Magnetic resonance imaging measurements of vascular permeability and extracellular volume fraction of breast tumors by dynamic Gd-DTPA-enhanced relaxometry

Vascular permeability (k(ep), min(-1)) and extracellular volume fraction (v(e)) are tissue parameters of great interest to characterize malignant tumor lesions. Indeed, it is well known that tumors with high blood supply better respond to therapy than poorly vascularized tumors, and tumors with large extracellular volume tend to be more malignant than tumors showing lower extracellular volume. Furthermore, the transport of therapeutic agents depends on both extracellular volume fraction and vessel permeability. Thus, before treatment, these tissue parameters may prove useful to evaluate tumor aggressiveness and to predict responsiveness to therapy and variations during cytotoxic therapies could allow to assess treatment efficacy and early modified therapy schedules in case of poor responsiveness. As a consequence, there is a need to develop methods that could be routinely used to determine these tissue parameters. In this work, blood-tissue permeability and extracellular volume fraction information were derived from magnetic resonance imaging dynamic longitudinal relaxation rate (R(1)) mapping obtained after an intravenous bolus injection of Gd-DTPA in a group of 92 female patients with breast lesions, 68 of these being histologically proven to be with carcinoma. For the sake of comparison, 24 benign lesions were studied. The measurement protocol based on two-dimensional gradient echo sequences and a monoexponential plasma kinetic model was that validated in the occasion of previous animal experiments. As a consequence of neoangiogenesis, results showed a higher permeability in malignant than in benign lesions, whereas the extracellular volume fraction value did not allow any discrimination between benign and malignant lesions. The method, which can be easily implemented whatever the imaging system used, could advantageously be used to quantify lesion parameters (k(ep) and v(e)) in routine clinical imaging. Because of its large reproducibility, the method could be useful for intersite comparisons and follow-up studies.     

An analysis of the pharmacokinetic parameter ratios in DCE-MRI using the reference region model

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is performed by obtaining sequential MRI images, before, during and after the injection of a contrast agent. It is usually used to observe the exchange of contrast agent between the vascular space and extravascular extracellular space (EES), and provide information about blood volume and microvascular permeability. To estimate the kinetic parameters derived from the pharmacokinetic model, accurate knowledge of the arterial input function (AIF) is very important. However, the AIF is usually unknown, and it remains very difficult to obtain such information noninvasively. In this article, without knowledge of the AIF, we applied a reference region (RR) model to analyze the kinetic parameters. The RR model usually depends on kinetic parameters found in previous studies of a reference region. However, both the assignment of reference region parameters (intersubject variation) and the selection of the reference region itself (intrasubject variation) may confound the results obtained by RR methods. Instead of using literature values for those pharmacokinetic parameters of the reference region, we proposed to use two pharmacokinetic parameter ratios between the tissue of interest (TOI) and the reference region. Specifically, one parameter K_R is calculated as the ratio between the volume transfer constant K^trans of the TOI and RR. Similarly, another parameter V_R is calculated as the ratio between the extravascular extracellular volume fraction v_e of the TOI and RR. To investigate the consistency of the two ratios, the K^trans of the RR was varied ranging from 0.1 to 1.0 min⁻¹, covering the cited literature values. A simulated dataset with different levels of Gaussian noises and an in vivo dataset acquired from five canine brains with spontaneous occurring brain tumors were used to study the proposed ratios. It is shown from both datasets that these ratios are independent of K^trans of the RR, implying that there is potentially no need to obtain information about literature values from the reference region for future pharmacokinetic modeling and analysis.     

Assessment of extravascular extracellular space fraction in human melanoma xenografts by DCE-MRI and kinetic modeling

Tumor aggressiveness and response to therapy are influenced by the extravascular extracellular space fraction (EESF) of the malignant tissue. The EESF may, therefore, be an important prognostic parameter for cancer patients. The aim of this study was to investigate whether gadopentetate dimeglumine (Gd-DTPA)-based dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can be used to assess the EESF of tumors. Amelanotic human melanoma xenografts (A-07, R-18) were used as preclinical models of human cancer. Images of E.F (E is the initial extraction fraction of Gd-DTPA and F is perfusion) and lambda (the partition coefficient of Gd-DTPA) were obtained by Kety analysis of DCE-MRI data. Our study was based on the hypothesis that lambda is governed by the EESF and is not influenced significantly by microvascular density (MVD) or blood perfusion. To test this hypothesis, we searched for correlations between lambda and E.F, MVD or EESF by comparing lambda images with E.F images, histological preparations from the imaged tissue and the radial heterogeneity in EESF obtained by invasive imaging. Positive correlations were found between lambda and EESF. Thus, median lambda was larger in A-07 tumors than in R-18 tumors by a factor of 4.2 (P<.00001), consistent with the histological observation that EESF is approximately fourfold larger in A-07 tumors than in R-18 tumors. The radial heterogeneity in lambda in A-07 and R-18 tumors was almost identical to the radial heterogeneity in EESF. Moreover, lambda was larger in tissue regions with high EESF than in tissue regions with low EESF in A-07 tumors (P=.048). On the other hand, significant correlations between lambda and MVD or E.F could not be detected. Consequently, Kety analysis of Gd-DTPA-based DCE-MRI series of xenografted tumors provides lambda images that primarily reflect the EESF of the tissue.     

Comparison of analytical and numerical analysis of the reference region model for DCE-MRI

This study compared three methods for analyzing DCE-MRI data with a reference region (RR) model: a linear least-square fitting with numerical analysis (LLSQ-N), a nonlinear least-square fitting with numerical analysis (NLSQ-N), and an analytical analysis (NLSQ-A). The accuracy and precision of estimating the pharmacokinetic parameter ratios K_R and V_R, where K_R is defined as a ratio between the two volume transfer constants, K^trans,TOI and K^trans,RR, and V_R is the ratio between the two extracellular extravascular volumes, v_e,TOI and v_e,RR, were assessed using simulations under various signal-to-noise ratios (SNRs) and temporal resolutions (4, 6, 30, and 60 s). When no noise was added, the simulations showed that the mean percent error (MPE) for the estimated K_R and V_R using the LLSQ-N and NLSQ-N methods ranged from 1.2% to 31.6% with various temporal resolutions while the NLSQ-A method maintained a very high accuracy (< 1.0×10^− 4 %) regardless of the temporal resolution. The simulation also indicated that the LLSQ-N and NLSQ-N methods appear to underestimate the parameter ratios more than the NLSQ-A method. In addition, seven in vivo DCE-MRI datasets from spontaneously occurring canine brain tumors were analyzed with each method. Results for the in vivo study showed that K_R (ranging from 0.63 to 3.11) and V_R (ranging from 2.82 to 19.16) for the NLSQ-A method were both higher than results for the other two methods (K_R ranging from 0.01 to 1.29 and V_R ranging from 1.48 to 19.59). A temporal downsampling experiment showed that the averaged percent error for the NLSQ-A method (8.45%) was lower than the other two methods (22.97% for LLSQ-N and 65.02% for NLSQ-N) for K_R, and the averaged percent error for the NLSQ-A method (6.33%) was lower than the other two methods (6.57% for LLSQ-N and 13.66% for NLSQ-N) for V_R. Using simulations, we showed that the NLSQ-A method can estimate the ratios of pharmacokinetic parameters more accurately and precisely than the NLSQ-N and LLSQ-N methods over various SNRs and temporal resolutions. All simulations were validated with in vivo DCE MRI data.     

A comparison of two methods for estimating DCE-MRI parameters via individual and cohort based AIFs in prostate cancer: A step towards practical implementation

Multi-parametric Magnetic Resonance Imaging, and specifically Dynamic Contrast Enhanced (DCE) MRI, play increasingly important roles in detection and staging of prostate cancer (PCa). One of the actively investigated approaches to DCE MRI analysis involves pharmacokinetic (PK) modeling to extract quantitative parameters that may be related to microvascular properties of the tissue. It is well-known that the prescribed arterial blood plasma concentration (or Arterial Input Function, AIF) input can have significant effects on the parameters estimated by PK modeling. The purpose of our study was to investigate such effects in DCE MRI data acquired in a typical clinical PCa setting. First, we investigated how the choice of a semi-automated or fully automated image-based individualized AIF (iAIF) estimation method affects the PK parameter values; and second, we examined the use of method-specific averaged AIF (cohort-based, or cAIF) as a means to attenuate the differences between the two AIF estimation methods.     

Nonuniversality and continuity of the critical covered volume fraction in continuum percolation

We establish, using mathematically rigorous methods, that the critical covered volume fraction (CVF) for a continuum percolation model with overlapping balls of random sizes is not a universal constant independent of the distribution of the size of the balls. In addition, we show that the critical CVF is a continuous function of the distribution of the radius random variable, in the sense that if a sequence of random variables converges weakly to some random variable, then the critical CVF based on these random variables converges to the critical CVF of the limiting random variable.     

Finite volume effects on the QCD chiral phase transition in the finite size de-pendent Nambu-Jona-Lasinio model

The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.     

On the relationship between the apparent diffusion coefficient and extravascular extracellular volume fraction in human breast cancer

MRI techniques have been developed that can noninvasively probe the apparent diffusion coefficient (ADC) of water via diffusion-weighted MRI (DW-MRI). These methods have found much application in cancer where it is often found that the ADC within tumors is inversely correlated with tumor cell density, so that an increase in ADC in response to therapy can be interpreted as an imaging biomarker of positive treatment response. Dynamic contrast enhanced MRI (DCE-MRI) methods have also been developed and can noninvasively report on the extravascular extracellular volume fraction of tissues (denoted by v_e). By conventional reasoning, the ADC should therefore also be directly proportional to v_e. Here we report measurements of both ADC and v_e obtained from breast cancer patients at both 1.5 and 3.0 T. The 1.5-T data were acquired as part of normal standard of care, while the 3.0-T data were obtained from a dedicated research protocol. We found no statistically significant correlation between ADC and v_e for the 1.5- or 3.0-T patient sets on either a voxel-by-voxel or a region-of-interest (ROI) basis. These data, combined with similar results from other disease sites in the literature, may indicate that the conventional interpretation of either ADC, v_e or their relationship is not sufficient to explain experimental findings.     

Simulation on simultaneous estimation of non-uniform temperature and soot volume fraction distributions in axisymmetric sooting flames

For visualizing non-uniform absorbing, emitting, non-scattering, axisymmetric sooting flames, because conventional two-color emission methods are no longer suitable, a three-color emission method for the simultaneous estimation of temperature and soot volume fraction distributions in these flames is studied in this paper. The spectral radiation intensities at wavelengths of red, green, and blue, which may be derived from color flame images, are simulated for the inverse analysis. Then the simultaneous estimation is carried out from the spectral radiation intensities by using a Newton-type iteration algorithm and the least-squares method. In this method, a factor is used to balance the wide variation of spectral radiation intensities due to both the wide ranges of temperature and wavelength of the flame radiation. The results indicate that the three-color method is suited for the reconstruction of flame structures with single or double peaks with small difference between the peak and valley. For a double-peaked flame structure with larger peak and valley difference, reasonable result can be obtained just when the mean square deviations of measurement data are small, for example, not more than 0.01.     

The numerical prediction of planar viscoelastic contraction flows using the pom–pom model and higher-order finite volume schemes

This study investigates the numerical solution of viscoelastic flows using two contrasting high-order finite volume schemes. We extend our earlier work for Poiseuille flow in a planar channel and the single equation form of the extended pom–pom (SXPP) model [M. Aboubacar, J.P. Aguayo, P.M. Phillips, T.N. Phillips, H.R. Tamaddon-Jahromi, B.A. Snigerev, M.F. Webster, Modelling pom–pom type models with high-order finite volume schemes, J. Non-Newtonian Fluid Mech. 126 (2005) 207–220], to determine steady-state solutions for planar 4:1 sharp contraction flows. The numerical techniques employed are time-stepping algorithms: one of hybrid finite element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggered-grid cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be implemented on structured or unstructured rectangular grids, utilising backtracking along the solution characteristics in time. For the hybrid scheme, we solve the momentum-continuity equations by a fractional-staged Taylor–Galerkin pressure-correction procedure and invoke a cell-vertex finite volume scheme for the constitutive law. A comparison of the two finite volume approaches is presented, concentrating upon the new features posed by the pom–pom class of models in this context of non-smooth flows. Here, the dominant feature of larger shear and extension in the entry zone influences both stress and stretch, so that larger stretch develops around the re-entrant corner zone as Weissenberg number increases, whilst correspondingly stress levels decline.     

Simulation study of a magnetocardiogram based on a virtual heart model: effect of a cardiac equivalent source and a volume conductor

In this paper,we present a magnetocardiogram(MCG) simulation study using the boundary element method(BEM) and based on the virtual heart model and the realistic human volume conductor model.The different contributions of cardiac equivalent source models and volume conductor models to the MCG are deeply and comprehensively investigated.The single dipole source model,the multiple dipoles source model and the equivalent double layer(EDL) source model are analysed and compared with the cardiac equivalent source models.Meanwhile,the effect of the volume conductor model on the MCG combined with these cardiac equivalent sources is investigated.The simulation results demonstrate that the cardiac electrophysiological information will be partly missed when only the single dipole source is taken,while the EDL source is a good option for MCG simulation and the effect of the volume conductor is smallest for the EDL source.Therefore,the EDL source is suitable for the study of MCG forward and inverse problems,and more attention should be paid to it in future MCG studies.     

A linear algorithm of the reference region model for DCE-MRI is robust and relaxes requirements for temporal resolution

Dynamic contrast enhanced MRI (DCE-MRI) has utility for improving clinical diagnoses of solid tumors, and for evaluating the early responses of anti-angiogenic chemotherapies. The Reference Region Model (RRM) can improve the clinical implementation of DCE-MRI by substituting the contrast enhancement of muscle for the Arterial Input Function that is used in traditional DCE-MRI methodologies. The RRM is typically fitted to experimental results with a non-linear least squares algorithm. This report demonstrates that this algorithm produces inaccurate and imprecise results when DCE-MRI results have low SNR or slow temporal resolution. To overcome this limitation, a linear least-squares algorithm has been derived for the Reference Region Model. This new algorithm improves accuracy and precision of fitting the Reference Region Model to DCE-MRI results, especially for voxel-wise analyses. This linear algorithm is insensitive to injection speeds, and has 300- to 8000-fold faster calculation speed relative to the non-linear algorithm. The linear algorithm produces more accurate results for over a wider range of permeabilities and blood volumes of tumor vasculature. This new algorithm, termed the Linear Reference Region Model, has strong potential to improve clinical DCE-MRI evaluations.     

Evaluation of numerical scattering in finite volume method for solving radiative transfer equation by a central laser incidence model

The numerical scattering caused by spatial discretization in finite volume method is discussed. Based on an analysis of the generation process of numerical scattering, a physical model of central laser incidence to a two-dimensional rectangle containing semitransparent medium is established to validate the numerical scattering, with Monte Carlo method as benchmark, in which numerical scattering does not exist. Numerical scattering will be affected by spatial grid number, spatial differential schemes and spectral absorption coefficient. With the spatial grid number increasing, numerical scattering will be decreased. The accuracy of the diamond scheme is the highest, and the exponential scheme is a bit lower, the lowest accuracy of the three schemes is the step scheme. The tendency of numerical scattering is reverse, i.e., the step scheme produces minimum numerical scattering, and exponential scheme produces more, while the diamond scheme produces maximum among three methods. When the bias of absorption efficient is high, the numerical scattering cannot be eliminated only by increasing the grid number. If we set the direction of laser incidence as central axis, it can be seen that numerical scattering distributed symmetry along the axis, which can be called as symmetrical cross-scattering. All of the three schemes show symmetrical cross-scattering.     

自旋结网圈表象中体积与面积本征值

利用抓算符作用的反称化和双元恒等式，通过计算，证明了3价和任意价自旋结网圈分别为体积和面积算符的本征态，并得到了体积本征值为2^-32l³₀∑ip_σp_τp_ρ和面积本征值为2^-1l²₀∑jp_l(j)的结果. 关键词： 体积算符 面积算符 本征值 自旋结网圈     

A reference agent model for DCE MRI can be used to quantify the relative vascular permeability of two MRI contrast agents

Dynamic Contrast Enhancement (DCE) MRI has been used to measure the kinetic transport constant, K^trans, which is used to assess tumor angiogenesis and the effects of anti-angiogenic therapies. Standard DCE MRI methods must measure the pharmacokinetics of a contrast agent in the blood stream, known as the Arterial Input Function (AIF), which is then used as a reference for the pharmacokinetics of the agent in tumor tissue. However, the AIF is difficult to measure in pre-clinical tumor models and in patients. Moreover the AIF is dependent on the Fahraeus effect that causes a highly variable hematocrit (Hct) in tumor microvasculature, leading to erroneous estimates of K^trans. To overcome these problems, we have developed the Reference Agent Model (RAM) for DCE MRI analyses, which determines the relative K^trans of two contrast agents that are simultaneously co-injected and detected in the same tissue during a single DCE-MRI session. The RAM obviates the need to monitor the AIF because one contrast agent effectively serves as an internal reference in the tumor tissue for the other agent, and it also eliminates the systematic errors in the estimated K^trans caused by assuming an erroneous Hct. Simulations demonstrated that the RAM can accurately and precisely estimate the relative K^trans (R^Ktrans) of two agents. To experimentally evaluate the utility of RAM for analyzing DCE MRI results, we optimized a previously reported multiecho ¹⁹F MRI method to detect two perfluorinated contrast agents that were co-injected during a single in vivo study and selectively detected in the same tumor location. The results demonstrated that RAM determined R^Ktrans with excellent accuracy and precision.     

The role of excluded volume and electrostatics from coarse-grain modeling of the interaction of gemini surfactants with like-charged membranes

Cationic systems composed of lipids and/or surfactants are of paramount importance in a variety of applications. Within these, gemini have attracted particular attention, mainly due to their improved aggregation properties and to the possibility of tuning offered by the presence of a spacer. In this work, a Monte Carlo simulation study with a coarse-grained model was employed to assess the interaction of cationic gemini surfactants with a like-charged model membrane. Separating the contribution of the excluded volume and that of the electrostatic effects in the organization of gemini–lipid membranes was the first goal of this work and the role of these factors was assessed varying the concentration, the spacer length and the headgroup charge of gemini surfactants. The results provide a new insight on the organization of lipid headgroups in the vicinity of gemini surfactants. It was found that the surfactant–lipid interaction is strongly affected by the surfactant spacer length, being controlled by an overall balance between excluded volume and surfactant–lipid and surfactant–surfactant electrostatic effects. It is also seen that the out-of-plane motion of the spacer has a significant effect upon membrane organization and counterion condensation. Good agreement was found with results previously obtained from atomistic simulation.     

Reproducibility of the gadolinium concentration measurements and of the fitting parameters of the vascular input function in the superior sagittal sinus in a patient population

It is widely recognised that the measurement of the arterial input function (AIF) is a key issue and a major source of errors in the pharmacokinetic modelling of dynamic, contrast-enhanced magnetic resonance imaging (DCE-MRI) data, and the modality of the AIF determination is still a matter of debate. In this study we addressed the problem of the intrinsic variability of the AIF within the imaged volume of a DCE-MRI scan by systematically investigating the change in the concentration of contrast agent over time and the fit parameters of the derived vascular input function (VIF) obtained from the superior sagittal sinus (SSS) of a patient population that was scanned longitudinally during treatment for high grade glioma. From a total of 82 scanning sessions, we compared the results obtained with three different DCE-MRI protocols and between two different fitting functions. We applied a correction algorithm to the measured concentration-time curves to minimize the effect of the low temporal resolution on the VIF, and investigated the effect of this algorithm on the reproducibility. Finally, where possible, we compared the signal obtained in the SSS to the signal obtained in the middle cerebral artery. We found a good intrapatient reproducibility of both the measured gadolinium concentrations and VIF parameters, and that the variation of the parameters due to slice location within a patient was significantly lower than the intra patient variation. Intrapatient, interscan differences were significantly less marked than inter-patient differences showing a good intraclass correlation coefficient. We did encounter a MRI protocol dependence of the VIF fitting parameters. The correction algorithm significantly improved the reproducibility of the fitting parameters. These results support the idea that the use of a patient specific measured AIF, not necessarily averaged over a large volume, offers a significant benefit with respect to an external AIF or a measured cohort average AIF.     

Tissue similarity maps (TSMs): A new means of mapping vascular behavior and calculating relative blood volume in perfusion weighted imaging

This study introduces a new processing means that uses the original signal (rather than contrast agent concentration) from dynamic susceptibility contrast (DSC) perfusion weighted imaging (PWI) to calculate a relative cerebral blood volume map and a tissue similarity map (TSM). Ten healthy volunteers and eight multiple sclerosis (MS) patients were studied using high resolution PWI. The TSM is found by choosing a reference region in one slice and comparing its signal in a mean squared error sense to the signal from every pixel in all images throughout the brain. The TSMs provide a means to determine which tissues have similar flow characteristics with high contrast and signal-to-noise ratios. The effective blood volume measured from this approach is nearly identical to that from conventional relative cerebral blood volume (rCBV) maps but with better signal-to-noise. Of interest is the fact that choosing one MS lesion as the reference tissue appears to be enough to find nearly all lesions throughout the brain. That is, these lesions all behave the same from a vascular point of view. The TSM results are robust within and across slices properly nulling the same type of tissue throughout the brain for a given reference region. TSM derived rCBV agrees well with the conventional derived rCBV using contrast agent concentration. TSM may provide a new means to study similarities between blood flow patterns in tissue in the brain and in better diagnosing vascular differences between tissues and lesions.     

动态最优多因子组合的华北汛期降水模式误差估计及预报

利用国家气候中心季节预报1983—2009年27年模式预报结果,结合74项环流指数及美国国家海洋局和大气管理局提供的40个气候指数和美国气候预报中心实际降水分析资料,采用资料诊断分析和数值模拟实验相结合的方法,通过多因子的历史相似信息提取预报相似年,获得预报场的误差订正项.在这一订正思路的基础上,考虑前期关键影响因子的选取、多因子组合的优化配置,构建适用于不同预报年的区域动力-统计模式预报误差订正方案.以华北为例,探索多因子最优组合的多元客观相似判据,发展基于多因子动力-统计模式预报误差的动态订正新技术,改善华北夏季降水预报效果,提高预报技巧.通过2005—2009年独立样本回报结果表明,动态最优多因子组合相似订正方法距平相关系数评分相对于系统订正方法有着显著的提高,该订正方案对华北地区的夏季降水预测有着很好的业务前景,具有重要的应用价值,即将投入业务运行. 关键词： 关键因子集 模式误差估计 汛期降水 预测