTS AND METHODS: Cytokines were determined before treatment by means of enzyme-linked immunosorbent assay (ELISA) in ascites fluid and serum of 76 patients with ovarian cancer. Cytokine levels were compared with each other and with standard clinicopathologic parameters. A stepwise logistic regression was calculated to rule out interdependence in the associations of the various variables. Survival analyses were performed with the Kaplan-Meier method and differences in survival were examined according to Mantel and Breslow. Cox proportional hazards analysis was used to identify independent prognostic factors. RESULTS: Whereas IL-10 and IL-12 were detectable in all ascites-fluid samples, IL-4 was measurable in only 43% of the specimens. With the exception of neopterin, macrophage colony-stimulating factor (M-CSF), and IL-4, determined cytokine levels were significantly elevated in ascites fluid compared with serum (P < .01). In univariate analyses, high ascitic-fluid concentrations of either neopterin, tumor necrosis factor-alpha (TNF-alpha), or IL-12 were associated with poor disease-free (P < .005) and overall (P < .01) survival. Multivariate Cox regression analysis showed ascitic-fluid IL-12 levels to be the only immunologic variable that retained independent prognostic significance (P < .03 for disease-free and P < .01 for overall survival), together with residual disease, Fédération Internationale de Gynécologie et d'Obstétrique (FIGO)-stage, and patient age. CONCLUSION: In ovarian cancer, high ascitic-fluid IL-12 levels, which may indicate a local Th1-generated immune response, are associated with disease progression.

Adult↗

PubMed2003

A PGSE study of propane gas flow through model porous bead packs.

We present a study of the probability density for molecular displacements of gas flowing through bead packs. The three bead packs to be described are composed of polydispersed porous PVC particles, 500 microm glass spheres, and 300 microm polystyrene spheres. A range of velocities (1 cm s(-1) to 1 m s(-1)) and observation times (3-500 ms), hence transport distances, are presented. For comparison we also measure the propagators for water flow in the polystyrene sphere pack. The exchange time between the moving and the stagnant portions of the flow is a strong function of the diffusion coefficient of the fluid. Comparing the propagators between water and propane flowing in similar porous media makes this clear. The gas propagators, for flowing and diffusing molecules, consistently show a feature at the average pore diameter. This feature has previously been observed for similar Peclet number studies in smaller monodispersed bead packs using liquids, but is now demonstrated for larger beads with gas. We analyze and discuss these propagators in the physically intuitive propagator space and also in the well-understood Fourier q space. The extension of NMR PGSE experiments to gas systems allows flow and diffusion information to be obtained over a wider range of length and time scales than with liquids, and also for a new range of physical environments and systems. Interactions between stochastic and deterministic motion are fundamental to the theoretical description of transport in porous media, and the time and length scale dependences are central to an understanding of the resultant dispersive motion.

Journal Article↗