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.     

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.     

Computer-aided diagnosis of breast DCE-MRI using pharmacokinetic model and 3-D morphology analysis

Three-dimensional (3-D) dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) consists of a large number of images in different enhancement phases which are used to identify and characterize breast lesions. The purpose of this study was to develop a computer-assisted algorithm for tumor segmentation and characterization using both kinetic information and morphological features of 3-D breast DCE-MRI. An integrated color map created by intersecting kinetic and area under the curve (AUC) color maps was used to detect potential breast lesions, followed by the application of a region growing algorithm to segment the tumor. Modified fuzzy c-means clustering was used to identify the most representative kinetic curve of the whole segmented tumor, which was then characterized by using conventional curve analysis or pharmacokinetic model. The 3-D morphological features including shape features (compactness, margin, and ellipsoid fitting) and texture features (based on the grey level co-occurrence matrix) of the segmented tumor were obtained to characterize the lesion. One hundred and thirty-two biopsy-proven lesions (63 benign and 69 malignant) were used to evaluate the performance of the proposed computer-aided system for breast MRI. Five combined features including rate constant (k_ep), volume of plasma (v_p), energy (G₁), entropy (G₂), and compactness (C₁), had the best performance with an accuracy of 91.67% (121/132), sensitivity of 91.30% (63/69), specificity of 92.06% (58/63), and A_z value of 0.9427. Combining the kinetic and morphological features of 3-D breast MRI is a potentially useful and robust algorithm when attempting to differentiate benign and malignant lesions.     

Limitations of the permeability-limited compartment model in estimating vascular permeability and interstitial volume fraction in DCE-MRI

Dynamic contrast-enhanced magnetic resonance imaging commonly uses compartment models to estimate tissue parameters in general and perfusion parameters in particular. Compartment models assume a homogeneous distribution of the injected tracer throughout the compartment volume. Since tracer distribution within a compartment cannot be assessed, the parameters obtained by means of a compartment model might differ from the actual physical values.This work systematically examines the widely used permeability-surface-limited one-compartment model to determine the reliability of the parameters obtained by comparing them with their actual values. A computer simulation was used to model spatial tracer distribution within the interstitial volume using diffusion of contrast agent in tissue. Vascular parameters were varied as well as tissue parameters. The vascular parameters used were capillary radius (4 and 12 μm), capillary permeability (from 0.03 to 3.3 μm/s) and intercapillary distances from 30 to 300 μm. The tissue parameters used were tortuosity (λ), porosity (α) and interstitial volume fraction (v_e).Our results suggest that the permeability-surface-limited compartment model generally underestimates capillary permeability for capillaries with a radius of 4 μm by factors from ≈0.03 for α=0.04, to ≈ 0.1 for α=0.2, to ≈ 0.5 for α=1.0. An overestimation of actual capillary permeability for capillaries with a radius of 12 μm by a factor of ≥1.3 was found for α=1.0, while α=0.2 yielded an underestimation by a factor of ≈0.3 and α=0.04 by a factor of ≈ 0.03. The interstitial volume fraction, v_e, obtained by the compartment model differed with increasing intercapillary distances and for low vessel permeability, whereas v_e was found to be estimated approximately accurately for P=0.3 μm/s and P=3.3 μm/s for vessel distances <100 μm.     

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.     

一维大气边界层光学折射率结构常数数值模式的敏感性分析

 提出了一种大气光学折射率结构常数的数值模式。通过敏感性分析发现，对折射率结构常数有显著影响的参数是：一年中的不同日期、土壤的热容量和含水量、雪地和水面上、云量等，风速大小几乎对折射率结构常数没有什么影响。     

A comparison of numerical and analytical radiative-transfer solutions for plane albedo of natural waters

Several numerical and analytical solutions of the radiative transfer equation (RTE) were compared for plane albedo in a problem of solar light reflection by sea water. The study incorporated the simplest case—a semi-infinite one-dimensional plane—parallel absorbing and scattering homogeneous layer illuminated by a monodirectional light beam. Inelastic processes (such as Raman scattering and fluorescence), polarization and air-water surface refraction-reflection effects, were not considered. Algorithms were based on the invariant imbedding method and two different variants of the discrete ordinate method (DOM). Calculations were performed using parameters across all possible ranges (single-scattering albedo ω₀ and refracted solar zenith angle θ₁), but with a special emphasis on natural waters. All computations were made for two scattering phase functions, which included an almost isotropic Rayleigh phase function and strongly anisotropic double-peaked Fournier-Forand-Mobley phase function. Models were validated using quasi-single-scattering (QSSA) and exponential approximations, which represent the extreme cases of ω₀→0 and ω₀→1, respectively. All methods yielded relative differences within 1.8% for modeled natural waters. An analysis of plane albedo behavior resulted in the development of a new extended QSSA approximation, which when applied in conjunction with the extended Hapke approximation developed earlier, resulted in a maximum relative error of 2.7%. The study results demonstrated that for practical applications, the estimation of inherent optical properties from observed reflectance can best be achieved using an extended Hapke approximation.     

考虑弯曲和轴向振动模态的一维梁压电阻抗模型及试验研究

同时考虑一维梁结构的弯曲和轴向振动,对其压电阻抗模型进行建模分析和试验验证。在0.02～42 kHz频段内区分并标记了一维钢梁弯曲振动模态前18阶及轴向振动模态前3阶。结果表明:在0.02～7.5kHz频段内,数值计算和试验结果中谐振峰对应频率的相对误差较大:11.7%～16.5%,其原因可能是低频时振动能量较低且波的传播受结构阻尼、边界条件及环境噪音等因素影响较为明显;在7.5～42kHz范围内,两者谐振峰位置符合良好,相对误差较小:0.11%～2.31%,表明该模型在高频段具有较好的适用性;轴向振动模态对应频率大于弯曲振动模态。本研究为结构健康监测过程中检测频段的选取及损伤信息的提取提供参考。     

空温式翅片管气化器结霜模型及数值模拟

以分形理论的DLA模型为基础,建立了空温式翅片管气化器深冷表面上霜晶生长的二维模型,模拟了深冷表面上的霜晶生长过程.采用计盒维数法对模拟出的霜晶生长图像进行了分形维数的计算,结果表明深冷表面上霜晶的分形维数较一般冷表面上的分形维数大,从而说明深冷表面上的霜晶具有更加复杂的结构,充满空间的能力更大.这对进一步理解空温式深...     

冷冻靶制备中辅助加热的理论和数值分析

 为了补偿惯性约束聚变（ICF）冷冻靶冷却过程中非球对称腔体的热流分布,通常在冷却的同时在腔外壁上施加辅助加热。在间接驱动靶中建立了1维热传导理论模型,分析所需辅助热流密度,同时在2维轴对称模型下,利用计算流体力学的FLUENT程序,对辅助加热机制进行了热力学模拟。当把辅助加热设在腔外壁的中平面上下各1.3 mm的范围时,得到了最佳辅助热流密度为635 W/m²,与理论结果基本一致。     

Analytical and numerical solutions of the density dependent diffusion Nagumo equation

In this Letter, we obtained solutions to a class of density dependent diffusion Nagumo equations. In particular, series solutions are obtained, along with a bound for the range of the convergence. Also, numerical solutions are obtained by the Runge-Kutta-Fehlberg 45 method. Moreover, the dependence of the traveling wave solutions on various parameters is discussed. Furthermore, we compare the series solutions with the numerical solutions to validate the numerical method. The results obtained in this study reveal many interesting behaviors that warrant further study on the Nagumo equation.     

激光诱导击穿光谱定量分析中的分析线自动选择方法

为了实现激光诱导击穿光谱分析中的分析线自动选择,定义了元素发射谱线的相对强度比(RDTIR)、波长偏差(WDDT)两个参数,并据此对检测谱线进行筛选,通过设定合理的阈值,剔除自吸收和干扰严重的谱线。通过对高合金钢(GBW01605)实验数据的分析,分别选定了样品中主要元素铁、铬、镍、锰、铜的分析线,选线结果符合谱线的选取原则。     

器件效应数值模拟中漂移扩散模型的误差分析

为了确定数值模拟过程中的误差来源,并针对误差来源改进软件,减小计算误差,对半导体器件数值模拟中的采用的漂移扩散模型进行了研究。结合自主开发的半导体器件效应软件GSRES,分析了软件中漂移扩散模型的理论近似,对计算模型中由于温度分布、载流子复合/产生率、载流子迁移率等项采取近似而导致的误差进行了分析。根据误差分析和数值模拟算例,认为误差主要来自于器件内部温度场分布和迁移率模型的近似,给出了软件的适用范围。结合半导体器件的研究热点和发展趋势,对该模型中需要进行改进的近似项进行了分析。     

器件效应数值模拟中漂移扩散模型的误差分析

为了确定数值模拟过程中的误差来源,并针对误差来源改进软件,减小计算误差,对半导体器件数值模拟中的采用的漂移扩散模型进行了研究。结合自主开发的半导体器件效应软件GSRES,分析了软件中漂移扩散模型的理论近似,对计算模型中由于温度分布、载流子复合/产生率、载流子迁移率等项采取近似而导致的误差进行了分析。根据误差分析和数值模拟算例,认为误差主要来自于器件内部温度场分布和迁移率模型的近似,给出了软件的适用范围。结合半导体器件的研究热点和发展趋势,对该模型中需要进行改进的近似项进行了分析。     

用于脉冲等离子体推力器烧蚀过程仿真的新型机电模型

用于脉冲等离子体推力器(PPT)工作过程仿真的一维机电模型, 具有模型简单、计算周期短等优点, 在PPT设计过程中得到了广泛应用. 本文针对机电模型假设工质烧蚀质量为常数和不考虑烧蚀过程这一局限, 提出了一种采用Teflon一维烧蚀模型计算工质烧蚀质量的改进模型, 并以LES-6 PPT为研究对象进行了仿真. 通过与LES-6 PPT实验数据进行对比, 仿真结果与实验数据符合, 充分验证了模型的可靠性. 此模型能够对Teflon工质在PPT工作过程中的温度变化和烧蚀过程进行仿真, 弥补了机电模型忽略烧蚀过程对仿真结果所造成的影响, 同时, 此模型依然保持了机电模型简单易于实现的优点, 对于脉冲等离子体推力器的设计具有重要意义. 关键词： 脉冲等离子体推力器 机电模型 烧蚀模型 数值仿真     

超声空化去毛刺的理论分析及数值仿真

随着制造业的不断发展,对产品的加工精度要求愈来愈高,然而微小毛刺的去除仍然是十分困难的。毛刺虽小但危害巨大。因此,有效去除毛刺已成为加工中不可或缺的工序。而超声波去毛刺法可以有效快速的去除复杂零件的微小毛刺,具有很高的实用价值。尽管超声波的相关理论日趋完善,但是超声去毛刺机理以及空化产生的高压对毛刺的影响缺乏一些理论参考。此文阐述了超声波去毛刺的基本原理,利用有限元软件ABAQUS对单个空化泡在毛刺上的溃灭过程进行数值仿真,证明了超声波去毛刺的可行性,通过实验验证,超声波能够有效的去除毛刺。其研究结果为进一步研究超声波去毛刺的理论提供了参考。     

Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation

The use of a top-mounted electromagnetic induction coil has been demonstrated as a contactless alternative to traditional ultrasonic treatment (UST) techniques that use an immersed mechanical sonotrode for the treatment of metals in the liquid state. This method offers similar benefits to existing UST approaches, including degassing, grain refinement, and dispersion of nanoparticles, while also preventing contact contamination due to erosion of the sonotrode. Contactless treatment potentially extends UST to high temperature or reactive melts. Generally, the method relies on acoustic resonance to reach pressure levels suitable for inertial cavitation and as a result the active cavitation volume tends to lie deep in the melt rather than in the small volume surrounding the immersed sonotrode probe. Consequently, (i) with suitable tuning of the coil supply frequency for resonance, the treatment volume can be made arbitrarily large, (ii) the problem of shielding and pressure wave attenuation suffered by the immersed sonotrode is avoided. However, relying on acoustic resonance presents problems: (i) the emergence of bubbles alters the speed of sound, resonance is momentarily lost, and cavitation becomes intermittent, (ii) as sound waves travel through and reflect on all the materials surrounding the melt, the sound characteristics of the crucible and supporting structures need to be carefully considered. The physics of cavitation coupled with this intermittent behaviour poses a challenge to sonotrode modelling orthodoxy, a problem we are trying to address in this publication. Two alternative approaches will be discussed, one of which is in the time domain and one in the frequency domain, which couple the solution of a bubble dynamics solver with that of an acoustics solver, to give an accurate prediction of the acoustic pressure generated by the induction coil. The time domain solver uses a novel algorithm to improve simulation time, by detecting an imminent bubble collapse and prescribing its subsequent behaviour, rather than directly solving a region that would normally require extremely small time steps. This way, it is shown to predict intermittent cavitation. The frequency domain solver for the first time couples the nonlinear Helmholtz model used for studying cavitation, with a background source term for the contribution of Lorentz forces. It predicts comparable RMS pressures to the time domain solver, but not the intermittent behaviour due to the underlying harmonic assumption. As further validation, the frequency domain method is also used to compare the generated acoustic pressure with that of traditional UST using a mechanical sonotrode.     

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.     

Electron density diagnostics by use of a collisional excitation model of the oxygen VI doublet in the solar transition region

ABSTRACT

For spectral diagnostics in the solar transition region under the collision–equilibrium condition, the method for electron density diagnostics by the collisional excitation is discussed in this paper. By using observed signal ratio of spectral lines produced by the oxygen VI ion, we discuss the electron density by this method. We find that this method is valid for a large region of signal ratio (from 2.001 to 4.162). We obtain that the electron density increases with increasing signal ratio of the oxygen VI doublet, and the plasma has an electron density on the order of magnitude of 10⁶–10⁷?cm^?3. This discussion will be significant for study on spectral diagnostics of the solar transition region.     

单电子晶体管电流解析模型及数值分析

本文首先建立单电子晶体管的电流解析模型, 然后将蒙特卡罗法与主方程法结合进行数值分析, 研究了栅极偏压、漏极偏压、温度与隧道结电阻等参数对器件特性的影响. 结果表明: 对于对称结, 库仑台阶随栅极偏压增大而漂移; 漏极电压增大, 库仑振荡振幅增强, 库仑阻塞则衰减; 温度升高将导致库仑台阶和库仑振荡现象消失. 对于非对称结, 源漏隧道结电阻比率增大, 库仑阻塞现象越明显. 关键词： 单电子晶体管 解析模型 蒙特卡罗法 主方程法