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.     

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.     

Quantitative analysis of arterial spin labeling FMRI data using a general linear model

Arterial spin labeling techniques can yield quantitative measures of perfusion by fitting a kinetic model to difference images (tagged-control). Because of the noisy nature of the difference images investigators typically average a large number of tagged versus control difference measurements over long periods of time. This averaging requires that the perfusion signal be at a steady state and not at the transitions between active and baseline states in order to quantitatively estimate activation induced perfusion. This can be an impediment for functional magnetic resonance imaging task experiments. In this work, we introduce a general linear model (GLM) that specifies Blood Oxygenation Level Dependent (BOLD) effects and arterial spin labeling modulation effects and translate them into meaningful, quantitative measures of perfusion by using standard tracer kinetic models. We show that there is a strong association between the perfusion values using our GLM method and the traditional subtraction method, but that our GLM method is more robust to noise.     

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.     

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.     

The effect of temporal sampling on quantitative pharmacokinetic and three-time-point analysis of breast DCE-MRI

The effects of temporal sampling on the previously published three-time-point (3TP) method are compared with those of a Tofts-Kety model using an arterial input function from the alternating minimization with model (AMM) method. Computer simulations are done to estimate the expected error in both the 3TP and Tofts-Kety models as a function of the temporal sampling rate of the data. The error in the 3TP model parameters remained essentially constant with respect to temporal sampling. The Tofts-Kety model showed a linear increase in parameter error with respect to temporal sampling. Both analysis methods were also applied to 87 clinically acquired breast scans. These scans were downsampled in time by a factor of 2 and 4, and the methods were reapplied. The spatial resolution was held constant throughout this study. At temporal resolutions less than 19.4 s, the Tofts-Kety model outperformed the 3TP model using receiver operating characteristic curve analysis (area under the ROC curve [AUC] of 0.94 compared to 0.91). As the temporal sampling rate decreased, the 3TP model outperformed the Tofts-Kety model (AUC of 0.89 versus 0.85). When the temporal sampling rate of the data was less than 20 s, the Tofts-Kety model with the AMM method had lower parameter error than the 3TP method.     

Interpolation of experimental data without a theoretical model

A new approach is proposed for the interpolation of experimental data when a theoretical model is unavailable. The method is based on the minimization of a modified likelihood function incorporating a generalized smoothness test of the theoretical curve. The conditions for applicability of the method are a sufficiently accurate estimate of the statistical errors of the experimental data (assuming that the results fit a Gaussian distribution in accordance with the resulting rms deviations) and smoothness of the theoretical curve. A FORTRAN 77 program for the interpolation of experimental data has been written to implement the proposed algorithm. The computing time and roundoff error are determined as functions of the number of experimental points. Zh. éksp. Teor. Fiz. 116, 760–776 (September 1999)     

Correcting saturation effects of the arterial input function in dynamic susceptibility contrast-enhanced MRI: a Monte Carlo simulation

To prevent systematic errors in quantitative brain perfusion studies using dynamic susceptibility contrast-enhanced magnetic resonance imaging (DSC-MRI), a reliable determination of the arterial input function (AIF) is essential. We propose a novel algorithm for correcting distortions of the AIF caused by saturation of the peak amplitude and discuss its relevance for longitudinal studies. The algorithm is based on the assumption that the AIF can be separated into a reliable part at low contrast agent concentrations and an unreliable part at high concentrations. This unreliable part is reconstructed, applying a theoretical framework based on a transport-diffusion theory and using the bolus-shape in the tissue. A validation of the correction scheme is tested by a Monte Carlo simulation. The input of the simulation was a wide range of perfusion, and the main aim was to compare this input to the determined perfusion parameters. Another input of the simulation was an AIF template derived from in vivo measurements. The distortions of this template was modeled via a Rician distribution for image intensities. As for a real DSC-MRI experiment, the simulation returned the AIF and the tracer concentration-dependent signal in the tissue. The novel correction scheme was tested by deriving perfusion parameters from the simulated data for the corrected and the uncorrected case. For this analysis, a common truncated singular value decomposition approach was applied. We find that the saturation effect caused by Rician-distributed noise leads to an overestimation of regional cerebral blood flow and regional cerebral blood volume, as compared to the input parameter. The aberration can be amplified by a decreasing signal-to-noise ratio (SNR) or an increasing tracer concentration. We also find that the overestimation can be successfully eliminated by the proposed saturation-correction scheme. In summary, the correction scheme will allow DSC-MRI to be expanded towards higher tracer concentrations and lower SNR and will help to increase the measurement to measurement reproducibility for longitudinal studies.     

Quantitative analysis of holographic particle data

There are several well known difficulties in forming and analysing holographic particle data in the micrometre and submicrometre size range. This paper suggests that these problems can be overcome by using a combination of research techniques. Firstly, it has been found that it is possible to record images of submicrometre particles by using conventional photographic materials. Essentially, a diffraction limited optical component has been used to provide aberration free particle images. Secondly, the sensitivity of the holographic material has been increased with the use of specialized holographic processing chemicals. Thirdly, it has been found that it is possible to encode holographically double, slightly displaced, particle images by using a pulse laser. Thus, Young's fringes can be obtained directly from the stored holographic data, and the particle velocity can be measured directly from the hologram. Fourthly, the holographic particle data can be automatically analysed, using a software program. Finally since the data is stored holographically, it is possible to obtain instantaneous 3-D particle velocities. This paper demonstrates that it is possible to perform holographic particle image velocimetry automatically, with only a small amount of preprocessing.     

Renal perfusion in acute kidney injury with DCE-MRI: Deconvolution analysis versus two-compartment filtration model

Purpose

To investigate the results of different pharmacokinetic models of a quantitative analysis of renal blood flow (RBF) in acute kidney injury using deconvolution analysis and a two-compartment renal filtration model.

Materials and methods

MRI data of ten male Lewis rats were analyzed retrospectively. Six animals were subjected to unilateral acute kidney injury and underwent perfusion imaging by dynamic contrast-enhanced MRI (DCE-MRI). Renal blood flow was estimated from regions-of-interest depicting the cortex in the DCE-MRI perfusion maps. The perfusion models were compared by a paired t-test and Bland–Altman plots.

Results

No significant difference was found between the two compartment model and the deconvolution analysis (P = 0.2807). Differences between healthy and diseased kidney in the AKI model were significant for both methods (P < 0.05). A Bland–Altman plot showed no systematic errors, and values were equally distributed around the mean difference between the methods lying within the range of 1.96 standard deviations.

Conclusion

Both quantification strategies could detect the kidneys that were impaired by AKI. When just aiming at RBF as a marker, a deconvolution analysis can provide similar values as the 2CFM. If functional parameters beyond RBF like glomerular filtration rate are needed, the 2CFM should be employed.     

Total emissivity measurements without use of an absolute reference

Total emissivity measurement by ordinary steady state radiometric methods are difficult at low temperature; besides, those methods require an emissivity reference. In this paper, several new periodic methods suitable for total emissivity measurements are presented. First it is shown that the thermal modulation of a sample allows direct emissivity measurements, even at low temperature, with an ordinary equipment involving no cooled vessel. Very accurate measurements have been performed within a few minutes at room temperature, on reflective materials. Second, it is shown that indirect total emissivity measurements are also feasible, provided source and sample temperatures are equal. This condition can be fulfilled with a modulated temperature hemispherical gray surface as IR source, or in a simpler way, with a mobile part of a hemisphere. Third, it is shown that if both sample and source temperatures are modulated, simultaneous direct and indirect measurements can be carried out. This results in an absolute emissivity measurement without reference. As an experimental validation, simultaneous direct and indirect measurements of the total directional emissivity are carried out on three samples at room temperature. Periodic radiometry methods are found to be reliable and accurate, emission and reflection measurements giving the same result.     

Effects of arterial input function selection on kinetic parameters in brain dynamic contrast-enhanced MRI

PurposeKinetic parameters derived from dynamic contrast-enhanced MRI (DCE-MRI) were suggested as a possible instrument for multi-parametric lesion characterization, but have not found their way into clinical practice yet due to inconsistent results. The quantification is heavily influenced by the definition of an appropriate arterial input functions (AIF). Regarding brain tumor DCE-MRI, there are currently several co-existing methods to determine the AIF frequently including different brain vessels as sources. This study quantitatively and qualitatively analyzes the impact of AIF source selection on kinetic parameters derived from commonly selected AIF source vessels compared to a population-based AIF model.Material and methods74 patients with brain lesions underwent 3D DCE-MRI. Kinetic parameters [transfer constants of contrast agent efflux and reflux K^trans and k_ep and, their ratio, v_e, that is used to measure extravascular-extracellular volume fraction and plasma volume fraction v_p] were determined using extended Tofts model in 821 ROI from 4 AIF sources [the internal carotid artery (ICA), the closest artery to the lesion, the superior sagittal sinus (SSS), the population-based Parker model]. The effect of AIF source alteration on kinetic parameters was evaluated by tissue type selective intra-class correlation (ICC) and capacity to differentiate gliomas by WHO grade [area under the curve analysis (AUC)].ResultsArterial AIF more often led to implausible v_e > 100% values (p < 0.0001). AIF source alteration rendered different absolute kinetic parameters (p < 0.0001), except for k_ep. ICC between kinetic parameters of different AIF sources and tissues were variable (0.08–0.87) and only consistent > 0.5 between arterial AIF derived kinetic parameters. Differentiation between WHO III and II glioma was exclusively possible with v_p derived from an AIF in the SSS (p = 0.03; AUC 0.74).ConclusionThe AIF source has a significant impact on absolute kinetic parameters in DCE-MRI, which limits the comparability of kinetic parameters derived from different AIF sources. The effect is also tissue-dependent. The SSS appears to be the best choice for AIF source vessel selection in brain tumor DCE-MRI as it exclusively allowed for WHO grades II/III and III/IV glioma distinction (by v_p) and showed the least number of implausible v_e values.     

Model-free arterial spin labelling for cerebral blood flow quantification: introduction of regional arterial input functions identified by factor analysis

PURPOSE: To identify regional arterial input functions (AIFs) using factor analysis of dynamic studies (FADS) when quantification of perfusion is performed using model-free arterial spin labelling. MATERIAL AND METHODS: Five healthy volunteers and one patient were examined on a 3-T Philips unit using quantitative STAR labelling of arterial regions (QUASAR). Two sets of images were retrieved, one where the arterial signal had been crushed and another where it was retained. FADS was applied to the arterial signal curves to acquire the AIFs. Perfusion maps were obtained using block-circulant SVD deconvolution and regional AIFs obtained by FADS. In the volunteers, the ASL experiment was repeated within 24 h. The patient was also examined using dynamic susceptibility contrast MRI. RESULTS: In the healthy volunteers, CBF was 64+/-10 ml/[min 100 g] (mean+/-S.D.) in GM and 24+/-4 ml/[min 100 g] in WM, while the mean aBV was 0.94% in GM and 0.25% in WM. DISCUSSION: Good CBF image quality and reasonable quantitative CBF values were obtained using the combined QUASAR/FADS technique. We conclude that FADS may be a useful supplement in the evaluation of ASL data using QUASAR.     

Nucleon spin with and without hyperon data: a new tool for analysis

We present a simple explanation of the underlying physics in the use of hyperon decay data to obtain information about proton spin structure. We also present an alternative input using nucleon magnetic moment data and show that the results from the two approaches are nearly identical. The role of symmetry breaking is clarified while pointing out that simple models explaining the violation of the Gottfried sum rule via pion emission tend to lose the good SU(3) predictions from Cabibbo theory for hyperon decays.     

Effective-range function for doublet nd scattering from an analysis of modern data

The parameters of the generalized effective-range function K(k ²) having a pole are found by using the results that were obtained by calculating the S-wave phase shift δ(E) for doublet nd scattering and the triton binding energy on the basis of Faddeev equations and within the N/D method and which were presented in the literature. The convergence of the expansion of K(k ²) in powers of momentum is studied. The binding energy of the virtual triton and the residues of the partial-wave scattering amplitudes at the poles corresponding to the bound and virtual states are calculated. Correlations between the binding energies of the bound and virtual states of the triton, on one hand, and the doublet scattering length for nd interaction, on the other hand, are considered. The function K(k ²) is also calculated within a two-body model featuring various potentials.     

Zeros of the finite-size scaling region partition function for a model with a wetting transition

We derive a finite-size scaling representation for the partition function for an Onsager-Temperley string model with a wetting transition, and analyze the zeros of this partition function in the complex scaled coupling parameter of relevance. The system models the one-dimensional interface between two phases in a rectangular two-dimensional region (x, y) ²,–L yL,oxN. The two phases are at coexistence. The string or interface has a surface tension 2KkT per unit length and an extra Boltzmann weighta per unit length if it touches the surfaces aty=±L. There is a critical valuea _c=1/2K and fora>a _c the string is confined to one of the surfaces, while fora a _c the string moves roughly in the rectangular region. The finite-size scaling parameters are =a _c ² N/L ² and =L(a–a _c)/a _c ² . We find that for || large, the zeros of the scaled partition function lie close to the lines arg()=±/4 with re()>0. We discuss the motion of all the zeros as changes by both analytic and numerical arguments.     

Exact solution of an evolutionary model without aging

We introduce an age-structured asexual population model containing all the relevant features of evolutionary aging theories. Beneficial as well as deleterious mutations, heredity, and arbitrary fecundity are present and managed by natural selection. An exact solution without aging is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated and indicate that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups like many protozoa and coelenterates is discussed.