Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Reactive halogen compounds in the marine boundary layer: method developments and field measurements

Reactive halogen compounds are known to play an important role in a wide variety of atmospheric processes such as atmospheric oxidation capacity and coastal new particle formation. In this work, novel analytical approaches combining diffusion denuder/impinger sampling techniques with gas chromatographic–mass spectrometric (GC–MS) determination are developed to measure activated chlorine compounds (HOCl and Cl2), activated bromine compounds (HOBr, Br2, BrCl, and BrI), activated iodine compounds (HOI and ICl), and molecular iodine (I2). The denuder/GC–MS methods have been used to field measurements in the marine boundary layer (MBL). High mixing ratios (of the order of 100 ppt) of activated halogen compounds and I2 are observed in the coastal MBL in Ireland, which explains the ozone destruction observed. The emission of I2 is found to correlate inversely with tidal height and correlate positively with the levels of O3 in the surrounding air. In addition the release is found to be dominated by algae species compositions and biomass density, which proves the “hot-spot” hypothesis of atmospheric iodine chemistry. The observations of elevated I2 concentrations substantially support the existence of higher concentrations of littoral iodine oxides and thus the connection to the strong ultra-fine particle formation events in the coastal MBL.

Development and application of an analytical method for the determination of total atmospheric biogenic non-methane organic carbon

Ein wesentlicher Anteil an organischem Kohlenstoff, der in der Atmosphäre vorhanden ist, wird als leichtflüchtige organische Verbindungen gefunden. Diese werden überwiegend durch die Biosphäre freigesetzt. Solche biogenen Emissionen haben einen großen Einfluss auf die chemischen und physikalischen Eigenschaften der Atmosphäre, indem sie zur Bildung von bodennahem Ozon und sekundären organischen Aerosolen beitragen. Um die Bildung von bodennahem Ozon und von sekundären organischen Aerosolen besser zu verstehen, ist die technische Fähigkeit zur genauen Messung der Summe dieser flüchtigen organischen Substanzen notwendig. Häufig verwendete Methoden sind nur auf den Nachweis von spezifischen Nicht-Methan-Kohlenwasserstoffverbindungen fokussiert. Die Summe dieser Einzelverbindungen könnte gegebenenfalls aber nur eine Untergrenze an atmosphärischen organischen Kohlenstoffkonzentrationen darstellen, da die verfügbaren Methoden nicht in der Lage sind, alle organischen Verbindungen in der Atmosphäre zu analysieren. Einige Studien sind bekannt, die sich mit der Gesamtkohlenstoffbestimmung von Nicht-Methan-Kohlenwasserstoffverbindung in Luft beschäftigt haben, aber Messungen des gesamten organischen Nicht-Methan-Verbindungsaustauschs zwischen Vegetation und Atmosphäre fehlen. Daher untersuchten wir die Gesamtkohlenstoffbestimmung organische Nicht-Methan-Verbindungen aus biogenen Quellen. Die Bestimmung des organischen Gesamtkohlenstoffs wurde durch Sammeln und Anreichern dieser Verbindungen auf einem festen Adsorptionsmaterial realisiert. Dieser erste Schritt war notwendig, um die stabilen Gase CO, CO2 und CH4 von der organischen Kohlenstofffraktion zu trennen. Die organischen Verbindungen wurden thermisch desorbiert und zu CO2 oxidiert. Das aus der Oxidation entstandene CO2 wurde auf einer weiteren Anreicherungseinheit gesammelt und durch thermische Desorption und anschließende Detektion mit einem Infrarot-Gasanalysator analysiert. Als große Schwierigkeiten identifizierten wir (i) die Abtrennung von CO2 aus der Umgebungsluft von der organischen Kohlenstoffverbindungsfaktion während der Anreicherung sowie (ii) die Widerfindungsraten der verschiedenen Nicht-Methan-Kohlenwasserstoff-verbindungen vom Adsorptionsmaterial, (iii) die Wahl des Katalysators sowie (iiii) auftretende Interferenzen am Detektor des Gesamtkohlenstoffanalysators. Die Wahl eines Pt-Rd Drahts als Katalysator führte zu einem bedeutenden Fortschritt in Bezug auf die korrekte Ermittlung des CO2-Hintergrund-Signals. Dies war notwendig, da CO2 auch in geringen Mengen auf der Adsorptionseinheit während der Anreicherung der leichtflüchtigen organischen Substanzen gesammelt wurde. Katalytische Materialien mit hohen Oberflächen stellten sich als unbrauchbar für diese Anwendung heraus, weil trotz hoher Temperaturen eine CO2-Aufnahme und eine spätere Abgabe durch das Katalysatormaterial beobachtet werden konnte. Die Methode wurde mit verschiedenen leichtflüchtigen organischen Einzelsubstanzen sowie in zwei Pflanzenkammer-Experimenten mit einer Auswahl an VOC-Spezies getestet, die von unterschiedlichen Pflanzen emittiert wurden. Die Pflanzenkammer-messungen wurden durch GC-MS und PTR-MS Messungen begleitet. Außerdem wurden Kalibrationstests mit verschiedenen Einzelsubstanzen aus Permeations-/Diffusionsquellen durchgeführt. Der Gesamtkohlenstoffanalysator konnte den tageszeitlichen Verlauf der Pflanzenemissionen bestätigen. Allerdings konnten Abweichungen für die Mischungsverhältnisse des organischen Gesamtkohlenstoffs von bis zu 50% im Vergleich zu den begleitenden Standardmethoden beobachtet werden.

Plasmonic nanoparticles as sensors : a novel approach to quantify adsorption and diffusion kinetics

Biosensors find wide application in clinical diagnostics, bioprocess control and environmental monitoring. They should not only show high specificity and reproducibility but also a high sensitivity and stability of the signal. Therefore, I introduce a novel sensor technology based on plasmonic nanoparticles which overcomes both of these limitations. Plasmonic nanoparticles exhibit strong absorption and scattering in the visible and near-infrared spectral range. The plasmon resonance, the collective coherent oscillation mode of the conduction band electrons against the positively charged ionic lattice, is sensitive to the local environment of the particle. I monitor these changes in the resonance wavelength by a new dark-field spectroscopy technique. Due to a strong light source and a highly sensitive detector a temporal resolution in the microsecond regime is possible in combination with a high spectral stability. This opens a window to investigate dynamics on the molecular level and to gain knowledge about fundamental biological processes.rnFirst, I investigate adsorption at the non-equilibrium as well as at the equilibrium state. I show the temporal evolution of single adsorption events of fibrinogen on the surface of the sensor on a millisecond timescale. Fibrinogen is a blood plasma protein with a unique shape that plays a central role in blood coagulation and is always involved in cell-biomaterial interactions. Further, I monitor equilibrium coverage fluctuations of sodium dodecyl sulfate and demonstrate a new approach to quantify the characteristic rate constants which is independent of mass transfer interference and long term drifts of the measured signal. This method has been investigated theoretically by Monte-Carlo simulations but so far there has been no sensor technology with a sufficient signal-to-noise ratio.rnSecond, I apply plasmonic nanoparticles as sensors for the determination of diffusion coefficients. Thereby, the sensing volume of a single, immobilized nanorod is used as detection volume. When a diffusing particle enters the detection volume a shift in the resonance wavelength is introduced. As no labeling of the analyte is necessary the hydrodynamic radius and thus the diffusion properties are not altered and can be studied in their natural form. In comparison to the conventional Fluorescence Correlation Spectroscopy technique a volume reduction by a factor of 5000-10000 is reached.

Molecular dynamics simulations of silicate and borate glasses and melts : structure, diffusion dynamics and vibrational properties

Molecular dynamics simulations of silicate and borate glasses and melts: Structure, diffusion dynamics and vibrational properties. In this work computer simulations of the model glass formers SiO2 and B2O3 are presented, using the techniques of classical molecular dynamics (MD) simulations and quantum mechanical calculations, based on density functional theory (DFT). The latter limits the system size to about 100−200 atoms. SiO2 and B2O3 are the two most important network formers for industrial applications of oxide glasses. Glass samples are generated by means of a quench from the melt with classical MD simulations and a subsequent structural relaxation with DFT forces. In addition, full ab initio quenches are carried out with a significantly faster cooling rate. In principle, the structural properties are in good agreement with experimental results from neutron and X-ray scattering, in all cases. A special focus is on the study of vibrational properties, as they give access to low-temperature thermodynamic properties. The vibrational spectra are calculated by the so-called ”frozen phonon” method. In all cases, the DFT curves show an acceptable agreement with experimental results of inelastic neutron scattering. In case of the model glass former B2O3, a new classical interaction potential is parametrized, based on the liquid trajectory of an ab initio MD simulation at 2300 K. In this course, a structural fitting routine is used. The inclusion of 3-body angular interactions leads to a significantly improved agreement of the liquid properties of the classical MD and ab initio MD simulations. However, the generated glass structures, in all cases, show a significantly lower fraction of 3-membered planar boroxol rings as predicted by experimental results (f=60%-80%). The largest boroxol ring fraction of f=15±5% is observed in the full ab initio quenches from 2300 K. In case of SiO2, the glass structures after the quantum mechanical relaxation are the basis for calculations of the linear thermal expansion coefficient αL(T), employing the quasi-harmonic approximation. The striking observation is a change change of sign of αL(T) going along with a temperature range of negative αL(T) at low temperatures, which is in good agreement with experimental results.

Eye movement and diffusion tensor imaging analysis of treatment effects in a Niemann-Pick Type C patient

New treatment options for Niemann-Pick Type C (NPC) have recently become available. To assess the efficiency and efficacy of these new treatment markers for disease status and progression are needed. Both the diagnosis and the monitoring of disease progression are challenging and mostly rely on clinical impression and functional testing of horizontal eye movements. Diffusion tensor imaging (DTI) provides information about the microintegrity especially of white matter. We show here in a case report how DTI and measures derived from this imaging method can serve as adjunct quantitative markers for disease management in Niemann-Pick Type C. Two approaches are taken--first, we compare the fractional anisotropy (FA) in the white matter globally between a 29-year-old NPC patient and 18 healthy age-matched controls and show the remarkable difference in FA relatively early in the course of the disease. Second, a voxelwise comparison of FA values reveals where white matter integrity is compromised locally and demonstrate an individualized analysis of FA changes before and after 1year of treatment with Miglustat. This method might be useful in future treatment trials for NPC to assess treatment effects.

Au@Hg nanoalloy formation through direct amalgamation: Structural, spectroscopic, and computational evidence for slow nanoscale diffusion

Dynamic core-shell nanoparticles have received increasing attention in recent years. This paper presents a detailed study of Au-Hg nanoalloys, whose composing elements show a large difference in cohesive energy. A simple method to prepare Au@Hg particles with precise control over the composition up to 15 atom% mercury is introduced, based on reacting a citrate stabilized gold sol with elemental mercury. Transmission electron microscopy shows an increase of particle size with increasing mercury content and, together with X-ray powder diffraction, points towards the presence of a core-shell structure with a gold core surrounded by an Au-Hg solid solution layer. The amalgamation process is described by pseudo-zero-order reaction kinetics, which indicates slow dissolution of mercury in water as the rate determining step, followed by fast scavenging by nanoparticles in solution. Once adsorbed at the surface, slow diffusion of Hg into the particle lattice occurs, to a depth of ca. 3 nm, independent of Hg concentration. Discrete dipole approximation calculations relate the UV-vis spectra to the microscopic details of the nanoalloy structure. Segregation energies and metal distribution in the nanoalloys were modeled by density functional theory calculations. The results indicate slow metal interdiffusion at the nanoscale, which has important implications for synthetic methods aimed at core-shell particles.

A novel isolation method of Brucella species and molecular tracking of Brucella suis biovar 2 in domestic and wild animals

Brucella suis biovar 2 is the most common aetiological agent of porcine brucellosis in Europe. B. suis biovar 2 is considered to have low zoonotic potential, but is a causative agent of reproductive losses in pigs, and it is thus economically important. The multilocus variable-number of tandem repeats genotyping analysis of 16 loci (MLVA-16) has proven to be highly discriminatory and is the most suitable assay for simultaneously identifying B. suis and tracking infections. The aim of this study was to investigate the relatedness between isolates of B. suis biovar 2 obtained during a brucellosis outbreak in domestic pigs and isolates from wild boars and hares collected from proximal or remote geographical areas by MLVA-16. A cluster analysis of the MLVA-16 data revealed that most of the isolates obtained from Switzerland clustered together, with the exception of one isolate. The outbreak isolates constituted a unique subcluster (with a genetic similarity >93.8%) distinct from that of the isolates obtained from wild animals, suggesting that direct transmission of the bacterium from wild boars to domestic pigs did not occur in this outbreak. To obtain a representative number of isolates for MLVA-16, alternative methods of Brucella spp. isolation from tissue samples were compared with conventional direct cultivation on a Brucella-selective agar. We observed an enhanced sensitivity when mechanical homogenisation was followed by host cell lysis prior to cultivation on the Brucella-selective agar. This work demonstrates that MLVA-16 is an excellent tool for both monitoring brucellosis and investigating outbreaks. Additionally, we present efficient alternatives for the isolation of Brucella spp.

Quantifying The Diffusion And Erosion Of Degradable Hydrogels Using A Microfluidic Technique

Hydrogels are composed of cross-linked networks of hydrophilic polymers that are biocompatible due to their high water content. Mass transfer through hydrogels has been suggested as an effective method of drug delivery, specifically in degradable polymers to minimize lasting effects within the body. Diffusion of small molecules in poly (ethylene glycol) diacrylate (PEG-DA) and dextran methacrylate (dex-MA) hydrogels was characterized in a microfluidic device and by complementary techniques. Microfluidic devices were prepared by crosslinking a formulation of hydrogel and photo-initiator, with and without visible dye, using photolithography to define a central microchannel. Channel sizes within the devices were approximately 600 ¿m to simulate vessels within the body. The microfluidic technique allows for both image and effluent analyses. To visualize the diffusive behavior within the dextran hydrogel, methylene blue and sulforhodamine 101 dyes were used in both elution and uptake experiments. Three analysis techniques for measuring diffusion coefficients were used to quantify the diffusion of solute in the hydrogel, including optical microscopy, characterization of device effluent, and NMR analyses. The optical microscopy technique analyzes images of the dye diffusion captured by a stereomicroscope to generate dye concentration v. position profiles. The data was fit to a diffusion model to determine diffusion coefficients and the dye release profile. In a typical elution experiment, aqueous solution is pumped through the microchannel and dye diffuses out of the hydrogel and into the aqueous phase. During elution, images are taken at regular time intervals and the effluent was collected. Analysis of the device effluent was performed using ultraviolet-visible (UV/Vis) spectroscopy to determine the effluent dye concentration and thus a short-time diffusion coefficient. Nuclear magnetic resonance (NMR) was used to determine a free diffusion coefficient of molecules in hydrogel without the effect of a concentration gradient. Diffusion coefficients for methylene blue and sulforhodamine 101 dyes in dex-MA hydrogel calculated using the three analysis methods all agree well. It was determined that utilizing a combination of the three techniques offers greater insight into molecular diffusion in hydrogels than employing each technique individually. The use of the same microfluidic devices used to measure diffusion is explored in the use of studying the degradation of dex-MA hydrogels. By combining what is known about the degradation rate in regards to the effect of pH and crosslinking and the ability to use a dye solution in contrast to establish the hydrogel boundaries could be a novel approach to studying hydrogel degradation.

Non-invasive method to predict viscosity and size using total internal reflection fluorescence microscopy (TIRFM) system

This study develops an automated analysis tool by combining total internal reflection fluorescence microscopy (TIRFM), an evanescent wave microscopic imaging technique to capture time-sequential images and the corresponding image processing Matlab code to identify movements of single individual particles. The developed code will enable us to examine two dimensional hindered tangential Brownian motion of nanoparticles with a sub-pixel resolution (nanoscale). The measured mean square displacements of nanoparticles are compared with theoretical predictions to estimate particle diameters and fluid viscosity using a nonlinear regression technique. These estimated values will be confirmed by the diameters and viscosities given by manufacturers to validate this analysis tool. Nano-particles used in these experiments are yellow-green polystyrene fluorescent nanospheres (200 nm, 500 nm and 1000 nm in diameter (nominal); 505 nm excitation and 515 nm emission wavelengths). Solutions used in this experiment are de-ionized (DI) water, 10% d-glucose and 10% glycerol. Mean square displacements obtained near the surface shows significant deviation from theoretical predictions which are attributed to DLVO forces in the region but it conforms to theoretical predictions after ~125 nm onwards. The proposed automation analysis tool will be powerfully employed in the bio-application fields needed for examination of single protein (DNA and/or vesicle) tracking, drug delivery, and cyto-toxicity unlike the traditional measurement techniques that require fixing the cells. Furthermore, this tool can be also usefully applied for the microfluidic areas of non-invasive thermometry, particle tracking velocimetry (PTV), and non-invasive viscometry.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Combined ultrasmall superparamagnetic particles of iron oxide-enhanced and diffusion-weighted magnetic resonance imaging reliably detect pelvic lymph node metastases in normal-sized nodes of bladder and prostate cancer patients

BACKGROUND: Lymph node staging of bladder or prostate cancer using conventional imaging is limited. Newer approaches such as ultrasmall superparamagnetic particles of iron oxide (USPIO) and diffusion-weighted magnetic resonance imaging (DW-MRI) have inconsistent diagnostic accuracy and are difficult to interpret. OBJECTIVE: To assess whether combined USPIO and DW-MRI (USPIO-DW-MRI) improves staging of normal-sized lymph nodes in bladder and/or prostate cancer patients. DESIGN, SETTING, AND PARTICIPANTS: Twenty-one consecutive patients with bladder and/or prostate cancer were enrolled between May and October 2008. One patient was excluded secondary to bone metastases detected on DW-MRI with subsequent abstention from surgery. INTERVENTION: Patients preoperatively underwent 3-T MRI before and after administration of lymphotropic USPIO using conventional MRI sequences combined with DW-MRI. Surgery consisted of extended pelvic lymphadenectomy and resection of primary tumors. MEASUREMENTS: Diagnostic accuracies of the new combined USPIO-DW-MRI approach compared with the "classic" reading method evaluating USPIO images without and with DW-MRI versus histopathology were evaluated. Duration of the two reading methods was noted for each patient. RESULTS AND LIMITATIONS: Diagnostic accuracy (90% per patient or per pelvic side) was comparable for the classic and the USPIO-DW-MRI reading method, while time of analysis with 80 min (range 45-180 min) for the classic and 13 min (range 5-90 min) for the USPIO-DW-MRI method was significantly shorter (p<0.0001). Interobserver agreement (three blinded readers) was high with a kappa value of 0.75 and 0.84, respectively. Histopathological analysis showed metastases in 26 of 802 analyzed lymph nodes (3.2%). Of these, 24 nodes (92%) were correctly diagnosed as positive on USPIO-DW-MRI. In two patients, one micrometastasis each (1.0x0.2 mm; 0.7x0.4 mm) was missed in all imaging studies. CONCLUSIONS: USPIO-DW-MRI is a fast and accurate method for detecting pelvic lymph node metastases, even in normal-sized nodes of bladder or prostate cancer patients.

Multimodal approach in the use of clinical scoring, morphological MRI and biochemical T2-mapping and diffusion-weighted imaging in their ability to assess differences between cartilage repair tissue after microfracture therapy and matrix-associated autologous chondrocyte transplantation: a pilot study

OBJECTIVE: The aim of the present pilot study is to show initial results of a multimodal approach using clinical scoring, morphological magnetic resonance imaging (MRI) and biochemical T2-relaxation and diffusion-weighted imaging (DWI) in their ability to assess differences between cartilage repair tissue after microfracture therapy (MFX) and matrix-associated autologous chondrocyte transplantation (MACT). METHOD: Twenty patients were cross-sectionally evaluated at different post-operative intervals from 12 to 63 months after MFX and 12-59 months after MACT. The two groups were matched by age (MFX: 36.0+/-10.4 years; MACT: 35.1+/-7.7 years) and post-operative interval (MFX: 32.6+/-16.7 months; MACT: 31.7+/-18.3 months). After clinical evaluation using the Lysholm score, 3T-MRI was performed obtaining the MR observation of cartilage repair tissue (MOCART) score as well as T2-mapping and DWI for multi-parametric MRI. Quantitative T2-relaxation was achieved using a multi-echo spin-echo sequence; semi-quantitative diffusion-quotient (signal intensity without diffusion-weighting divided by signal intensity with diffusion weighting) was prepared by a partially balanced, steady-state gradient-echo pulse sequence. RESULTS: No differences in Lysholm (P=0.420) or MOCART (P=0.209) score were observed between MFX and MACT. T2-mapping showed lower T2 values after MFX compared to MACT (P=0.039). DWI distinguished between healthy cartilage and cartilage repair tissue in both procedures (MFX: P=0.001; MACT: P=0.007). Correlations were found between the Lysholm and the MOCART score (Pearson: 0.484; P=0.031), between the Lysholm score and DWI (Pearson:-0.557; P=0.011) and a trend between the Lysholm score and T2 (Person: 0.304; P=0.193). CONCLUSION: Using T2-mapping and DWI, additional information could be gained compared to clinical scoring or morphological MRI. In combination clinical, MR-morphological and MR-biochemical parameters can be seen as a promising multimodal tool in the follow-up of cartilage repair.

Living Renal Allograft Transplantation: Diffusion-weighted MR Imaging in Longitudinal Follow-up of the Donated and the Remaining Kidney.

Purpose To determine whether diffusion-weighted (DW) magnetic resonance (MR) imaging in living renal allograft donation allows monitoring of potential changes in the nontransplanted remaining kidney of the donor because of unilateral nephrectomy and changes in the transplanted kidney before and after transplantation in donor and recipient, respectively, and whether DW MR parameters are correlated in the same kidney before and after transplantation. Materials and Methods The study protocol was approved by the local ethics committee; written informed consent was obtained. Thirteen healthy kidney donors and their corresponding recipients prospectively underwent DW MR imaging (multiple b values) in donors before donation and in donors and recipients at day 8 and months 3 and 12 after donation. Total apparent diffusion coefficient (ADCT) values were determined; contribution of microcirculation was quantified in perfusion fraction (FP). Longitudinal changes of diffusion parameters were compared (repeated-measures one-way analysis of variance with post hoc pairwise comparisons). Correlations were tested (linear regression). Results ADCT values in nontransplanted kidney of donors increased from a preexplantation value of (188 ± 9 [standard deviation]) to (202 ± 11) × 10(-5) mm(2)/sec in medulla and from (199 ± 11) to (210 ± 13) × 10(-5) mm(2)/sec in cortex 1 week after donation (P < .004). Medullary, but not cortical, ADCT values stayed increased up to 1 year. ADCT values in allografts in recipients were stable. Compared with values obtained before transplantation in donors, the corticomedullary difference was reduced in allografts (P < .03). Cortical ADCT values correlated with estimated glomerular filtration rate in recipients (R = 0.56, P < .001) but not donors. Cortical ADCT values in the same kidney before transplantation in donors correlated with those in recipients on day 8 after transplantation (R = 0.77, P = .006). FP did not show significant changes. Conclusion DW MR imaging depicts early adaptations in the remaining nontransplanted kidney of donors after nephrectomy. All diffusion parameters remained constant in allograft recipients after transplantation. This method has potential monitoring utility, although assessment of clinical relevance is needed. © RSNA, 2013 Online supplemental material is available for this article.