Multi-exponential Model Research Articles

From discrete multi-exponential model to lifetime distribution model and power law fluorescence decay function

Experimental and theoretical studies of the fluorescence intensity decays in biomolecular systems showed that under constraints of typical experiment fluorescence lifetime distribution is given by gamma function, which led to a power-like decay function. The latter well fits complex (heterogeneous) as well as simple mono-exponential decays. Fluorescence decay kinetics is described by mean value of lifetime distribution characterizing the average rate of the excited-state decay, and one new parameter of heterogeneity (1 <q <3/2) describing the relative variance of distribution, and objectively reflecting physical heterogeneity of the system. In the classical limit, when q → 1, the gamma distribution becomes the Dirac delta function, and decay function converges from power-like form to the single-exponential form. Numerous examples illustrate successful applications of this model to rational analysis of complex fluorescence decays of biomacromolecules, e.g., complexes of E. coli purine nucleoside phosphorylase (PNP-I) with formycin A (FA, inhibitor) and orthophosphate (Pi, cosubstrate), which led to identification of the mechanism of deactivation of excited state and the N(2)H tautomeric form of FA selectively bound by PNP-I. The latter is of great importance for the studies of the mechanism of protein (enzyme) action as well as for more rational drug design.

From discrete multi-exponential model to lifetime distribution model and power law fluorescence decay function

Experimental and theoretical studies of the fluorescence intensity decays in biomolecular systems showed that under constraints of typical experiment fluorescence lifetime distribution is given by gamma function, which led to a power-like decay function. The latter well fits complex (heterogeneous) as well as simple mono-exponential decays. Fluorescence decay kinetics is described by mean value of lifetime distribution characterizing the average rate of the excited-state decay, and one new parameter of heterogeneity (1 &lt; q &lt; 3/2) describing the relative variance of distribution, and objectively reflecting physical heterogeneity of the system. In the classical limit, when q → 1, the gamma distribution becomes the Dirac delta function, and decay function converges from power-like form to the single-exponential form. Numerous examples illustrate successful applications of this model to rational analysis of complex fluorescence decays of biomacromolecules, e.g., complexes ofE. colipurine nucleoside phosphorylase (PNP-I) with formycin A (FA, inhibitor) and orthophosphate (Pi, cosubstrate), which led to identification of the mechanism of deactivation of excited state and the N(2)H tautomeric form of FA selectively bound by PNP-I. The latter is of great importance for the studies of the mechanism of protein (enzyme) action as well as for more rational drug design.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

The general properties of a class of two-dimensional dilaton gravity (DG) theories with multi-exponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is treated in detail. A combination of parameters of the equations should satisfy a certain constraint that is identified and solved for the general model. It follows that in DG the integrable Toda equations, generally, cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville DG is to solve the energy-momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to finding its analytic solution. Then we consider a subclass of integrable two-dimensional theories, in which scalar matter satisfy the Toda equations while the two-dimensional metric is trivial. We also show how the wave-like solutions of the general Toda-Liouville systems can be simply derived. In DG, these solutions describe nonlinear waves coupled to gravity as well as static states and cosmologies. For the static states and cosmologies we propose and study a more general one-dimensional Toda-Liouville model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. A special attention is paid to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible, with the aim to gain a better understanding of realistic theories reduced to dimensions 1+1 and 1+0 or 0+1.

Robust estimation of the apparent diffusion coefficient (ADC) in heterogeneous solid tumors

The least-squares algorithm is known to bias apparent diffusion coefficient (ADC) values estimated from magnitude MR data, although this effect is commonly assumed to be negligible. In this study the effect of this bias on tumor ADC estimates was evaluated in vivo and was shown to introduce a consistent and significant underestimation of ADC, relative to those given by a robust maximum likelihood approach (on average, a 23.4 +/- 12% underestimation). Monte Carlo simulations revealed that the magnitude of the bias increased with ADC and decreasing signal-to-noise ratio (SNR). In vivo, this resulted in a much-reduced ability to resolve necrotic regions from surrounding viable tumor tissue compared with a maximum likelihood approach. This has significant implications for the evaluation of diffusion MR data in vivo, in particular in heterogeneous tumor tissue, when evaluating bi- and multiexponential tumor diffusion models for the modeling of data acquired with larger b-values (b > 1000 s/mm(2)) and for data with modest SNR. Use of a robust approach to modeling magnitude MR data from tumors is therefore recommended over the least-squares approach when evaluating data from heterogeneous tumors.

Plasma turnover of 3,4-didehydroretinol (vitamin A2) increases in vitamin A-deficient rats fed low versus high dietary fat

Relationships between increased adiposity and fat-soluble vitamin storage and metabolism are poorly understood. To examine these associations, 6% or 21% dietary fat was fed to rats for 11 weeks and tissue vitamin A storage determined. Two levels of supplemental vitamin A were administered. At the end of the tenth week, 3,4-didehydroretinol (DR) was administered orally, and its kinetics were followed for 1 week in serum and tissues. Model-based compartmental analysis was applied to these data. Kidney total retinol (R) concentrations were elevated in rats fed 6% compared with 21% dietary fat (n = 24/group). The fractional transfer coefficient (FTC) describing the movement of tracer from plasma to extravascular stores was two times higher in the 6% compared with the 21% fat group. Consistent with the elevated renal R in 6% fat fed rats, there was a 2-fold increase in the FTC representing tracer distribution from plasma to kidney in the 6% compared with 21% fat group. Taken together with a fat main effect on renal vitamin A, our data support the evidence that faster turnover of kidney R may help set the mechanism governing vitamin A tissue distribution during deficiency. Rats fed 21% versus 6% dietary fat conserved hepatic R more efficiently.

Voltage-Dependent Conformational Changes of the Voltage Sensor of KVAP Measured with LRET

The opening and closing of voltage-dependent ions channels depend upon conformational changes initiated in the voltage-sensors. The nature and extent of this rearrangement has been widely investigated in K+ channels, using various techniques, but so far, there is no agreement on this fundamental mechanism in K+-channel gating.We investigated the voltage-sensor operation using a LRET technique employing Tb3+ ions bound to several Lanthanide-Binding-Tags (LBT) genetically encoded at the top of the S3 and S4 segments of the KvAP channel. A fluorescently-labeled pore-blocking toxin, the Agitoxin-2, was conveniently used as an acceptor placed at a non-mobile position near the pore-axis. Three mutations, S179G, K181D and P176E, were systematically introduced in the pore region to increase toxin binding. Various fluorophores were covalently attached to cysteines individually inserted at positions N5, Q13 and D20 of the agitoxin. After purification, mutant channels were reconstituted into proteoliposomes and submitted to a Nernst-clamp procedure combining the use of valinomycin and a K+ chelator. This method allowed us to stably clamp the liposomal electrical potential at negative and positive potentials. Thus, this allowed us to stabilize the voltage-sensor in its closed state and in its open-inactivated state during the data acquisition period. Channels were then blocked with the fluorescent toxins and LRET measurements were recorded. Sensitized emissions of the acceptors were fitted with a square-base pyramidal multi-exponential model (Posson and Selvin, 2008) allowing the extraction of the four distances separating the position of the acceptor near the pore and the position of the donors located further away in the four subunits. The voltage-dependent coordinates of the LBTs indicate a rotational movement of the top of S4, with little participation of the top of the S3 segment.Support: FWF and AHA0725763Z, NIHGM068044 and GM30376.

Influence of the annealing temperature on the properties of undoped indium oxide thin films obtained by the sol–gel method

Undoped indium oxide thin films were deposited on glass slides by the sol–gel method, starting from a simple precursor solution. The effect of the annealing temperature on the electrical, optical and structural properties of the films was studied. The structural and optical characterization techniques used were X-ray diffraction and ultraviolet–visible spectroscopy. The electrical characterization was made by Hall effect, four probes method and photoconductivity decay measurements. The crystalline indium oxide was formed with a first annealing (in air) at 300 °C and it showed the type-bixbyite phase. A second annealing treatment in controlled atmosphere enhanced the crystalline quality of the films. The grain size increased with this second annealing, for the films previously annealed in air at temperature lower than 500 °C. All the films showed photoconductive effect when they were only subjected to the first annealing. This effect decreased when they were again annealed. The energy of the traps responsible for this effect was evaluated by considering a multi-exponential model. The highest conductivity value of 10 2 Ω cm, corresponded to the films with the first annealing at 300 °C and the second annealing at 500 °C. When the films were thermally treated under these conditions, the conductivity value neither changed in time, nor in the presence of light. The films were highly transparent and had a direct band gap value around 3.65 eV.

A Time Domain Fluorescence Tomography System for Small Animal Imaging

We describe the application of a time domain diffuse fluorescence tomography system for whole body small animal imaging. The key features of the system are the use of point excitation in free space using ultrashort laser pulses and noncontact detection using a gated, intensified charge-coupled device (CCD) camera. Mouse shaped epoxy phantoms, with embedded fluorescent inclusions, were used to verify the performance of a recently developed asymptotic lifetime-based tomography algorithm. The asymptotic algorithm is based on a multiexponential analysis of the decay portion of the data. The multiexponential model is shown to enable the use of a global analysis approach for a robust recovery of the lifetime components present within the imaging medium. The surface boundaries of the imaging volume were acquired using a photogrammetric camera integrated with the imaging system, and implemented in a Monte-Carlo model of photon propagation in tissue. The tomography results show that the asymptotic approach is able to separate axially located fluorescent inclusions centered at depths of 4 and 10 mm from the surface of the mouse phantom. The fluorescent inclusions had distinct lifetimes of 0.5 and 0.95 ns. The inclusions were nearly overlapping along the measurement axis and shown to be not resolvable using continuous wave (CW) methods. These results suggest the practical feasibility and advantages of a time domain approach for whole body small animal fluorescence molecular imaging, particularly with the use of lifetime as a contrast mechanism.

Advantages of prostate-specific antigen (PSA) clearance model over simple PSA half-life computation to describe PSA decrease after prostate adenomectomy

Objectives A population kinetic approach based on PSA clearance (CL PSA) may be a more rational strategy to characterize prostate-specific antigen (PSA) decrease profile after prostate surgery than the commonly used method (half-life from mono/bi-exponential models). Methods We used 182 post-adenomectomy PSA concentrations from 56 benign prostatic hyperplasia patients to build, with NONMEM software, a multi-exponential and a CL PSA model for comparison. Results The best multi-exponential model was PSA(t) = 4.96e − 0.269t + 3.10e − 0.16t + 0.746e + 0.0002t with a stable median residual PSA at 0.64 ng/mL. The best model parametrized with clearance was CL PSA = 0.0229 ⁎ (AGE/69) 3.78. Akaike information criteria and standard errors favored the CL PSA model. Median peripheral zone and transitional zone productions were 0.034 ng/mL/cm 3 and 0.136 ng/mL/g. A threshold at 2 ng/mL on day 90 allowed for a diagnostic of biochemical relapse diagnostic. Conclusions The population CL PSA model was superior to the multi-exponential approach for investigating individual post-adenomectomy PSA decreases.

Fluorescence intensity decays of 2-aminopurine solutions: Lifetime distribution approach

The fluorescent adenine analog 2-aminopurine (2AP) has been used extensively to monitor conformational changes and macromolecular binding events involving nucleic acids because its fluorescence properties are highly sensitive to changes in chemical environment. Furthermore, site-specific incorporation of 2AP permits local DNA and RNA conformational events to be discriminated from the global structural changes monitored by UV–Vis spectroscopy and circular dichroism. However, although the steady-state fluorescence properties of 2AP have been well defined in diverse settings, interpretation of 2AP fluorescence lifetime parameters has been hampered by the heterogeneous nature of multiexponential 2AP intensity decays observed across populations of microenvironments. To resolve this problem, we tested the utility of multiexponential versus continuous Lorentzian lifetime distribution models to describe fluorescence intensity decays from 2AP in diverse chemical backgrounds and within the context of RNA. Heterogeneity was introduced into 2AP intensity decays by mixing solvents of differing polarities or by adding quenchers under high viscosity to evaluate the transient effect. Heterogeneity of 2AP fluorescence within the context of a synthetic RNA hairpin was introduced by structural remodeling using a magnesium salt. In each case except folded RNA (which required a bimodal distribution), 2AP lifetime properties were well described by single Lorentzian distribution functions, abrogating the need to introduce additional discrete lifetime subpopulations. Rather, heterogeneity in fluorescence decay processes was accommodated by the breadth of each distribution. This approach also permitted solvent relaxation effects on 2AP emission to be assessed by comparing lifetime distributions at multiple wavelengths. Together, these studies provide a new perspective for the interpretation of 2AP fluorescence lifetime properties that will further the utility of this fluorophore in analyses of the complex and heterogeneous structural microenvironments associated with nucleic acids.

Frequency Domain Fluorescence Lifetime Study of Crude Petroleum Oils

Frequency domain (FD) fluorescence lifetime data was collected for a series of 20 crude petroleum oils using a 405 nm excitation source and over a spectral range of approximately 426 to approximately 650 nm. Average fluorescence lifetimes were calculated using three different models: discrete multi-exponential, Gaussian distribution, and Lorentzian distribution. Fitting the data to extract accurate average lifetimes using the various models proved easier and less time consuming for the FD data than with Time Correlated Single Photon Counting (TCSPC) methods however the analysis of confidence intervals to the computed average lifetimes proved cumbersome for both methods. The uncertainty in the average lifetime was generally larger for the discrete lifetime multi-exponential model when compared to the distribution-based models. For the lifetime distributions, the data from the light crude oils with long lifetimes generally fit to a single decay term. Heavier oils with shorter lifetimes required multiple decay terms. The actual value for the average lifetime is more dependant on the specific fitting model employed than the data acquisition method used. Correlations between average fluorescence lifetimes and physical and chemical parameters of the crude oils were made with a view to developing a quantitative model for predicting the gross chemical composition of crude oils. It was found that there was no significant benefit gained by using FD over TCSPC other than more rapid data analysis in the FD case. For the FD data the Gaussian distribution model for fluorescence lifetime gave the best correlations with chemical composition allowing a qualitative correlation to some bulk oil parameters.

An approach of NMR relaxometry for understanding water in saturated compacted bentonite

1H NMR relaxometry is applied for investigation of water state in compacted saturated bentonites (Kunipia-F, Kunigel-V1 and Kunigel-V1/sand mixture). The dry density is varied from 0.4 to 2.0 g/cm 3. The analyses of the magnetization decay to obtain relaxation time constants were implemented by two kinds of methods: discrete and continuous relaxation time distribution, as multi-exponential models. Assuming the relaxation time with 3-hydrated layer which is used as a threshold whether bulk-like water (pore water), the proportion of bulk-like water to total water were evaluated. The proportion of bulk-like water obtained from continuous distribution analysis of relaxation time were well in agreement with XRD results in the past. The knowledge of water state related to the dry density was given that bulk-like water was disappeared in compacted saturated Kunipia-F at high dry density (>1.2 g/cm 3), on the contrary bulk-like water of about 10% remained in Kunigel-V1 and Kunigel-V1/sand mixture regardless of high dry density (>1.6 g/cm 3).

Tunable Visible-Light Emission from CdS Nanocrystallites Prepared under Microwave Irradiation

The microwave (MW)-assisted reaction of cadmium acetate with thiourea in N,N-dimethylformamide (DMF) was controlled by controlling the MW irradiation time in the presence of 1 -thioglycerol as a capping agent. The peak position of the absorption band of the CdS nanocrystallites, dispersed in chloroform, shifts toward longer wavelength with increasing MW irradiation time, indicating growth of particle size under prolonged MW irradiation. However, the peak position of absorption band remains at the same wavelength, and only the intensity of the absorption band is increased when the MW irradiation of the colloidal solution of CdS nanocrystallites in DMF is periodically interrupted, keeping the solution at room temperature (27 °C) before each irradiation. This suggests that the particle growth occurs only during the continuous irradiation of MW and stops when the system is cooled down. From the spectral absorption edge, the diameter of CdS nanoparticles has been estimated. Photoluminescence of the CdS nanocrystallites, dispersed in chloroform, observed in the visible range shifts toward higher wavelength with increased duration of MW irradiation. When the MW irradiation was repeated for a fixed duration in colloidal solution of CdS nanocrystallites in DMF, enhancement in PL intensity was noticed without any change in the emission peak position. The relative PL quantum yield of the CdS nanocrystallites was estimated under various experimental conditions. Time-correlated single-photon counting experiments were performed to study the time-resolved photoluminescence of CdS nanocrystallites. The observed emission decay profiles have been simulated by using the multiexponential model.

The Sense and Nonsense of Exponential Models in Clinical Research

Exponential models are very popular for the assessment of clinical research. Nature is unpredictable and exponential models may be adequate for simple organisms but less so for human beings. Theobjective was to review the potential advantages and limitations of this approach. The following models were reviewed: Cox proportional hazard regression, Markow modeling, polynomial regression for Laplace transformed multi-exponential models, and logistic regression. Real and hypothesized data were used as examples.In conclusion, the advantages include: the possibility to conveniently study subgroup effects, otherwise called confounders; the possibility to derive pharmacokinetic parameters; andthe possibility to make long-term predictions from observational data. Limitations include: the exponential models may not fit the data well enough; they may give rise to some serious misinterpretations of the data; most of the statistical software for exponential models assumes that confounders are homogeneous, while, in reality, this is virtually never true; and the exponential models are a major simplification for the description of research data in human beings. We underline that exponential modeling, although a very interesting tool for exploratory research, is not adequately reliable for confirmational research. It is to be hoped that this paper will help investigators to more cautiously interpret the results of their exponential data analysis.

A new approach to interpretation of heterogeneity of fluorescence decay: Effect of induced tautomeric shift and enzyme → ligand fluorescence resonance energy transfer

Fluorescence decays in protein–ligand complexes are described by a new efficient model of continuous distribution of fluorescence lifetimes, and compared with multi-exponential models. Resulted analytical power-like decay function provides good fits to highly complex fluorescence kinetics. Moreover, this is a manifestation of so-called Tsallis q-exponential function, which is suitable for description of the systems with long-range interactions, memory effect, as well as with fluctuations of the characteristic lifetime of fluorescence. The proposed decay function was used to study effect of the interaction of E. coli purine nucleoside phosphorylase (PNP-I, the product of the deoD gene) with its specific inhibitor, viz. formycin A (FA), on fluorescence decays of ligand and enzyme tyrosine residues, in the presence of orthophosphate (P i, a natural co-substrate). The power-like function provides new information about enzyme–ligand complex formation based on the excited state mean lifetime, heterogeneity parameter ( q) and a number ( N) of decay channels obtained from the variance of gamma distribution of fluorescence decay rates. With FA, which exists as a 85:15 mixture of the N(1)–H and N(2)–H tautomeric forms in aqueous solution, fluorescence intensity decay ( λ exc / λ em 270/335 nm) is described by q ∼ 1 and N ∼ 200. Consequently power-like decay function converges to the single-exponential form, and lifetime distribution to the Dirac delta function. In contrast, selective excitation of the N(2)–H tautomer at higher wavelength led to a highly heterogenic fluorescence decay characterized by q > 1 and 10-fold lower number of decay channels. Heterogeneity of fluorescence decays of both PNP-I and FA is enhanced by PNP–FA–P i complex formation, reflecting a shift of the tautomeric equilibrium of FA in favor of the N(2)–H species, and fluorescence resonance energy transfer (FRET) from protein tyrosine residue (Tyr160) to the bound N(2)–H tautomer. Moreover, proposed model is simple, and objectively describes heterogeneous nature of studied systems.

W 3MAMCAT: A world wide web based tool for mammillary and catenary compartmental modeling and expert system distinguishability

W 3MAMCAT is a new web-based and interactive system for building and quantifying the parameters or parameter ranges of n-compartment mammillary and catenary model structures, with input and output in the first compartment, from unstructured multiexponential (sum-of- n-exponentials) models. It handles unidentifiable as well as identifiable models and, as such, provides finite parameter interval solutions for unidentifiable models, whereas direct parameter search programs typically do not. It also tutorially develops the theory of model distinguishability for same order mammillary versus catenary models, as did its desktop application predecessor MAMCAT+. This includes expert system analysis for distinguishing mammillary from catenary structures, given input and output in similarly numbered compartments. W 3MAMCAT provides for universal deployment via the internet and enhanced application error checking. It uses supported Microsoft technologies to form an extensible application framework for maintaining a stable and easily updatable application. Most important, anybody, anywhere, is welcome to access it using Internet Explorer 6.0 over the internet for their teaching or research needs. It is available on the Biocybernetics Laboratory website at UCLA: www.biocyb.cs.ucla.edu.

Formation of positronium: Multi-exponentials versus blob model

Lifetime spectra were obtained for amorphous poly(aryl ether ether ketone) (PEEK), in the temperature range of (−170, +150) °C and were analysed by the standard multi-exponential model, and by the non-exponential blob model. The main results of this analysis are that the electron–ion recombination time in the blob τ b≈20 ps, and that the formation of Positronium is a radiochemical process which mainly depends on the positron–electron reaction constant.

Energy Transfer among Chlorophylls in Trimeric Light-harvesting Complex II of &amp;lt;italic&amp;gt;Bryopsis corticulans&amp;lt;/italic&amp;gt;

A study on energy transfer among chlorophylls (Chls) in the trimeric unit of the major light-harvesting complex II (LHC II) from Bryopsis corriculan, was carried out using time-correlated single photon counting. In the chlorophyll Q region of LHC II, six molecules characterized as Chlb628, Chlb646, Chlb652(654,657), Chla664(666), Chla674(677,680) and Chla682(683) were discriminated according to their absorption spectrum and fluorescence emission spectrum. Then, excited by pulsed light of 628 nm, fluorescence kinetics spectra in the chlorophyll Q region were measured. In accordance with the principles of fluorescence kinetics, these kinetics data were analyzed with a multi-exponential model. Time constants on energy transfer were obtained. An overwhelming percentage of energy transfer among chlorophylls undergoes a process longer than 97 picoseconds (ps), which shows that, before transferring energy to another Chl, the excited Chl might convert energy to vibrations of a lower state with different multiplicity (intersystem crossing). Energy transfer at the level of approximately 10 ps was also obtained, which was interpreted as the excited Chls may go through internal conversion before transferring energy to another Chl. Although with a higher standard deviation, time constants at the femtosecond level can not be entirely excluded, which can be attributed to the ultrafast process of direct energy transfer. Owing to the arrangement and direction of the dipole moment of Chls in LHC II, the probability of these processes is different. The fluorescence lifetimes of Chlb652(654,657), Chla664(666), Chla674(677,680) and Chla682(683) were determined to be 1.44 ns, 1.43 ns, 636 ps and 713 ps, respectively. The percentages of energy dissipation in the pathway of fluorescence emission were no more than 40% in the trimeric unit of LHC II. These results are important for a better understanding of the relationship between the structure and function of LHC II.

Verification of the exponential model of body temperature decrease after death in pigs

The authors have conducted a systematic study in pigs to verify the models of post-mortem body temperature decrease currently employed in forensic medicine. Twenty-four hour automatic temperature recordings were performed in four body sites starting 1.25 h after pig killing in an industrial slaughterhouse under typical environmental conditions (19.5-22.5 degrees C). The animals had been randomly selected under a regular manufacturing process. The temperature decrease time plots drawn starting 75 min after death for the eyeball, the orbit soft tissues, the rectum and muscle tissue were found to fit the single-exponential thermodynamic model originally proposed by H. Rainy in 1868. In view of the actual intersubject variability, the addition of a second exponential term to the model was demonstrated to be statistically insignificant. Therefore, the two-exponential model for death time estimation frequently recommended in the forensic medicine literature, even if theoretically substantiated for individual test cases, provides no advantage as regards the reliability of estimation in an actual case. The improvement of the precision of time of death estimation by the reconstruction of an individual curve on the basis of two dead body temperature measurements taken 1 h apart or taken continuously for a longer time (about 4 h), has also been proved incorrect. It was demonstrated that the reported increase of precision of time of death estimation due to use of a multiexponential model, with individual exponential terms to account for the cooling rate of the specific body sites separately, is artifactual. The results of this study support the use of the eyeball and/or the orbit soft tissues as temperature measuring sites at times shortly after death. A single-exponential model applied to the eyeball cooling has been shown to provide a very precise estimation of the time of death up to approximately 13 h after death. For the period thereafter, a better estimation of the time of death is obtained from temperature data collected from the muscles or the rectum.

Sci-PM Thurs - 06: Diffusion studies of human brain tissue in-vivo by MRI

Diffusion MRI has become one of the most powerful tools for the detection of acute stroke. The signal attenuation caused by the diffusion process is normally assumed to be exponential. The decay constant which is often called the “apparent diffusion coefficient” (ADC) is measured by 2 or 3 points in clinical applications yielding mono-exponential decay curves. The diffusion signal attenuation of water molecules on human brain was measured with a certain pulse sequence. The sequence was modified to work over a range of diffusion times and high gradients. The decay was measured precisely for 96 b-values up to the maximum possible gradient amplitude of 28.8 mT/m. A significant deviation from mono-exponential behavior was observed consistent to the multi-exponential model. The NNLS-diff computational code, using a non-negative least squares (NNLS) algorithm was developed for the data analysis. The diffusion time dependence of human brain tissue was studied for diffusion times between 20 to 53 ms using 16 b-values ranged from b=0 to the maximum possible b-value in each case. At all diffusion times there was a diffusion coefficient at approximately 1×10−3 mm2/s and another at about 7×10−5 mm2/s. For some diffusion times a small contribution at about 1×10−2 mm2/s was also detected. Our results were consistent with work of others. However, we observe a small diffusion time dependence for the smallest diffusion coefficient which has not previously been reported. More work is required to identify the source of the new observation.