Monoexponential Behavior Research Articles

Femtosecond fluorescence up-conversion spectroscopy of adenine and adenosine: experimental evidence for the πσ* state?

Femtosecond time-resolved fluorescence up-conversion spectroscopy has been used in a study of the excited electronic state lifetimes of the purine base adenine (Ade) and its ribonucleoside adenosine (Ado) in aqueous solution. The molecules were excited at wavelengths in the range 245 ⩽ λ exc ⩽ 280 nm using tunable UV pulses from a frequency doubled non-collinear optical parametric amplifier (NOPA). The observed biexponential temporal fluorescence profiles of Ade could be fitted using a fast decay time between τ 1 = (0.34 ± 0.07) ps at the shorter excitation wavelengths and τ 1 = (0.67 ± 0.14) ps at the longer excitation wavelengths and, independent of the excitation wavelength, a slow decay time of τ 2 = (8.4 ± 0.8) ps. The two values were assigned to the “canonical” 9H-Ade tautomer ( τ 1) and the less stable 7H-Ade tautomer ( τ 2) which are known to be present in aqueous solution. The excited state lifetime of 9H-Ade in H 2O is thus sub-picosecond even around the electronic origin of the first excited ππ* state, in contrast to a report for the 0–0 level in the gas phase (≳9 ps). The fluorescence decay profiles of Ado, in which the 9H atom is substituted by the ribose, could be described assuming monoexponential behavior with a lifetime τ = (0.31 ± 0.05) ps. The results are consistent with fast radiationless electronic relaxation from the excited ππ* to the S 0 ground state. The apparent step in the lifetime of 9H-Ade centered at λ exc ≈ 265 nm might be interpreted as evidence for the opening of an additional radiationless electronic relaxation pathway, which could arise from the πσ* state predicted at about that energy.

Comparison of dexamethasone pharmacokinetics in female rats after intravenous and intramuscular administration

This study seeks a route of drug administration that would produce a pharmacokinetic profile for dexamethasone not significantly different from the intravenous route in female rats and would offer reproducible drug input with minimal stress to the animals. The intramuscular (i.m.) route of drug administration vs intravenous (i.v.) injection were compared in three female Wistar rats administered 1 mg/kg dexamethasone phosphate. Dexamethasone plasma concentrations were measured by a normal phase HPLC assay for 12 h after drug administration. Dexamethasone exhibited monoexponential behavior after intravenous dosing and was absorbed rapidly after intramuscular dosing (absorption half-life of 14 min) with 86% bioavailability. Dexamethasone had a terminal half-life of 2.3 h after drug administration by either route. The volume of distribution of 0.78 l/kg and the clearance of 0.23 l/h/kg are in good agreement with reported pharmacokinetic parameters in male rats. Intravenous dosing can be replaced by intramuscular dosing without causing any marked difference in dexamethasone pharmacokinetics.

Recombination dynamics of localized excitons in InGaN quantum dots

Indium-rich fluctuations in ultrathin InGaN layers act at low temperatures as a dense ensemble of quantum dots (QD). This leads to a complex potential landscape with localization sites of widely varying depth for excitons. We report on investigations of the recombination mechanisms of excitons localized in InGaN∕GaN QD structures by time-resolved and spatially resolved photoluminescence (PL) measurements. The structures were grown by metal-organic chemical-vapor deposition on Si (111) substrates. Sharp lines originating from single QDs could be observed. Their PL decays show monoexponential behavior. Similar transition energies have different time constants. Thus, the well-known nonexponential PL decay of the QD ensemble is assigned to the summation of monoexponential decays originating from individual QDs with different exciton lifetimes.

Analysis of a large number of clinical studies for breast cancer radiotherapy: estimation of radiobiological parameters for treatment planning

Numerous studies of early-stage breast cancer treated with breast conserving surgery (BCS) and radiotherapy (RT) have been published in recent years. Both external beam radiotherapy (EBRT) and/or brachytherapy (BT) with different fractionation schemes are currently used. The present RT practice is largely based on empirical experience and it lacks a reliable modelling tool to compare different RT modalities or to design new treatment strategies. The purpose of this work is to derive a plausible set of radiobiological parameters that can be used for RT treatment planning. The derivation is based on existing clinical data and is consistent with the analysis of a large number of published clinical studies on early-stage breast cancer.A large number of published clinical studies on the treatment of early breast cancer with BCS plus RT (including whole breast EBRT with or without a boost to the tumour bed, whole breast EBRT alone, brachytherapy alone) and RT alone are compiled and analysed. The linear quadratic (LQ) model is used in the analysis. Three of these clinical studies are selected to derive a plausible set of LQ parameters. The potential doubling time is set a priori in the derivation according to in vitro measurements from the literature. The impact of considering lower or higher Tpot is investigated. The effects of inhomogeneous dose distributions are considered using clinically representative dose volume histograms. The derived LQ parameters are used to compare a large number of clinical studies using different regimes (e.g., RT modality and/or different fractionation schemes with different prescribed dose) in order to validate their applicability. The values of the equivalent uniform dose (EUD) and biologically effective dose (BED) are used as a common metric to compare the biological effectiveness of each treatment regime.We have obtained a plausible set of radiobiological parameters for breast cancer: α = 0.3 Gy−1, α/β = 10 Gy and sub-lethal damage repair time Trep = 1 h (mono-exponential behaviour is assumed). This set of parameters is consistent with in vitro experiments and with previously reported analyses. Using this set of parameters, we have found that most of the studies, using BCS plus whole breast RT and a boost to the tumour bed, have EUDs ranging from 60–70 Gy. No correlation is found between BED and the local recurrence rate. The treatments of BCS plus brachytherapy alone have a wide range of EUD (30–50 Gy), which is significantly lower than the treatments with whole breast EBRT plus a boost of the tumour bed. The studies with different fractionation schemes for whole breast EBRT also show a significant variation of EUD. Carefully designed clinical studies with large numbers of patients are required to determine clinically the relative effectiveness of these treatment variations.The derived LQ parameter set based on clinical data is consistent with in vitro experiments and previous studies. As demonstrated in the present work, these radiobiological parameters can be potentially useful in radiotherapy treatment planning for early breast cancer, e.g., in comparing biological effectiveness of different radiotherapy modalities, different fractionation schemes and in designing new treatment strategies.

Characterization of normal brain and brain tumor pathology by chisquares parameter maps of diffusion-weighted image data

Objective: To characterize normal and pathologic brain tissue by quantifying the deviation of diffusion-related signal from a simple monoexponential decay, when measured over a wider than usual range of b-factors. Methods and materials: Line scan diffusion imaging (LSDI), with diffusion weighting at multiple b-factors between 100 and 5000 s/mm 2, was performed on 1.5 T clinical scanners. Diffusion data of single slice sections were acquired in five healthy subjects and 19 brain tumor patients. In-patients, conventional T2-weighted and contrast-enhanced T1-weighted images were obtained for reference purposes. The chisquare ( χ 2) error parameter associated with the monoexponential fits of the measured tissue water signals was then used to quantify the departure from a simple monoexponential signal decay on a pixel-by-pixel basis. Results: Diffusion-weighted images over a wider b-factor range than typically used were successfully obtained in all healthy subjects and patients. Normal and pathologic tissues demonstrated signal decays, which clearly deviate from a simple monoexponential behavior. The χ 2 of cortical and deep grey matter was considerably lower than in white matter. In peritumoral edema, however, χ 2 was 68% higher than in normal white matter. In highly malignant brain tumors, such as glioblastoma multiforme (GBM) or anaplastic astrocytoma, χ 2 values were on average almost 400% higher than in normal white matter, while for one low grade astrocytoma and two cases of metastasis, χ 2 was not profoundly different from the χ 2 value of white matter. Maps of the χ 2 values provide good visualization of spatial details. However, the tumor tissue contrast generated appeared in many cases to be different from the enhancement produced by paramagnetic contrast agents. For example, in cases where the contrast agent only highlighted the rim of the tumor, χ 2 enhancement was present within the solid part of the tumor. Conclusion: The deviation from a purely monoexponential diffusion signal decay becomes evident as diffusion encoding is extended well beyond the normal range. The χ 2 error parameter as a measure of this deviation seems to provide sufficient lesion contrast to permit differentiation of malignant brain tumors from normal brain tissue.

Thermal redistribution and dephasing of localized excitons in CdSe/ZnSSe quantum island structures

Temperature-dependent photoluminescence measurements of CdSe/ZnSSe quantum island structures show a blueshift of the emission maximum and a significant broadening of the emission band above 50 K. The features originate from a thermal activation of localized excitons and a redistribution of the occupation within the inhomogeneous island ensemble. The presence of exciton states with different localization at comparable transition energies is indicated by a multiexponential decay of the four-wave mixing photon echo observed at low temperatures. Upon increasing the temperature above 50 K, the decay of the four-wave mixing signal changes into a monoexponential behavior. Polarization-dependent measurements unhide strong exciton-exciton interaction and signify the formation of biexcitons with biexciton binding energies around 12 meV. The features indicate the dominance of weakly localized quantum-well-like precursor states of CdSe islands on the high-energy side of the emission band.

Water‐Exchange and Relaxometric Studies of Gd(III) Complexes with DTPA‐bis(amide) Ligands

AbstractThe water 1H and 17O NMR relaxation properties of aqueous solutions containing Gd(III) che lates of the DTPA‐BIPA, DTPA‐BAA, DTPA‐BDEA and DTPA‐BMA ligands were investigated, and the results were compared with those previously reported for the Gd(III) complex with DTPA ligand. The significant deviation from the monoexponential behavior at the estimation of temperature dependence of 1H longitudinal relaxation rate for Gd(III) complexes with DTPA‐BIPA, DTPA‐BAA and DTPA‐BDEA ligands is characteristic of the slow chemical ex change. The measurements of 17O NMR trans verse relaxation rates and EPR transverse electronic relaxation rates in the range 276–343 K, allowed the assessment of the water‐exchange lifetime between the coordination site and the bulk solvent. With this approach, we obtained the water‐exchange life time (τM) of 1515, 1429, 1538 and 2128 ns for [Gd(DTPA‐BIPA)(H2O)], [Gd(DTPA‐BAA)(H2O)], [Gd(DTPA‐BDEA)(H2O)] and [Gd(DTPA‐BMA)(H2O)], respectively. Compared with the τM value of 303 ns for [Gd(DTPA)(H2O)]2−, we are able to conclude that the water residence life time in creases when the two terminal carboxylate groups of DTPA were substituted by two amide groups.

Cryoporometry and relaxometry of water in silica-gels

Both cryoporometry and relaxometry are tools to determine the pore size distribution (PSD) of a porous material with NMR. The melting point depression is described by the Gibbs-Thomson equation, yielding the PSD from cryoporometry. The enhanced relaxivity is caused by the surface of the porous material, yielding the PSD from relaxometry. The description in the classical paper of Brownstein and Tarr is only valid for one pore (size). The extended theory of McCall et al. is needed to describe a heterogeneous coupled porous system. As testing material a series of silica-gels called Nucleosil is chosen with typical pore sizes of 5, 10, 12 and 30 nm. Transverse relaxation time distributions are measured using a CPMG-sequence for every temperature of the cryoporometry measurement. These show a mono exponential behaviour, indicating a strongly coupled porous structure. Using the cryoporometry data, an attempt is made to reproduce the averaged relaxivity. Agreement is found for pores with typical pore sizes between 10 nm and 1 μm. The model is not valid for pores smaller than 10 nm.

Holographic multiplexing in photorefractive polymers

A new multiplexing schedule is derived for multiplexing holograms in photorefractive polymers which do not exhibit mono-exponential recording behavior. An M-number ( M/#) of 0.3 was measured experimentally by recording 20 holograms of roughly equal strength in a single location of 125-μm-thick material using peristrophic multiplexing. The effects of hologram dark-decay on the time-evolution of the M/# and the relative strengths of individual holograms is investigated.

An interleaved sampling strategy for MR spectroscopy in vivo: Applications on human calf musculature☆

Assessment of relaxation times, magnetization transfer rates, or apparent diffusion coefficients by volume selective 1H MR spectroscopy requires data from several single spectra with variable sequence parameters. Unintentional movements during the examination lead to inaccuracies, especially if the spatial distribution of concentrations is inhomogeneous. Improved comparability of the single spectra in a series recorded in vivo were obtained using a modified spectroscopic technique with INTerleaved ACquisi Tion of multiple SPECtra (INTACTSPEC). INTACTSPEC series of spectra from the tibialis anterior muscle (m. tib. ant.), soleus muscle (m. soleus), and tibial bone marrow of 20 healthy volunteers were analyzed. Transverse relaxation times T 2 of methylene signals in muscular lipid stores ranged from 77 ms (intramyocellular methylene component in m. tib. ant.) to 88 ms (intramyocellular methylene component in m. soleus) and were similar to those from yellow tibial bone marrow (T 2 = 84 ms). Echo time-dependent signal intensities of choline and creatine deviated markedly from a monoexponential behavior in m. tib. ant., but were nearly exponential in m. soleus. Results from water diffusion measurements parallel and perpendicular to the axis of the lower leg showed significant differences between m. tib. ant. and m. soleus, probably due to the spatial orientation of the muscle fibers. Apparent diffusion coefficients along the leg axis were found to be higher in m. tib. ant. (2.10 ± 0.08 × 10 −3 mm 2/s) compared to m. soleus (1.78 ± 0.11 × 10 −3 mm 2/s), but m. soleus showed less restricted diffusion in perpendicular orientation (1.59 ± 0.19 × 10 −3 mm 2/s versus 1.20 ± 0.08 × 10 −3 mm 2/s in m. tib. ant.). Magnetization transfer experiments with various RF preparation pulse amplitudes led to very similar results for m. tib. ant. and m. soleus.

31P MRS studies of exercising human muscle at high temporal resolution.

Methods for measuring mitochondrial activity from 31P magnetic resonance spectroscopy data collected during and after exercise were compared in controls, weight lifters, and peripheral vascular occlusive disease (PVOD) patients. There were trends toward increasing mitochondrial activity during exercise in order from PVOD patients, moderately active controls, highly active controls, to weight lifters. Results from PVOD patients show divergence of some measures due to 1) the non-exponential nature of phosphocreatine recovery, and 2) potential breakdown of [ADP] control of the mitochondria due to lack of oxygen (for Qmax calculation). These results demonstrate the utility of obtaining and directly analyzing high time resolution data rather than assuming monoexponential behavior of metabolite recovery.

Photochromism and Thermochromism of Phenanthrospirooxazine in Poly(Alkyl Methacrylates)

The decay of the photomerocyanine (MC) formed after flash irradiation of a phenanthrospirooxazine (SO) was studied in polymer films of poly(methyl-), poly(ethyl-), and poly(isobutyl methacrylate) and compared with similar data of a benzospiropyran (SP). The decays in the dark depart from monoexponential behavior. The data were analyzed by a Gaussian distribution model and by a matrix relaxation model. The rate constant at the center of the Gaussian distribution is equal in all polymers and equal to the unimolecular rate constant reported in nonpolar liquids. This may be related to the inability of the polymer to solvate the transition state. The polymer matrix affects the width of the activation energy distribution; this distribution is broader in more rigid media. The relaxation model is able to provide a mean value for the relaxation time of the matrix, which is relevant for the decay. The Arrhenius activation energy of this relaxation time is similar in each polymer for the MC forms of SO and of SP and...

Mathematical analysis and experimental investigation of noise in quantitative magnetic resonance imaging applied in polymer gel dosimetry

In polymer gel dosimetry, the spin–spin relaxation rate R2=1/ T2, is related to the absorbed dose that is delivered to a gel phantom by high-energy radiation beams. In a two-points method, R2 is calculated from two differently T2-weighted images. In the many-points method, R2 is calculated by fitting the pixel intensities of a set of differently exponentially T2-weighted images. An analysis of the influence of noise on the resulting R2 image may contribute considerably to the enhancement of the accuracy of the dose map. The relation between the noise level in the differently T2-weighted images and the noise level in the R2 image is derived mathematically. This relation is dependent on the actual R2, on the choice of the echo times in the sequences used, and the fitting algorithm. Both a least square fit to the semi-logarithmic T2-relaxation plot and a maximum-likelihood estimation on the T2-relaxation plot were investigated. It was found that dose images obtained from R2 images through calibration will contain noise that originates from the noise in the R2 image and from the probability distribution of the coefficients of the calibration curve. We present a method for optimizing the echo times in order to maximize the signal-to-noise ratio (SNR) in the resulting R2 image for both methods and for both fitting algorithms. The mathematical considerations on the SNR as presented, can also be applied on other data sets which display a mono-exponential behavior (e.g. diffusion measurements, T1 relaxation).

Spectroscopic Properties of 2,5,8,11-Tetra-tert-butylperylene in Polymer Films

The spectroscopic properties of 2,5,8,11-tetra-tert-butylperylene in poly(vinyl alcohol) have been studied. To this end, the absorption and fluorescescence excitation and emission spectra have been measured. The shape of the spectra in poly(vinyl alcohol) is virtually identical with that in propanediol and lipid systems. The Forster radius calculated from the spectra was found to be 3.7 ± 0.3 nm. The natural fluorescence lifetime of 2,5,8,11-tetra-tert-butylperylene in poly(vinyl alcohol) was also calculated from the spectra and found to be 5.3 ± 0.2 ns. The fluorescence decay in poly(vinyl alcohol) exhibits monoexponential behavior with a lifetime of 4.5 ± 0.3 ns. It is shown that the fluorescence anisotropy of 2,5,8,11-tetra-tert-butylperylene in the polymer matrix does not decay, indicating that its motion is quenched on the time scale of the fluorescence decay. The initial value of the fluorescence anisotropy, r(0), for excitation at 260 nm and emission at 455 nm is −0.16 ± 0.02 while for excitation a...

Decay characteristics of bone marrow in the presence of a trabecular bone network: in vitro and in vivo studies showing a departure from monoexponential behavior.

In this study, we examine MRI T2' decay characteristics for bone marrow in trabecular bone networks, using an asymmetric spin-echo sequence to isolate the inhomogeneous decay due to susceptibility variations between bone and marrow or water. In in vitro measurements on trabecular bone specimens from human vertebral bodies, tibia, and radii, we find significant deviations from a monoexponential signal decay. The initial decay is seen to have a Gaussian decay character, switching to a primarily exponential decay at later decay times. A similar trend is observed in in vivo measurements in the distal radius. Unlike an exponential decay, which may be characterized by a single decay rate, this is indicative of a significant variation in the decay rate with time. The deviations from exponential decay are seen to be orientation dependent, being most significant when the primary trabecular orientation is perpendicular to the static magnetic field.

Age-related changes in the human lens as monitored by detection of porphyrin excited states.

Previous studies have shown that the triplet state lifetimes of various porphyrins are increased by several orders of magnitude when they are bound to lens protein. Flash photolysis studies of mesotetra (p-sulfonatophenyl)porphyrin (TPPS) on intact bovine lenses indicated a biexponential decay of the triplet state with lifetimes of 160 microsecond and 1.6 ms. Here we extend those measurements to TPPS associated with intact human lenses. Steady-state fluorescence measurements indicate that TPPS binds to both young and old human lenses. In an intact young human lens, the TPPS triplet state is observed to decay biexponentially with lifetimes of 50 and 680 microsecond. As the age of the lens increases, the lifetime of the shorter-lived component lengthens while that of the longer-lived component decreases slightly. In order human lenses, the two lifetimes coalesce and the triplet decay exhibits purely monoexponential behavior. These photophysical characteristics apparently are due to age-related modification(s) of the protein in the human lens resulting in an increasingly more homogeneous environment around the porphyrin.

Nuclear relaxation times in vivo and in vitro of human and rabbit lenses

Nuclear relaxation times T 1 and T 2 of water in human eye lenses were measured in vivo and in vitro in the temperature range 35–41°C. Measurements were also done for rabbit lenses in vitro in the temperature range from 20 to −45°C. Measurements in vitro for both types of lens showed monoexponential spin—lattice ( T 1) and biexponential spin—spin ( T 2) relaxation behaviour. Such relaxation time behaviour can be explained by a two-phase model of water in the lens. The monoexponential behaviour of T 1 is shown to be due to rapid exchange occurring in water molecules in the lens, termed free water. The biexponential character of T 2 results from the absence of fast exchange processes between the above types of water. One can distinguish two T 2 values: T 2A is ascribed to so-called free water, with an activation energy of 10.5 ± 1.5 kJ mol −1 for human lenses and 13.9 ± 2.0 kJ mol −1 for rabbit lenses, while the shorter T 2B time is ascribed to water strongly bound to proteins, with an activation energy equal to 32.1 ± 5.0 kJ mol −1 for human lenses and 8.5 ± 2.0 kJ mol −1 for rabbit lenses. Moreover, a distribution of correlation times has been assumed for both phases in order to explain significant differences between the T 1 and T 2 values. The results of in vivo measurements are discussed as well as the applicability of this technique for early diagnosis of pathological changes in a human lens.

NMR proton relaxation and chemical exchange in the system H162O/H172O-[2H6]dimethylsulphoxide

NMR proton relaxation rates of normal and 17O enriched water in a mixture of 68 mol% water and 32 mol% [2H6]dimethylsulphoxide were measured for temperatures between 298 K and 183 K. In the range between 240 K and 204 K the limit of fast proton-proton exchange between H16 2O and H17 2O is not obeyed, and relaxation curves deviate from mono-exponential behaviour. By fitting the relaxation curves to a model of NMR two-phase relaxation the proton-proton exchange rate within the aqueous component could be obtained. With decreasing temperature, proton-proton exchange slows down and a residence time of about 125 ms at 215 K is found, but it becomes faster again for still lower temperatures. From the phase-averaged relaxation rates of water in the 17O enriched mixtures, the 17O induced proton relaxation rate was derived as a function of temperature. This yields the rotational correlation times of the water molecule in the mixture and the dipolar spin-lattice coupling parameter. The latter is considerably lower t...

Multiexponential Proton Spin-Spin Relaxation in MR Imaging of Human Brain Tumors

In vivo measurements of proton relaxation processes in human brain tumors have been performed by magnetic resonance (MR) imaging using a whole-body superconductive MR scanner, operating at 1.5 T. The T1 and T2 relaxation time measurements were based on a combined Carr-Purcell/Carr-Purcell-Meiboom-Gill sequence with two interleaved repetition times and 32 echoes. First, comparative measurements in the imager and with the spectrometer of relaxation times were performed on phantoms containing fluids of different T1 and T2 to evaluate accuracy. A maximum deviation of approximately 10% was found. Multislicing with a gap width of one slice thickness influenced the accuracy of T1 relaxation measurement. A gap width of at least two times the slice thickness was necessary for reliable determination of T1. No influence on T2 values was observed by multislicing. Second, in human head imaging the multiexponential behavior of the T2 decay curves has been analyzed in each pixel, where the mean square deviation has been used as a criterion to discriminate between mono- and biexponential behavior. Mean values of monoexponential T1 and multiexponential T2 relaxation data for white matter, gray matter, CSF, edema, and tumor were sampled in 12 patients with brain tumors. T2 showed monoexponential behavior in white and gray matter, whereas CSF, edema, and tumor showed distinct biexponentiality. The biexponential analysis generally yields "fast" and "slow" components with T2f = 80 +/- 17 ms and T2s = 2,030 +/- 210 ms for CSF (partial volume effect), T2f = 104 +/- 25 ms and T2s = 677 +/- 152 ms for edematous tissues, T2f = 97 +/- 19 ms and T2s = 756 +/- 99 ms for tumor tissues, respectively. Using a stepwise discriminant analysis by forward selection, the two best discriminating parameters of the multiexponential relaxation analysis for each pair of classification groups have been selected. For the discrimination of edematous and tumor tissues a retrospective overall accuracy of 94% has been found.

Evaluation of Biexponential Relaxation Processes by Magnetic Resonance Imaging

Despite the complexity of biologic tissues, a monoexponential behaviour is usually assumed when estimating relaxation processes in vivo by magnetic resonance imaging (MRI). This study was designed to evaluate the potential of biexponential decomposition of T1 and T2 relaxation curves obtained at 1.5 tesla (T). Measurements were performed on a phantom of bicompartmental perspex boxes with combinations of different CuSO4 concentrations. T1 determination was based on a 12-points partial saturation inversion recovery pulse sequence. T2 determination was provided by a multiple spin echo sequence with 32 echoes. Applying biexponential curve analysis, a significant deviation from a monoexponential behaviour was recognized at a ratio of corresponding relaxation rates of about 3 and 2, estimating T1 and T2 relaxation, respectively (p less than 0.01, F-test). Requiring an SD less than or equal to 10 per cent for each set of parameters, the biexponential model was accepted when this ratio exceeded a factor of 5 and 8, respectively. Referring to 'expected' T1 and T2 values, however, an accuracy within 20 per cent only was observed at ratios of at least 6 and 15. It is concluded that quantitative estimation of individual and specific relaxation components in complex biologic tissues by MRI may prove very difficult.