Relevant bibliographies by topics / Transverse and Longitudinal Relaxation Methods

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Transverse and Longitudinal Relaxation Methods'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Transverse and Longitudinal Relaxation Methods"

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TODICA, M. "NMR OBSERVATION OF THE SPIN-LATTICE AND SPIN-SPIN RELAXATION IN SOME POLIBUTADIENES WITH DIFFERENT VINYL CONTENTS." International Journal of Modern Physics B 19, no. 13 (May 20, 2005): 2167–74. http://dx.doi.org/10.1142/s0217979205029705.

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Some polybutadienes with different vinyl contents were observed by NMR methods in order to disclose the influence of the microstructure of the polymeric chains on the relaxation of the longitudinal and transverse magnetization. The relaxation process is correlated with the dynamic properties of the polymeric chains. The residual dipolar interaction determined by the rigidity of the polymeric chains is observed by the pseudo-solid echo method and is associated with the vinyl contents of the samples.
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Chance, Brent H., and Don E. Bray. "Nondestructive Monitoring of Stress Relaxation in Welded Steel Plates." Journal of Pressure Vessel Technology 124, no. 3 (July 26, 2002): 343–48. http://dx.doi.org/10.1115/1.1491581.

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This study investigates transverse stress relaxation in welded steel plates. Two different methods of stress measurement were used; strain gages and critically refracted longitudinal LCR waves. The material investigated was ASTM 1008/1010 steel. T-shaped slots were cut from each edge of each specimen in order to provide a uniaxial tension stress field in the area of investigation. After the plates were stress-relieved by annealing, the transverse slots were then welded and allowed to cool. Strain gages were applied to the bridge area joining the middle of the plate and oriented parallel to the long side of the plate. Initial strain gage and ultrasonic measurements were then performed. At different time intervals, cutting through a sample plate’s welds relieved the stresses. Strain gage and ultrasonic measurements were then repeated. Both the strain gage and LCR methods indicate that there is a measurable stress relaxation in the plates, and that it occurs in a time-dependent and predictable manner.
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Wei, Mengmeng, Wenbin Yu, Min Zhou, Wei Huang, Yuanxing Liu, and Xinye Xu. "Three techniques for measuring the transverse relaxation time of cesium atoms." AIP Advances 13, no. 3 (March 1, 2023): 035327. http://dx.doi.org/10.1063/5.0140593.

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The transverse relaxation time ( T2) is an important indicator to determine the fundamental sensitivity limit of alkali-metal atomic magnetometers. We propose a method based on the principle of longitudinal field modulation that obtains T2 by scanning the transverse static magnetic field. The previous technique of extracting T2 from the linewidth of the modulation frequency and the traditional magnetic-resonance-broadening-fitting method are also described. The T2 measurements of Cesium (Cs) atoms are carried out through these three methods, whose operating environments are applicable to different atomic magnetometers, respectively. The method that we propose can be used for obtaining the T2 of Cs atoms as well as detecting the transverse static magnetic field and is customized for the study of the Cs–Xenon ensemble for the construction of nuclear magnetic resonance gyroscopes. Moreover, the relationship between the limit sensitivities and cell temperatures is further studied in the experiment.
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Monaretto, Tatiana, Tiago Bueno Moraes, and Luiz Alberto Colnago. "Recent 1D and 2D TD–NMR Pulse Sequences for Plant Science." Plants 10, no. 5 (April 21, 2021): 833. http://dx.doi.org/10.3390/plants10050833.

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Time domain nuclear magnetic resonance (TD–NMR) has been widely applied in plant science in the last four decades. Several TD–NMR instruments and methods have been developed for laboratory, green-house, and field studies. This mini-review focuses on the recent TD–NMR pulse sequences applied in plant science. One of the sequences measures the transverse relaxation time (T2) with minimal sample heating, using a lower refocusing flip angle and consequently lower specific absorption rate than that of conventional CPMG. Other sequences are based on a continuous wave free precession (CWFP) regime used to enhance the signal-to-noise ratio, to measure longitudinal (T1) and transverse relaxation time in a single shot experiment, and as alternative 2D pulse sequences to obtain T1–T2 and diffusion-T1 correlation maps. This review also presents some applications of these sequences in plant science.
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TODICA, M. "COMPARATIVE OBSERVATION OF THE NMR SPIN-LATTICE AND SPIN-SPIN RELAXATION IN MOLTEN AND CROSS-LINKED POLIBUTADIENE." International Journal of Modern Physics B 19, no. 10 (April 20, 2005): 1771–81. http://dx.doi.org/10.1142/s0217979205029353.

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The molten and cross-linked polybutadiene were observed by NMR methods in order to disclose the influence of the presence of the temporary and permanent junctions between the polymeric chains on the relaxation of the longitudinal and transverse magnetization. The residual dipolar interaction determined by the entanglements of the polymeric chains is observed by the pseudo-solid echo method and is associated with the existence of the temporary network.
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Chen, Jianfei, Jingyu Chu, Wenchun Jiang, Bin Yao, Fan Zhou, Zhenbo Wang, and Pengcheng Zhao. "Experimental and Numerical Simulation to Study the Reduction of Welding Residual Stress by Ultrasonic Impact Treatment." Materials 13, no. 4 (February 12, 2020): 837. http://dx.doi.org/10.3390/ma13040837.

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In this study, the effects of ultrasonic impact treatment (UIT) on the residual stress in a repair welding joint are investigated by experimental and finite element methods. A three-dimensional numerical analysis approach including a thermomechanical-coupled welding simulation and dynamic elastic-plastic UIT simulation is developed, which has been validated by X-ray diffraction measurement and indentation strain method. The results show that longitudinal residual stresses basically turned into the small tensile stress state from the large tensile stress state, and transverse residual stresses have mainly turned into compressive stresses from large tensile stress after the UIT. In the thickness direction, the average decrease of longitudinal residual stress is 259.9 MPa, which is larger than the 149.1 MPa of transverse residual stress. The calculated residual stress distribution after the UIT of the thin plate is compared with that of the thick plate in the literature, with the results showing the stress accumulation layer inside the thick plate. The simulation results show that the elastic strains are decreased slightly and the equivalent plastic strain is increased markedly after UIT, which explains the mechanism of residual stress relaxation.
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Haribabu, Viswanathan, Palani Sharmiladevi, Najim Akhtar, Abubacker Sulaiman Farook, Koyeli Girigoswami, and Agnishwar Girigoswami. "Label Free Ultrasmall Fluoromagnetic Ferrite-clusters for Targeted Cancer Imaging and Drug Delivery." Current Drug Delivery 16, no. 3 (February 1, 2019): 233–41. http://dx.doi.org/10.2174/1567201816666181119112410.

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Objective: The label free ultrasmall fluorescent ferrite clusters have been engineered in a controlled fashion which was stabilized by serum protein and functionalized by folic acid for the application of targeted multimodal optical and Magnetic Resonance (MR) cancer imaging. Methods: The ultra-small manganese ferrite nanoclusters (PMNCs) with a diameter of 4 nm have a commendable effect on the longitudinal (T1) and transverse (T2) relaxation in MR imaging that was evident from the phantom and animal MRI. Results: The calculated longitudinal molar relaxivity of nanoclusters was found to be 6.9 ± 0.10 mM-1 S-1 which was exactly 2.22 times better than the conventional Gd-DOTA and their 4.01 ratio of the transverse (r2) and longitudinal (r1) relaxivities made them a potential candidate for both T1 and T2 contrast agents in MRI. In addition, the fluorescence-based small animal imaging showed folic acid driven accumulated fluorescent signal at the tumour site to conclude the capacity of PMNCs for targeted fluorescence imaging of cancer diagnosis. Conclusion: The cytotoxicity assay and histopathology studies were the evidence for their safe biodistribution in animal systems. Furthermore, the protein encapsulated clusters have the ability to deliver the anticancer drug Methotrexate (MTX) to the cancer tissues with a sustained manner. Therefore, one can conclude the remarkable efficacy of architect nanoclusters for theragnosis.
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Uddin, Md Nasir, R. Marc Lebel, Peter Seres, Gregg Blevins, and Alan H. Wilman. "Spin echo transverse relaxation and atrophy in multiple sclerosis deep gray matter: A two-year longitudinal study." Multiple Sclerosis Journal 22, no. 9 (July 19, 2016): 1133–43. http://dx.doi.org/10.1177/1352458515614091.

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Background: Deep gray matter (DGM) is affected in relapsing–remitting multiple sclerosis (RRMS) and may be studied using short-term longitudinal MRI. Objective: To investigate two-year changes in spin-echo transverse relaxation rate (R2) and atrophy in DGM, and its relationship with disease severity in RRMS patients. Methods: Twenty six RRMS patients and 26 matched controls were imaged at 4.7 T. Multiecho spin-echo R2 maps and atrophy measurements were obtained in DGM at baseline and two-year follow-up. Differences between MRI measures and correlations to disease severity were examined. Results: After two years, mean R2 values in the globus pallidus and pulvinar increased by ~4% ( p<0.001) in patients and <1.7% in controls. Two-year changes in R2 showed significant correlation to disease severity in the globus pallidus, pulvinar, substantia nigra, and thalamus. Multiple regression of the two-year R2 difference using these four DGM structures as variables, yielded high correlation with disease severity ( r=0.83, p<0.001). Two-year changes in volume and R2 showed significant correlation only for the globus pallidus in multiple sclerosis (MS) ( p<0.05). Conclusions: Two-year difference R2 measurements in DGM correlate to disease severity in MS. R2 mapping and atrophy measurements over two years can be used to identify changes in DGM in MS.
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Zhang, Yapeng, Jingjing Cheng, and Wenzhong Liu. "Characterization and Relaxation Properties of a Series of Monodispersed Magnetic Nanoparticles." Sensors 19, no. 15 (August 2, 2019): 3396. http://dx.doi.org/10.3390/s19153396.

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Magnetic iron oxide nanoparticles are relatively advanced nanomaterials, and are widely used in biology, physics and medicine, especially as contrast agents for magnetic resonance imaging. Characterization of the properties of magnetic nanoparticles plays an important role in the application of magnetic particles. As a contrast agent, the relaxation rate directly affects image enhancement. We characterized a series of monodispersed magnetic nanoparticles using different methods and measured their relaxation rates using a 0.47 T low-field Nuclear Magnetic Resonance instrument. Generally speaking, the properties of magnetic nanoparticles are closely related to their particle sizes; however, neither longitudinal relaxation rate r 1 nor transverse relaxation rate r 2 changes monotonously with the particle size d . Therefore, size can affect the magnetism of magnetic nanoparticles, but it is not the only factor. Then, we defined the relaxation rates r i ′ (i = 1 or 2) using the induced magnetization of magnetic nanoparticles, and found that the correlation relationship between r 1 ′ relaxation rate and r 1 relaxation rate is slightly worse, with a correlation coefficient of R 2 = 0.8939, while the correlation relationship between r 2 ′ relaxation rate and r 2 relaxation rate is very obvious, with a correlation coefficient of R 2 = 0.9983. The main reason is that r 2 relaxation rate is related to the magnetic field inhomogeneity, produced by magnetic nanoparticles; however r 1 relaxation rate is mainly a result of the direct interaction of hydrogen nucleus in water molecules and the metal ions in magnetic nanoparticles to shorten the T 1 relaxation time, so it is not directly related to magnetic field inhomogeneity.
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Wernersson, Sven, Göran Carlström, Andreas Jakobsson, and Mikael Akke. "Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled <i>R</i><sub>1<i>ρ</i></sub> accordion experiments." Magnetic Resonance 2, no. 2 (July 12, 2021): 571–87. http://dx.doi.org/10.5194/mr-2-571-2021.

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Abstract. Multidimensional, heteronuclear NMR relaxation methods are used extensively to characterize the dynamics of biological macromolecules. Acquisition of relaxation datasets on proteins typically requires significant measurement time, often several days. Accordion spectroscopy offers a powerful means to shorten relaxation rate measurements by encoding the “relaxation dimension” into the indirect evolution period in multidimensional experiments. Time savings can also be achieved by non-uniform sampling (NUS) of multidimensional NMR data, which is used increasingly to improve spectral resolution or increase sensitivity per unit time. However, NUS is not commonly implemented in relaxation experiments, because most reconstruction algorithms are inherently nonlinear, leading to problems when estimating signal intensities, relaxation rate constants and their error bounds. We have previously shown how to avoid these shortcomings by combining accordion spectroscopy with NUS, followed by data reconstruction using sparse exponential mode analysis, thereby achieving a dramatic decrease in the total length of longitudinal relaxation experiments. Here, we present the corresponding transverse relaxation experiment, taking into account the special considerations required for its successful implementation in the framework of the accordion-NUS approach. We attain the highest possible precision in the relaxation rate constants by optimizing the NUS scheme with respect to the Cramér–Rao lower bound of the variance of the estimated parameter, given the total number of sampling points and the spectrum-specific signal characteristics. The resulting accordion-NUS R1ρ relaxation experiment achieves comparable precision in the parameter estimates compared to conventional CPMG (Carr–Purcell–Meiboom–Gill) R2 or spin-lock R1ρ experiments while saving an order of magnitude in experiment time.
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Dissertations / Theses on the topic "Transverse and Longitudinal Relaxation Methods"

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Huen, Isaac Kwong-Ping. "Assessment of placental and fetal oxygenation in normal and abnormal pregnancy using magnetic resonance imaging." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/assessment-of-placental-and-fetal-oxygenation-in-normal-and-abnormal-pregnancy-using-magnetic-resonance-imaging(8cd3f9a2-22cb-4c95-bee3-06b5c4bfc2d2).html.

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Fetal growth restriction (FGR) is a common pregnancy complication resulting in increased neonatal mortality and morbidity. The aetiology of fetal growth restriction is not fully understood, but abnormalities in placental development are, leading to abnormalities in placental structure which are thought to affect supply of oxygen to the fetus. The source of fetal hypoxia is unknown due to the difficulty in obtaining oxygenation data in the context of pregnancy using existing techniques. There is also an absence of data relating to oxygenation in FGR pregnancies. Oxygen-Enhanced MRI (OE-MRI) and Blood Oxygen-Level Dependent (BOLD) MRI permit noninvasive acquisition of data related to changes in the concentration of dissolved oxygen (pO2) and changes in hemoglobin saturation (sO2) under air- and oxygen- breathing (hyperoxic challenge).The aim of this project was to determine whether MRI methods can provide information relating to placental oxygenation in normal and FGR-compromised pregnancy, to investigate fetal brain oxygenation and to assess the potential confound of placental perfusion changes under hyperoxic challenge. After optimization of sequences in non-pregnant volunteers, similar pO2 and sO2 increases under hyperoxic challenge were seen in normal and FGR pregnancy. This suggested placental oxygenation was similar and that fetal extraction of oxygen may be a likelier cause of fetal hypoxia. Normal fetal brain oxygenation was found not to increase under hyperoxic challenge, which may be due to hemodynamic adaptation to limit cerebral hyperoxygenation. Finally, the robustness of these oxygenation results was supported by the lack of placental perfusion changes observed under hyperoxia using Arterial Spin Labeling (ASL).In conclusion, MRI methods successfully provided information on placental and fetal oxygenation in normal and abnormal pregnancy, obtaining novel data informing the aetiology of FGR and the physiology of the fetal brain.
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Aveiro, Susana Seabra. "The p22HBP heme binding protein: an NMR study of the dynamics and heme-protein interactions." Doctoral thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/14278.

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Doutoramento em Bioquímica
The work presented in this Thesis investigates the dynamics and molecular interactions of p22HBP and the p22HBP-tetrapyrrole complex. Specifically, the key residues involved when a tetrapyrrole binds to p22HBP were sought. Previous molecular modelling studies identified three possible charged residues R56, K64 and K177 as possibly being important in tetrapyrrole binding via electrostatic interactions with the propionate groups of the tetrapyrrole. A number of variants of murine p22HBP were therefore prepared and fluorescence quenching and NMR used to verify the integrity of the variants and their interaction with tetrapyrrole. The same molecular modelling studies identified a mobile loop Y171-R180 in p22HBP that decreased in mobility on tetrapyrrole binding, therefore to confirm this mobility change dynamics studies based on NMR relaxation experiments were carried out. Finally in order to obtain a non heme-binding form of human p22HBP a chimeric p22HBP was designed and constructed. This construct, and the resulting protein, will be important for future siRNA knockdown studies where rescue or recovery of function experiments are required to prove the knockdown results. Chapter one discusses the current state of the art in terms of the biological, structural and functional aspects of p22HBP. The main objectives of the Thesis are also introduced here. Chapter two presents a detailed description of the different expression vectors (pNJ2 and pet28-a) and procedures used for overexpression and purification of murine p22HBP and its variants and human p22HBP. All expression and purification systems used gave good yields and allowed isotopic labeling to be carried out. The fluorescence quenching results for tetrapyrrole binding to murine p22HBP and variants are presented in chapter three along with the dissociation constants that were found to be in the nanomolar range for wild type murine and human p22HBP. The same studies were performed for murine p22HBP variants, with hydrophobic and polar changes being introduced at R56, K64 and K177. The dissociation constants were found to double in some cases but no significant changes in the strength of hemin-protein interactions were observed. The tetrapyrrole interaction with p22HBP was also followed by NMR spectroscopy, where chemical shift mapping was used to identify binding pocket location. All the variants and wild type human p22HBP were found to bind at the same location. Chapter 4 contains the data from 2D and 3D experiments carried out on 15N/13C labelled human p22HBP that was used to obtain backbone assignments. Comparison with wild type murine p22HBP assignments, PPIX titrations and theoretical calculations based on chemical shifts (Talos+) allowed 82% of the backbone resonances to be assigned. The results from the relaxation experiments used to probe the dynamics of the mobile loop in p22HBP on binding to tetrapyrrole are presented in chapter 5. The overall protein was found to tumble isotropically in the free and bound forms however the results to probe mobility changes in the 171-180 loop on tetrapyrrole binding proved inconclusive as only residue could be assigned and this did not seem to become significantly less mobile. The final chapter describes the design and construction of a chimeric p22HBP. For these purpose, the alfa1-helix sequence of human p22HBP in the phHBP1 plasmid was replaced by its homologous sequence in hSOUL, a non heme-binding protein with identical 3D structure. The results however indicated that either the incorrect sequence was introduced into the plasmid or the purification procedure was inadequate.
O trabalho apresentado nesta Tese focou-se na dinâmica e nas interações moleculares da p22HBP e do complexo p22HBP-tetrapirrol, nomeadamente nos resíduos chave envolvidos nesta interação. Estudos prévios de modelação molecular identificaram três possíveis resíduos chave R56, K64 e K177 como sendo importantes na interação com os tetrapirróis, através de interações eletrostáticas com os grupos propionato do tetrapirrol. Foram desenhados e construídos variantes da p22HBP murina e foram desenvolvidos estudos de extinção de fluorescência e RMN para avaliar a integridade dos variantes e a sua interação com os tetrapirróis. Os mesmos estudos de modelação molecular identificaram ainda uma zona flexível (Y171-R180) na p22HBP que diminui a mobilidade com a interação do tetrapirrol. Para confirmar esta alteração de mobilidade, foram realizados estudos de dinâmica, baseados em RMN. Por fim, com o intuito de obter uma versão não funcional da p22HBP humana, foi planeada e construída uma versão quimérica da p22HBP humana. No futuro, esta nova versão da p22HBP quimérica, será importante para os estudos de knockdown envolvendo siRNA. O capítulo um introduz uma revisão dos aspetos biológicos da p22HBP nomeadamente os estudos estruturais e as possíveis funções que foram identificadas. Os principais objetivos da tese são também apresentados neste capítulo. No capítulo dois é apresentada uma descrição detalhada dos diferentes vectores de sobreexpressão (pNJ2 e pet28-a) e dos métodos de sobreexpressão e purificação da p22HBP murina e respectivos variantes, bem como da p22HBP humana. Todos os sistemas de sobreexpressão e purificação utilizados obtiveram bons rendimentos e permitiram a marcação isotópica das proteínas. No capítulo 3 são apresentados os resultados de extinção de fluorescência para a interação da p22HBP murina e humana com hemina através das constantes de dissociação determinadas na ordem dos nanomolar. Os mesmos estudos foram realizados para os variantes da p22HBP murina, com alterações hidrofóbicas e de polaridade nos resíduos R56, K64 e K177. Em alguns casos, as constantes de dissociação determinadas são mais elevadas, embora não se tenham verificado alterações significativas na força da interação proteína-hemo. As interações tetrapirrólicas com a p22HBP foram também estudadas por espectroscopia de RMN, onde foram mapeadas as diferenças nos desvios químicos para identificar a localização da zona de interação. A localização da zona de interação dos variantes da p22HBP e a p2HBP humana mantém-se igual à p22HBP murina. No capítulo 4 encontram-se os resultados das experiências 2D e 3D realizadas na p22HBP humana, isotopicamente marcada com 15N/13C, para identificar as ressonâncias da cadeia principal. 82% dos sistemas de spin da cadeia principal foram identificados através da comparação com a p22HBP murina, das titulações com PPIX e de cálculos teóricos baseados nos desvios químicos (Talos+). No capítulo 5 são apresentados os resultados das experiências de relaxação, usados para comprovarem a dinâmica do loop na p22HBP aquando da interação com o tetrapirrol. A proteína no seu todo move-se de uma forma isotrópica na forma livre e ligada. No entanto os resultados para comprovar as alterações de mobilidade no loop 171-180 na presença de hemo, foram inconclusivos uma vez que só a um resíduo foi atribuído um sistema de spin, e não foi indicativo da perda significativa de mobilidade. O último capítulo descreve o planeamento e a construção da p22HBP quimérica. Para tal, a sequência que codifica a hélix alfa 1 da p22HBP humana, no plasmídeo phHBP1, foi substituída pela sequência homóloga da SOUL humana, uma proteína com uma estrutura 3D semelhante mas não liga ao hemo. Os resultados no entanto demonstraram que ou a sequência não foi introduzida corretamente no plasmídeo ou o sistema de purificação não foi adequado.
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Papadopoulos, Konstantinos. "Investigation of magnetic order in nickel-5d transition metal systems." Thesis, Uppsala universitet, Molekyl- och kondenserade materiens fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-383009.

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Double perovskite materials exhibit alterations in magnetic order through manipulation oftheir crystal structure. Certain ultra thin metallic bilayers can create an exotic magnetic stateof confined spin textures called skyrmions. In both cases, new atomic arrangements leadto new electrical and magnetic properties. The following work comprises two studies, bothof which examine the magnetic properties of transition metals in either powder or thin filmsamples. The first part is dedicated to a series of muon spin rotation and relaxation (muSR)experiments on a LaSrNiReO6, double perovskite, powder sample. In the muSR technique, aspin polarized muon beam is focused onto a powder envelope in low pressure and temperatureconditions. The spins of the implanted muons evolve depending on the intrinsic or externallyapplied magnetic field according to Larmor precession. The measurement is based onthe detection of decay positrons that carry this precession information on their preferreddecay directions. Measurements that were realized in wTF, ZF and LF setups, reveal asecond transition to magnetic order at Tc ≃ 22K, below a transition that was observed at T =261K from magnetic susceptibility measurements. The experimental results point to threemagnetic phases, paramagnetic for T > 261K, dilute ferrimagnetic for 22 < T < 261K and amagnetically ordered state for T < 22K, that may implicate ferro- and antiferromagnetismfrom Ni sublattices and Ni-Re interactions. The second part follows an attempt to produce and characterize ultra thin bilayer filmsfor the observation of interfacial chiral structures and skyrmions. Co/Fe/MgO (100) andW/Ni/Cu (100) bilayers were grown with magnetron sputter deposition in various layerthicknesses and their structure was determined by X-ray reflectometry (XRR). The XRRscans presented a relatively thick-layered Co/Fe/MgO film, while extremely thin and roughW/Ni/Cu bilayers, for the purposes of studying films with broken interfacial inversionsymmetry. This study was concluded with indicative magneto-transport measurements thatalso point to the reconfiguration of the growth procedure.
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Wu, Yi Ying, and 吳奕螢. "Correction of Longitudinal and Transverse Relaxation Effects of Contrast Agent Extravasation in Dynamic Susceptibility Contrast MRI at 3T." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/84415322147113507022.

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碩士
長庚大學
醫學物理暨影像科學研究所
97
Contrast agent extravasation in dynamic susceptibility contrast- (DSC-) MRI of brain tumors may cause significant errors in the estimation of relative cerebral blood volume (rCBV) which can mislead the tumor diagnosis or treatment. The current model for correcting the contrast agent leakage (termed LT1 model in this paper) only takes the T1 effect into account, which may fail the cases when the T2* effect is pronounced. This study proposed a two-compartmental model, LT1+T2 model, that was able to describe the measured DSC-MRI signals with the combined T1 and T2* effects from the contrast agent leakage. Results from computer simulation showed that the T2* effect was more dominant with longer TE, at higher field strength and when the leakage was more severe. DSC-MRI was performed on three patients with brain tumors at a clinical 3T scanner. Images were analyzed using the LT1+T2 model, as well as the LT1 model for comparison, and the rCBV maps were corrected correspondingly. The T2* effect dominated the measured signal time curves in all our experimental data, which were well fitted by both LT1 and LT1+T2 model. However, negative leakage indices (K2) were obtained with the LT1 model, whereas those with the LT1+T2 model were positive and thus more meaningful. Corrected rCBV maps with these two models demonstrated similar patterns that exhibited values decreased from the uncorrected ones in tumor regions with high contrast extravasation. The ratios of corrected/uncorrected normalized rCBV maps (to normal deep white matters) ranged 0.40-0.60 and 0.89-0.99 for regions-of-interest in tumors and gray matters, respectively. The proposed LT1+T2 model is expected to be capable of correcting the contrast agent extravasation effects in DSC-MRI signals acquired at different clinical platforms and imaging parameters.
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HOSEK, TOMAS. "Development of new NMR methods to study intrinsically disordered proteins." Doctoral thesis, 2015. http://hdl.handle.net/2158/969485.

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PIAI, ALESSANDRO. "Characterizing structural disorder through NMR: new methods and applications." Doctoral thesis, 2015. http://hdl.handle.net/2158/1015862.

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Intrinsically Disordered Proteins (IDPs) are flexible proteins that challenge structural biology due to the fact that they cannot be studied with the standard methods developed to characterize well-folded proteins. In the last decades, the discovery of their widespread presence and involvement in many biological functions, despite their deviation from the structure-function paradigm, has pushed the scientific community towards a growing acceptance of the importance of IDPs and to the development of new tools for studying their structure, dynamics and functions. In this context, Nuclear Magnetic Resonance (NMR) spectroscopy plays the leading role of most suitable technique to characterize IDPs. In this doctoral thesis, my contribution to the advancement of NMR spectroscopy, achieved by developing new experiments to study IDPs, is described. The new methods enable the characterization of structural disorder and allow to address topics of general interest such as the study of protein linkers and low-complexity regions, two areas of high biological relevance for which only very limited atomic resolution information is available so far. The methodological progress in NMR and the findings on the studied IDPs reported here give a contribution to the discovery of new roles for structural disorder and prompt towards an unified understanding of structure-dynamicsdisorder/function relationships.
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Books on the topic "Transverse and Longitudinal Relaxation Methods"

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Kudinov, Igor', Anton Eremin, Konstantin Trubicyn, Vitaliy Zhukov, and Vasiliy Tkachev. Vibrations of solids, liquids and gases taking into account local disequilibrium. ru: INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1859642.

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The monograph presents the results of the development and research of new mathematical models of the processes of vibrations of solids, liquids and gases, taking into account local disequilibrium. To derive differential equations, the Navier—Stokes equations, Newton's second law and modified formulas of the classical empirical laws of Fourier, Hooke, Newton are used, which take into account the velocities and accelerations of the driving forces (gradients of the corresponding quantities) and their consequences (heat flow, normal and tangential stresses). The conditions for the occurrence of shock waves of stresses and displacements in dynamic thermoelasticity problems formulated taking into account relaxation phenomena in thermal and thermoelastic problems are investigated, new results are obtained in the study of longitudinal and transverse vibrations of rods, strings, liquids and gases, and the conditions for the excitation of gas self-oscillations arising from a time-constant heat source are determined. It is intended for scientific and technical workers specializing in mathematics, thermophysics, thermoelasticity, as well as teachers and students of technical universities.
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Book chapters on the topic "Transverse and Longitudinal Relaxation Methods"

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Klieber, Christoph, Thomas Pezeril, Stéphane Andrieu, and Keith A. Nelson. "GHz Longitudinal and Transverse Acoustic Waves and Structural Relaxation Dynamics in Liquid Glycerol." In Springer Series in Chemical Physics, 499–501. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-95946-5_162.

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Garteiser, Philippe, Octavia Bane, Sabrina Doblas, Iris Friedli, Stefanie Hectors, Gwenaël Pagé, Bernard E. Van Beers, and John C. Waterton. "Experimental Protocols for MRI Mapping of Renal T1." In Methods in Molecular Biology, 383–402. New York, NY: Springer US, 2021. http://dx.doi.org/10.1007/978-1-0716-0978-1_22.

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AbstractThe water proton longitudinal relaxation time, T1, is a common and useful MR parameter in nephrology research. Here we provide three step-by-step T1-mapping protocols suitable for different types of nephrology research. Firstly, we provide a single-slice 2D saturation recovery protocol suitable for studies of global pathology, where whole-kidney coverage is unnecessary. Secondly, we provide an inversion recovery type imaging protocol that may be optimized for specific kidney disease applications. Finally, we also provide imaging protocol for small animal kidney imaging in a clinical scanner.This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers. This analysis protocol chapter is complemented by two separate chapters describing the basic concept and experimental procedure.
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Müller, Andreas, and Martin Meier. "Assessment of Renal Volume with MRI: Experimental Protocol." In Methods in Molecular Biology, 369–82. New York, NY: Springer US, 2021. http://dx.doi.org/10.1007/978-1-0716-0978-1_21.

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AbstractRenal length and volume are important parameters in the clinical assessment of patients with diabetes mellitus, kidney transplants, or renal artery stenosis. Kidney size is used in primary diagnostics to differentiate between acute (rather swollen kidneys) and chronic (rather small kidney) pathophysiology. Total kidney volume is also an established biomarker in studies for the treatment of autosomal dominant polycystic kidney disease (ADPKD). There are several factors influencing kidney size, and there is still a debate on the value of the measured kidney size in terms of renal function or cardiovascular risk. The renal volume is most often calculated by measuring the three axes of the kidney, on the assumption that the organ resembles an ellipsoid. By default, the longitudinal and transverse diameters of the kidney are measured. In animal models renal length and volume1 are also important parameters in the assessment of organ rejection after transplantation and in determination of kidney failure due to renal artery stenosis, recurrent urinary tract infections, or diabetes mellitus. In general total kidney volume (TKV) is a valuable parameter for predicting prognosis and monitoring disease progression in animal models of human diseases like polycystic kidney disease (PKD) or acute kidney injury (AKI) and chronic kidney disease (CKD).This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers. This analysis protocol is complemented by two separate chapters describing the basic concept and experimental procedure.
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"Relaxation and the NOE." In Essential Mathematics for NMR and MRI Spectroscopists, 636–69. The Royal Society of Chemistry, 2016. http://dx.doi.org/10.1039/bk9781782627975-00636.

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The relaxation of spins to an equilibrium state makes itself apparent the first time one encounters a free induction decay (FID). The two major types of relaxation in magnetic resonance spectroscopy, T1 and T2 relaxation, are examined. Spin temperature is discussed to emphasise the flow of energy to and from spin systems during an experiment. Longitudinal (T1) relaxation is presented visually as the movement of the transverse magnetisation vector towards the equilibrium z-axis position and is modelled as an exponential process. Transverse relaxation (T2) is also shown visually as a de-coherence of the phases of the many transverse vectors representing the many spin magnetic moments in the sample and is also modelled as an exponential process. The spectral density function is derived from the Fourier transform of the autocorrelation function for stochastic molecular motions and its properties are examined. The dipolar relaxation mechanism that is dominant in solution NMR spectroscopy is discussed in detail using material from earlier chapters. The Nuclear Overhauser Enhancement (NOE) is then introduced, using the results from the dipolar relaxation section.
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"Lecture 12: A Relaxation Theory of Nuclear Spin States." In Lectures On Spin Dynamics: The Theoretical Minimum, 143–62. The Royal Society of Chemistry, 2022. http://dx.doi.org/10.1039/9781837670871-00143.

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In this lecture, I discuss a semi-classical relaxation theory of nuclear spin states, the so-called Wangsness–Bloch–Redfield (WBR) theory. I first discuss the concept of relaxation to an equilibrium configuration in a qualitative manner, in order to introduce the two most important relaxation decay constants: T1 and T2. Later, I derive a compact expression for the dynamics under incoherent Hamiltonians, define its validity regime and introduce the concept of a relaxation superoperator. Finally, the dipolar contribution to the relaxation superoperator is derived and put to use to calculate the longitudinal and transverse relaxation decay rate constants due to such a mechanism.
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Fushman, David, and David Cowburn. "Nuclear Magnetic Resonance Relaxation in Determination of Residue-Specific 15N Chemical Shift Tensors in Proteins in Solution: Protein Dynamics, Structure, and Applications of Transverse Relaxation Optimized Spectroscopy." In Methods in Enzymology, 109–26. Elsevier, 2001. http://dx.doi.org/10.1016/s0076-6879(01)39312-6.

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Qasrawi, Radwan, Diala Abu Al-Halawa, Omar Daraghmeh, Mohammad Hjouj, and Rania Abu Seir. "Medical Image Processing and Analysis Techniques for Detecting Giant Cell Arteritis." In Giant-Cell Arteritis [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.97161.

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Medical image segmentation and classification algorithms are commonly used in clinical applications. Several automatic and semiautomatic segmentation methods were used for extracting veins and arteries on transverse and longitudinal medical images. Recently, the use of medical image processing and analysis tools improved giant cell arteries (GCA) detection and diagnosis using patient specific medical imaging. In this chapter, we proposed several image processing and analysis algorithms for detecting and quantifying the GCA from patient medical images. The chapter introduced the connected threshold and region growing segmentation approaches on two case studies with temporal arteritis using ultrasound (US) and magnetic resonance imaging (MRI) imaging modalities extracted from the Radiopedia Dataset. The GCA detection procedure was developed using the 3D Slicer Medical Imaging Interaction software as a fast prototyping open-source framework. GCA detection passes through two main procedures: The pre-processing phase, in which we improve and enhances the quality of an image after removing the noise, irrelevant and unwanted parts of the scanned image by the use of filtering techniques, and contrast enhancement methods; and the processing phase which includes all the steps of processing, which are used for identification, segmentation, measurement, and quantification of GCA. The semi-automatic interaction is involved in the entire segmentation process for finding the segmentation parameters. The results of the two case studies show that the proposed approach managed to detect and quantify the GCA region of interest. Hence, the proposed algorithm is efficient to perform complete, and accurate extraction of temporal arteries. The proposed semi-automatic segmentation method can be used for studies focusing on three-dimensional visualization and volumetric quantification of Giant Cell Arteritis.
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"variety of span lengths, widths, number of grlders and slab thickness were analyzed. For two 50 ft. spans with seven girders (slab aspect ratio of 0.12) the value of D in the S/D formula varies between 6.1 and 7.96 for midspan center girder depending on the slab to girder stiffness ratio. This is in lieu of the 5.5 specified in AASHTO Standard Specification. Perhaps more representative are results for a 100 ft., two span continuous bridge with five girders spaced at 9 ft, where D varies between 8.4 and 10.8. Another Interesting result in Walker's report is regarding the structural idealization of the bridge. It has been found that the simple grid model can represent the essential behavior of the bridge as the more exact models do. The grid model was constructed such that the transverse beams represent the equivalent slab and diaphragms (if present) and the longitudinal beams represent the longitudinal composite girders. The fact that the grid model gives good representation of the essential behavior of the bridge can not be generalized. The grid model has certain limitations, however it gives a better representation of the bridge behavior than does a simple two-value S/D rule. A simple micro computer implementation of a grid model is seen by Walker as a better method than the S/D formula to predict lateral load distribution. Recently Hays, Sessions and Berry (8), have demonstrated that the effect of span length, which is neglected in AASHTO can be considerable. They found that AASHTO results are slightly unconservative for short spans and quite conservative for longer spans. Furthermore they compared the results of a finite element analysis with field test results and concluded that the comparison showed generally good agreement. A wide range of load distribution methods are available in the technical literature (9-17). These methods range from empirical methods, as the one recommended by AASHTO and described above, to sophisticated computer-based solution techniques which take into consideration the three-dimensional response of the bridge. The computer methods utilize a wide rang of structural idealization. Some use a simple equivalent anisotropic plate or grid work while others use sophisticated finite element models that consider detailed aspects of the interaction between the components of the bridge superstructure. The parameters which influence the load distribution most are; the number of girders and their spacing, the span length, and the girder moment of Inertia and slab thickness." In Composite Steel Structures, 46. CRC Press, 1987. http://dx.doi.org/10.1201/9781482286359-7.

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Conference papers on the topic "Transverse and Longitudinal Relaxation Methods"

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Shtark, Abraham, Hagay Grosbein, Guy Sameach, and Harry H. Hilton. "An Alternative Protocol for Determining Viscoelastic Material Properties Based on Tensile Tests Without the Use of Poisson’s Ratios." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41068.

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Analytical and experimental protocols are formulated and outlined in detail wherein unidirectional tensile creep or relaxation experiments are performed on viscoelastic specimen. A combination of a photogrametric system and a tensile testing machine provides stress data in the loaded direction and strains in both longitudinal and transverse directions. The data is integrated through the use of the integral constitutive relations, and produce values for the creep compliance parameters. Subsequently, the viscoelastic Young’s, shear and bulk moduli are determined without the use of viscoelastic Poisson’s ratios. Experimental results indicate strong time, stress and stress history dependencies of viscoelastic PRs. Current experimental results are compared with traditional methods based on assumed time independent Poisson ratios. Maximum errors in strain values from 160% to 205% for the constant PR approach are demonstrated when its results are compared to results for the experimental time interval.
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Jang, Chang Doo, Ha Cheol Song, and Young Chun Jo. "Fatigue Life Assessment of Fillet Welded Joint Considering the Relaxation and Redistribution of Residual Stresses." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51400.

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This paper presents the fatigue life assessment procedure for the welded joint of ship structure. Test model is a boxing fillet specimen, the idealized welded joint model of longitudinal and transverse members in ship structure. Fatigue test was executed according to the 14-points S-N method of JSME, and experimental data were presented in the S-N curve based on HSS (Hot Spot Stress) approach. To define the fatigue life of crack initiation and crack propagation, S-N data for each length of crack were appraised. In this study, the new FE analysis algorithms for the estimation of residual stress relaxation due to external load and residual stress redistribution due to crack propagation were proposed to assess the effect of residual stresses on crack growth precisely. Initial welding residual stress field was obtained by thermal elasto-plastic analysis considering temperature dependent material properties, and the amount of residual stress relaxation and redistribution were assessed by subsequent elasto-plastic analysis. In the analysis of crack propagation, the SIF (Stress Intensity Factor) range was evaluated by 1/4-point displacement extrapolation method, and the effect of welding residual stresses on fatigue behaviors was considered by introducing the effective SIF concept. The test results of crack propagations were compared with the predicted data from the analysis.
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Scola, Mallory R., Joe N. Kornegay, James F. Howard, Timothy C. Nichols, and Caterina M. Gallippi. "Viscoelastic Strain Response (ViSR) Ultrasound in Pre-Clinical and Clinical Application." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65596.

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Viscoelastic Strain Response (ViSR) ultrasound is a novel acoustic radiation force (ARF)-based imaging method that noninvasively interrogates the viscoelastic properties of tissue by measuring the relaxation time constant for constant stress in the Voigt biomechanical model. The time constant is defined as the ratio of coefficient of viscosity to elastic modulus, so ViSR differentiates tissue with disparate viscosities and elasticities. ViSR ultrasound is performed by delivering two successive ARF impulses to a single region of exciation (ROE) and tracking the micrometer-scale displacements induced by the propagating longitudinal waves. ViSR does not rely on transverse wave propagation, which can be disrupted and difficult to track in heterogeneous and/or geometrically complex media. Another advantage to ViSR ultrasound is a large axial range relative to conventional ARF Impulse (ARFI) ultrasound. In this overview, ViSR methods are discussed and demonstrated in calibrated viscoelastic tissue mimicking materials. ViSR ultrasound is then applied to differentiating fatty and fibrous deposition in muscle in a golden retriever muscular dystrophy (GRMD) dog model and in boys with Duchenne muscular dystrophy (DMD) with correlation to standard physical testing. ViSR is also applied to delineating the structure and composition of atherosclerotic plaques in a hypercholesterolemic pig model with histochemical validation. ViSR’s key advantages and disadvantages are discussed in regard to its general clinical utility.
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Khanna, Faqir. "Ward-Takahashi Relations: Longitudinal and Transverse." In Fifth International Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2007. http://dx.doi.org/10.22323/1.031.0003.

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Luca Motoc, Dana. "Dynamic Mechanical Characterization of CF/GF Hybrid Reinforced Polymeric Composite Structures." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82185.

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The importance of dynamic mechanical analysis (DMA) as a research tool in the study of polymeric composite structures behavior has been already demonstrated in the literature. Many papers were approaching the relaxation phenomenon within the polymer based composite structures and thereby their behavior under various conditions of stress and temperature. Supplementary, the effect of fillers geometry, orientation and volume fraction have been extensively approached while considering the micromechanical level and their role in the mechanical properties were suitable stated. Hybridization of two different fillers has proven to an effective method in material design allowing their developers to tailor their properties according to the application driven imposed requirements. The herein paper attempts to present a comparative study centered on the development and characterization of a hybrid polymeric composite structures made up from different combinations of carbon and glass fibers by evaluating their dynamic mechanical properties. The samples were measured using the Dynamic Mechanical Analyzer (DMA) from NETZSCH-DMA 242 C, in the 3-point bending mode, nitrogen atmosphere, at a scanning rate of 3 K/min from −40 to 180° C with a fixed frequency of 1 Hz. Storage and loss modulus, loss tangent were recorded as function of temperature both on longitudinal and transverse direction of the unidirectional carbon fibers, in two consecutive heating cycles. A reference sample was set up to aid the comparison analysis, made entire from one filler type. The effect of the fillers type, fillers relative volume fraction and temperature on the storage and loss moduli will be deeply investigated.
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Manolis, George, and George Dadoulis. "PASSIVE CONTROL ISSUES ON THE LONGITUDINAL AND TRANSVERSE VIBRATIONS OF FLEXIBLE PYLONS." In 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Methods in Structural Dynamics and Earthquake Engineering. Athens: Institute of Structural Analysis and Antiseismic Research National Technical University of Athens, 2021. http://dx.doi.org/10.7712/120121.8693.19669.

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Fu, yangying, and Jie Yuan. "Investigation on the methods to extend the transverse relaxation time of polarized alkali atoms." In Fourteenth National Conference on Laser Technology and Optoelectronics, edited by Huai-Liang Xu, Feng Chen, Lingfei Ji, Buhong Li, Xiaoping Xie, Yuxin Leng, Zhengming Sheng, et al. SPIE, 2019. http://dx.doi.org/10.1117/12.2532465.

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Obreja, Dan C., Radoslav Nabergoj, Liviu I. Crudu, and Sandita Pacuraru-Popoiu. "Transverse Stability of a Cargo Ship at Parametric Rolling on Longitudinal Waves." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57768.

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Unfavourable environmental conditions associated with an insufficient stability margin adopted in the design process may determine ship capsizing. One of the most critical situations is generated when the ship moves on longitudinal waves, at parametric resonance condition. In this paper, the theoretical and experimental investigations on transverse stability of a cargo ship on regular longitudinal waves are considered. During the seakeeping model tests on longitudinal waves, the occurrence of induced roll motions were observed and measured. The restoring moment on longitudinal waves was determined based on theoretical and experimental methods. A computer code has been implemented in order to calculate the main parts of the restoring moment i.e. Froude-Krylov, diffraction and radiation components. In order to reproduce the real physical phenomenon, captive and semi-captive model tests were correlated. The radiation and diffraction forces and moments and the restoring moment on regular longitudinal waves were measured. The agreement of the calculated solutions with the experimental results indicates the possibility of using the adopted hydrodynamic model in the design process.
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Nemirovskii, Yu V., and S. V. Tikhonov. "Longitudinal-Transverse bending of reinforced concrete rods on the basis of nonlinear diagrams of deformation of phase materials." In NUMERICAL METHODS FOR SOLVING PROBLEMS IN THE THEORY OF ELASTICITY AND PLASTICITY (EPPS 2021). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0073289.

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Ma, Yanbao. "Heat Pulse Propagation in Pure Sodium Fluoride at Low Temperatures From Ballistic to Diffusive Conduction." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64284.

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In this paper, heat pulse propagation in pure NaF at low temperature is studied by using hydrodynamic equations of a weakly interacting phonon gas. The observed longitudinal waves, transverse waves, second sound waves, and diffusive waveforms from the experiments conducted in early 1970s are numerically reconstructed. In the numerical simulations, the phase velocities of the longitudinal waves and the transverse waves are based on the experimental results, while two relaxation times for normal scattering process (τN) and resistive scattering process (τR) respectively are adjusted to fit the arrival time of second sound or to fit the observed waveforms observed in the experiments. The waveforms based on numerical results can fit the observed waveforms quite well. It is elucidated how heat pulse is transmitted by different waves in the dielectric crystal from ballistic to diffusive regions.
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Reports on the topic "Transverse and Longitudinal Relaxation Methods"

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Jury, William A., and David Russo. Characterization of Field-Scale Solute Transport in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, January 1994. http://dx.doi.org/10.32747/1994.7568772.bard.

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This report describes activity conducted in several lines of research associated with field-scale water and solute processes. A major effort was put forth developing a stochastic continuum analysis for an important class of problems involving flow of reactive and non reactive chemicals under steady unsaturated flow. The field-scale velocity covariance tensor has been derived from local soil properties and their variability, producing a large-scale description of the medium that embodies all of the local variability in a statistical sense. Special cases of anisotropic medium properties not aligned along the flow direction of spatially variable solute sorption were analysed in detail, revealing a dependence of solute spreading on subtle features of the variability of the medium, such as cross-correlations between sorption and conductivity. A novel method was developed and tested for measuring hydraulic conductivity at the scale of observation through the interpretation of a solute transport outflow curve as a stochastic-convective process. This undertaking provided a host of new K(q) relationships for existing solute experiments and also laid the foundation for future work developing a self-consistent description of flow and transport under these conditions. Numerical codes were developed for calculating K(q) functions for a variety of solute pulse outflow shapes, including lognormal, Fickian, Mobile-Immobile water, and bimodal. Testing of this new approach against conventional methodology was mixed, and agreed most closely when the assumptions of the new method were met. We conclude that this procedure offers a valuable alternative to conventional methods of measuring K(q), particularly when the application of the method is at a scale (e.g. and agricultural field) that is large compared to the common scale at which conventional K(q) devices operate. The same problem was approached from a numerical perspective, by studying the feasibility of inverting a solute outflow signal to yield the hydraulic parameters of the medium that housed the experiment. We found that the inverse problem was solvable under certain conditions, depending on the amount of noise in the signal and the degree of heterogeneity in the medium. A realistic three dimensional model of transient water and solute movement in a heterogeneous medium that contains plant roots was developed and tested. The approach taken was to generate a single realization of this complex flow event, and examine the results to see whether features were present that might be overlooked in less sophisticated model efforts. One such feature revealed is transverse dispersion, which is a critically important component in the development of macrodispersion in the longitudinal direction. The lateral mixing that was observed greatly exceeded that predicted from simpler approaches, suggesting that at least part of the important physics of the mixing process is embedded in the complexity of three dimensional flow. Another important finding was the observation that variability can produce a pseudo-kinetic behavior for solute adsorption, even when the local models used are equilibrium.
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