Accuracy of deconvolution analysis based on singular value decomposition for quantification of cerebral blood flow using dynamic susceptibility contrast-enhanced magnetic resonance imaging

Simultaneous correction of sensitivity and spatial resolution in projection-based magnetic particle imaging

PURPOSE

The purpose of this study was to develop a method to simultaneously correct the spatial resolution and inhomogeneous sensitivity of a receiving coil in projection-based magnetic particle imaging - and to investigate its efficacy through simulation and experimental studies.

METHODS

Magnetic particle imaging (MPI) images were reconstructed using the simultaneous algebraic reconstruction technique (SART), and simultaneous corrections to sensitivity and spatial resolution were performed by incorporating the sensitivity map of the receiving coil and the system function into the SART algorithm. After each SART update, the regularization method - with total variation (TV) minimization - was used to suppress noise amplification and artifact generation. For comparison, MPI images were also reconstructed using the filtered backprojection (FBP) method and the FBP-truncated singular value decomposition (TSVD) method, in which the system function was deconvolved from the projection data using TSVD. In simulation studies, the sensitivity map of a second-order, gradiometer-type receiving coil was generated using the Biot-Savart law, while the system function was obtained by calculating the MPI signals induced by magnetic nanoparticles at various distances from a field-free line (FFL), using a lock-in-amplifier model. The effects of a regularization parameter for TV minimization (α), number of iterations (N), and signal-to-noise ratio (SNR) of the MPI signals on the reconstructed MPI images of a numerical phantom were evaluated, using the image profiles and percent root mean square error (PRMSE). Experimental studies involved the calculation of the system function using a tube phantom. Projection data for an A-shaped phantom were acquired using our MPI scanner, and their MPI images were reconstructed from the projection data, as described above.

RESULTS

When both the sensitivity and spatial resolution were corrected (SART-SR), the quality of the reconstructed images was seen to have improved, compared to when the spatial resolution was not corrected - or when the FBP and FBP-TSVD methods were used. When SNR was low (20), a larger α value yielded a better image. The minimum PRMSE occurred at N ≈ 200-400 and increased with increasing N thereafter. When SNR was high (100), the image quality was generally not dependent on the α value within its studied range. The PRMSE decreased slowly with increasing N, and tended to converge to a constant value. The full width at half maximum (FWHM) of the profile was obtained from the A-shaped phantom, reconstructed using the SART-SR algorithm with α = 0.05 and N = 1000. The FWHM value of the tube (2 mm diameter) in the A-shaped phantom image was found to be 2.2 mm on average, whereas those calculated from the images obtained by the FBP and FBP-TSVD methods were 4.4 and 3.0 mm on average, respectively. Spatial resolution improved when using the FBP-TSVD method as compared to the FBP method but image distortion and artifacts were observed.

CONCLUSIONS

Although further studies are necessary to optimize the parameters used in the SART algorithm and in TV minimization, the present results suggest that the proposed method is useful for improving the image quality of projection-based MPI.

Quantification of intracranial arterial blood flow using noncontrast enhanced 4D dynamic MR angiography

PURPOSE

Noncontrast enhanced dynamic magnetic resonance angiography delineates the pattern of dynamic blood flow of the cerebral vasculature. A model-free solution was proposed to quantify arterial blood flow (aBF) by using the monotonic property of the residual function.

THEORY AND METHODS

Analytical simulations and in-vivo studies were performed to evaluate the performance of the proposed method by comparing the aBF values generated from the proposed and conventional singular value decomposition methods. The aBF values were compared with blood flow velocity measured by 2D phase contrast MRI, and compared between balanced steady-state free precession-based radial and spoiled GRE-based Cartesian acquisitions. Hemodynamic parametric maps were generated in 1 patient with arteriovenous malformation.

RESULTS

The proposed method generates reliable aBF measurement at different signal-to-noise ratio levels, whereas overestimation/underestimation of aBF was observed when a high/low threshold was applied in the singular value decomposition method. Average aBF in large vascular branches was 214.4 and 214.5 mL/mL/min with radial and Cartesian acquisitions, respectively. Significant correlations were found between aBF and blood flow velocity measured by phase contrast MRI (P = 0.0008), and between Cartesian and radial acquisitions (P < 0.0001). Altered hemodynamics were observed at the lesion site of the arteriovenous malformation patient.

CONCLUSION

A robust analytical solution was proposed for quantifying aBF. This model-free method is robust to noise, and its clinical value in the diagnosis of cerebrovascular disorders awaits further evaluation.

Detection of severity in Alzheimer's disease (AD) using computational modeling

The prevalent cause of dementia - Alzheimer's disease (AD) is characterized by an early cholinergic deficit that is in part responsible for the cognitive deficits (especially memory and attention defects). Prolonged AD leads to moderate-to-severe AD, which is one of the leading causes of death. Placebo-controlled, randomized clinical trials have shown significant effects of Acetyl cholin esterase inhibitors (ChEIs) on function, cognition, activities of daily living (ADL) and behavioral symptoms in patients. Studies have shown comparable effects for ChEIs in patients with moderate-to-severe or mild AD. Setting a fixed measurement (e.g. a Mini-Mental State Examination score, as a 'when to stop treatment limit) for the disease is not clinically rational. Detection of changed regional cerebral blood flow in mild cognitive impairment and early AD by perfusion-weighted magnetic resonance imaging has been a challenge. The utility of perfusion-weighted magnetic resonance imaging (PW-MRI) for detecting changes in regional cerebral blood flow (rCBF) in patients with mild cognitive impairment (MCI) and early AD was evaluated. We describe a computer aided prediction model to determine the severity of AD using known data in literature. We designed an automated system for the determination of AD severity. It is used to predict the clinical cases and conditions with disagreements from specialist. The model described is useful in clinical practice to validate diagnosis.

Unenhanced and Contrast-Enhanced MR Angiography and Perfusion Imaging for Suspected Pulmonary Thromboembolism

OBJECTIVE

This article discusses the basics of unenhanced MR angiography (MRA) and MR venography (MRV), time-resolved contrast-enhanced (CE) MRA and dynamic first-pass CE perfusion MRI, and unenhanced and CE MRV, in addition to assessing the clinical relevance of these techniques for evaluating patients with suspected pulmonary thromboembolism and deep venous thrombosis.

CONCLUSION

Since the 1990s, the efficacy of MRA or MRV and dynamic perfusion MRI for patients with suspected pulmonary thromboembolism and deep venous thrombosis has been evaluated. On the basis of the results of single-center trials, comprehensive MRI protocols, including pulmonary unenhanced and CE MRA, perfusion MRI, and MRV, promise to be safe and time effective for assessing patients with suspected pulmonary thromboembolism, although future multicenter trials are required to assess the real clinical value of MRI.

Automatic determination of the arterial input function in dynamic susceptibility contrast MRI: comparison of different reproducible clustering algorithms

Introduction

Arterial input function (AIF) plays an important role in the quantification of cerebral hemodynamics. The purpose of this study was to select the best reproducible clustering method for AIF detection by comparing three algorithms reported previously in terms of detection accuracy and computational complexity.

Methods

First, three reproducible clustering methods, normalized cut (Ncut), hierarchy (HIER), and fast affine propagation (FastAP), were applied independently to simulated data which contained the true AIF. Next, a clinical verification was performed where 42 subjects participated in dynamic susceptibility contrast MRI (DSC-MRI) scanning. The manual AIF and AIFs based on the different algorithms were obtained. The performance of each algorithm was evaluated based on shape parameters of the estimated AIFs and the true or manual AIF. Moreover, the execution time of each algorithm was recorded to determine the algorithm that operated more rapidly in clinical practice.

Results

In terms of the detection accuracy, Ncut and HIER method produced similar AIF detection results, which were closer to the expected AIF and more accurate than those obtained using FastAP method; in terms of the computational efficiency, the Ncut method required the shortest execution time.

Conclusion

Ncut clustering appears promising because it facilitates the automatic and robust determination of AIF with high accuracy and efficiency.

Influence of blood/tissue differences in contrast agent relaxivity on tracer-based MR perfusion measurements

PURPOSE

Perfusion assessment by monitoring the transport of a tracer bolus depends critically on conversion of signal intensity into tracer concentration. Two main assumptions are generally applied for this conversion; (1) contrast agent relaxivity is identical in blood and tissue, (2) change in signal intensity depends only on the primary relaxation effect. The purpose of the study was to assess the validity and influence of these assumptions.

MATERIALS AND METHODS

Blood and cerebral tissue relaxivities r1, r2, and r2* for gadodiamide were measured in four pigs at 1.5 T. Gadolinium concentration was determined by inductively coupled plasma atomic emission spectroscopy. Influence of the relaxivities, secondary relaxation effects and choice of singular value decomposition (SVD) regularization threshold was studied by simulations.

RESULTS

In vivo relaxivities relative to blood concentration [in s(-1) mM(-1) for blood, gray matter (GM), white matter (WM)] were for r1 (2.614 ± 1.061, 0.010 ± 0.001, 0.004 ± 0.002), r2 (5.088 ± 0.952, 0.091 ± 0.008, 0.059 ± 0.014), and r2* (13.292 ± 3.928, 1.696 ± 0.157, 0.910 ± 0.139). Although substantial, by a nonparametric test for paired samples, the differences were not statistically significant. The GM to WM blood volume ratio was estimated to 2.6 ± 0.9 by r1, 1.6 ± 0.3 by r2, and 1.9 ± 0.2 by r2*. Secondary relaxation was found to reduce the tissue blood flow, as did the SVD regularization threshold.

CONCLUSION

Contrast agent relaxivity is not identical in blood and tissue leading to substantial errors. Further errors are introduced by secondary relaxation effects and the SVD regularization.

Evaluating the feasibility of an agglomerative hierarchy clustering algorithm for the automatic detection of the arterial input function using DSC-MRI

During dynamic susceptibility contrast-magnetic resonance imaging (DSC-MRI), it has been demonstrated that the arterial input function (AIF) can be obtained using fuzzy c-means (FCM) and k-means clustering methods. However, due to the dependence on the initial centers of clusters, both clustering methods have poor reproducibility between the calculation and recalculation steps. To address this problem, the present study developed an alternative clustering technique based on the agglomerative hierarchy (AH) method for AIF determination. The performance of AH method was evaluated using simulated data and clinical data based on comparisons with the two previously demonstrated clustering-based methods in terms of the detection accuracy, calculation reproducibility, and computational complexity. The statistical analysis demonstrated that, at the cost of a significantly longer execution time, AH method obtained AIFs more in line with the expected AIF, and it was perfectly reproducible at different time points. In our opinion, the disadvantage of AH method in terms of the execution time can be alleviated by introducing a professional high-performance workstation. The findings of this study support the feasibility of using AH clustering method for detecting the AIF automatically.

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.

Comparison of K-means and fuzzy c-means algorithm performance for automated determination of the arterial input function

The arterial input function (AIF) plays a crucial role in the quantification of cerebral perfusion parameters. The traditional method for AIF detection is based on manual operation, which is time-consuming and subjective. Two automatic methods have been reported that are based on two frequently used clustering algorithms: fuzzy c-means (FCM) and K-means. However, it is still not clear which is better for AIF detection. Hence, we compared the performance of these two clustering methods using both simulated and clinical data. The results demonstrate that K-means analysis can yield more accurate and robust AIF results, although it takes longer to execute than the FCM method. We consider that this longer execution time is trivial relative to the total time required for image manipulation in a PACS setting, and is acceptable if an ideal AIF is obtained. Therefore, the K-means method is preferable to FCM in AIF detection.

Contrast-enhanced multidetector-row computed tomography vs. Time-resolved magnetic resonance angiography vs. contrast-enhanced perfusion MRI: assessment of treatment response by patients with inoperable chronic thromboembolic pulmonary hypertension

PURPOSE

To compare therapeutic effect assessment capability of multidetector-row computed tomography (MDCT), magnetic resonance angiography (MRA), and dynamic perfusion MRI for chronic thromboembolic pulmonary hypertension (CTEPH) patients.

MATERIALS AND METHODS

Twenty-four consecutive CTEPH patients treated with conventional therapy underwent pre- and posttherapeutic MDCT, MRA, dynamic perfusion MRI, 6-minute walk distance (6-MWD), cardiac ultrasound (US), and right heart catheterization. According to therapeutic results, all patients were divided into response (n = 13) and nonresponse (n = 11) groups. CTEPH indexes for MDCT (CTEPH(CT) ) and MRA (CTEPH(MRA) ) were calculated on the basis of embolic burden. Pulmonary perfusion parameter maps were generated from all perfusion MR data, followed by determination of improvements in mean perfusion parameter at regions of interest (ROIs) for each patient. Receiver operating characteristic (ROC)-based positive tests were performed to determine the feasible threshold values for distinguishing two groups. Finally, diagnostic capabilities were compared by means of McNemar's test.

RESULTS

When feasible threshold values adapted, specificity (90.9 〈10/11〉%, P < 0.05) and accuracy (95.8 〈23/24〉%, P < 0.05) for improvement in pulmonary blood flow were significantly higher than those for CTEPH(CTA) (specificity: 36.4 〈4/11〉%, accuracy: 70.8 〈17/24〉%).

CONCLUSION

Dynamic perfusion MRI has better capability for assessment of therapeutic effect on CTEPH patients than does MDCT.

Correction of arterial input function in dynamic contrast-enhanced MRI of the liver

PURPOSE

To develop a postprocessing method to correct saturation of arterial input function (AIF) in T1-weighted dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for quantification of hepatic perfusion.

MATERIALS AND METHODS

The saturated AIF is corrected by parameterizing the first pass of the AIF as a smooth function with a single peak and minimizing a least-squares error in fitting the liver DCE-MRI data to a dual-input single-compartment model. Sensitivities of the method to the degree of saturation in the AIF first-pass peak and the image contrast-to-noise ratio were assessed. The method was also evaluated by correlating portal venous perfusion with an independent overall liver function measurement.

RESULTS

The proposed method corrects the distorted AIF with a saturation ratio up to 0.45. The corrected AIF improved hepatic arterial perfusion by -23.4% and portal venous perfusion by 26.9% in a study of 12 patients with liver cancers. The correlation between the mean voxelwise portal venous perfusion and overall liver function measurement was improved by using the corrected AIFs (R(2) = 0.67) compared with the saturated AIFs (R(2) = 0.39).

CONCLUSION

The method is robust for correcting AIF distortion and has the potential to improve quantification of hepatic perfusion for assessment of liver tissue response to treatment in patients with hepatic cancers.

Perfusion MRI using dynamic-susceptibility contrast MRI: quantification issues in patient studies

OBJECTIVES

Measurement of perfusion accurately, noninvasively, and with good spatial resolution offers the chance to characterize abnormal tissue in many clinical conditions. Dynamic-susceptibility contrast (DSC) MRI, also known as bolus-tracking MRI, is a dynamic MRI method to measure perfusion and other related hemodynamic parameters. This review article describes the principles involved in perfusion quantification using DSC-MRI as well as discusses the main issues affecting its quantification in patient studies.

CONCLUSIONS

It is shown that DSC-MRI is a very powerful technique that provides important information regarding cerebral hemodynamics. The relatively high contrast-to-noise ratio, fast acquisition, and wealth of information available have made DSC-MRI the most commonly used MRI technique for the rapid assessment of the brain hemodynamics in clinical investigations. While very important advances have been achieved in the last 2 decades, there are still some remaining limitations that users should be aware of to avoid misinterpretation of the findings and to make the most of the invaluable information provided by perfusion MRI.

Assessment of clinical data of nonlinear stochastic deconvolution versus block-circulant singular value decomposition for quantitative dynamic susceptibility contrast magnetic resonance imaging

Dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) allows the noninvasive assessment of brain hemodynamics alterations by quantifying, via deconvolution, the cerebral blood flow (CBF) and mean transit time (MTT). Singular value decomposition (SVD) and block-circulant SVD (cSVD) are the most widely adopted deconvolution method, although they bear some limitations, including unphysiological oscillations in the residue function and bias in the presence of delay and dispersion between the tissue and the arterial input function. A nonlinear stochastic regularization (NSR) has been proposed, which performs better than SVD and cSVD on simulated data both in the presence and absence of dispersion. Moreover, NSR allows to quantify the dispersion level. Here, cSVD and NSR are compared for the first time on a group of nine patients with severe atherosclerotic unilateral stenosis of internal carotid artery before and after carotid stenting to investigate the effect of arterial dispersion. According to region of interest-based analysis, NSR characterizes the pathologic tissue more accurately than cSVD, thus improving the quality of the information provided to physicians for diagnosis. In fact, in 7 (78%) of the 9 subjects, CBF and MTT maps provided by NSR allow to correctly identify the pathologic hemisphere to the physician. Moreover, by emphasizing the difference between pathologic and healthy tissues, NSR may be successfully used to monitor the subject's recovery after the treatment and/or surgery. NSR also generates dispersion level and non-dispersed CBF and MTT maps. The dispersion level provides information on CBF and MTT estimates reliability and may also be used as a clinical indicator of pathological tissue state complementary to CBF and MTT, thus increasing the clinical information provided by DSC-MRI analysis.

Dynamic MR perfusion imaging: capability for quantitative assessment of disease extent and prediction of outcome for patients with acute pulmonary thromboembolism

PURPOSE

To compare directly the capabilities of multidetector-row computed tomography (MDCT) and MRI for disease severity assessment and outcome prediction for acute pulmonary thromboembolism (APTE) patients.

MATERIALS AND METHODS

Fifty consecutive APTE patients underwent MDCT, MR angiography, dynamic perfusion MRI, treatment and follow-up examination. Pulmonary blood flow (PBF), pulmonary blood volume, and mean transit time maps were generated from perfusion MRI, and all segmental parameters were determined by using region of interest measurements. Receiver operator curve analyses were used to determine the most accurate parameter for diagnosis of the APTE segment. Then, APTE index from perfusion MRI (PE(perfusion MRI) index), right ventricle/left ventricle (RV/LV) diameter ratio and APTE indexes from embolic burdens observed on MDCT (PE(CT) index) and MR angiography (PE(MRA) index) were calculated. Finally, ability to differentiate mortality (n = 8) from survival (n = 42) groups and to predict patient outcome were statistically assessed.

RESULTS

PBF was a significantly more accurate parameter than others (P < 0.05). When feasible threshold value was applied, specificity and accuracy of RV/LV diameter ratio and PE(Perfusion MRI) index were significantly higher than those of PE(CT) and PE(MRA) indexes (P < 0.05). Logistic regression analysis demonstrated that each index was a significant predictor (P < 0.05).

CONCLUSION

Dynamic perfusion MRI can be effective for disease extent assessment and outcome prediction for APTE patients.

A fully automated method for quantitative cerebral hemodynamic analysis using DSC-MRI

Dynamic susceptibility contrast (DSC)-based perfusion analysis from MR images has become an established method for analysis of cerebral blood volume (CBV) in glioma patients. To date, little emphasis has, however, been placed on quantitative perfusion analysis of these patients, mainly due to the associated increased technical complexity and lack of sufficient stability in a clinical setting. The aim of our study was to develop a fully automated analysis framework for quantitative DSC-based perfusion analysis. The method presented here generates quantitative hemodynamic maps without user interaction, combined with automatic segmentation of normal-appearing cerebral tissue. Validation of 101 patients with confirmed glioma after surgery gave mean values for CBF, CBV, and MTT, extracted automatically from normal-appearing whole-brain white and gray matter, in good agreement with literature values. The measured age- and gender-related variations in the same parameters were also in agreement with those in the literature. Several established analysis methods were compared and the resulting perfusion metrics depended significantly on method and parameter choice. In conclusion, we present an accurate, fast, and automatic quantitative perfusion analysis method where all analysis steps are based on raw DSC data only.

Technical aspects of MR perfusion

The most common methods for measuring perfusion with MRI are arterial spin labelling (ASL), dynamic susceptibility contrast (DSC-MRI), and T(1)-weighted dynamic contrast enhancement (DCE-MRI). This review focuses on the latter approach, which is by far the most common in the body and produces measures of capillary permeability as well. The aim is to present a concise but complete overview of the technical issues involved in DCE-MRI data acquisition and analysis. For details the reader is referred to the references. The presentation of the topic is essentially generic and focuses on technical aspects that are common to all DCE-MRI measurements. For organ-specific problems and illustrations, we refer to the other papers in this issue. In Section 1 "Theory" the basic quantities are defined, and the physical mechanisms are presented that provide a relation between the hemodynamic parameters and the DCE-MRI signal. Section 2 "Data acquisition" discusses the issues involved in the design of an optimal measurement protocol. Section 3 "Data analysis" summarizes the steps that need to be taken to determine the hemodynamic parameters from the measured data.

Quantitative pulmonary perfusion magnetic resonance imaging: influence of temporal resolution and signal-to-noise ratio

PURPOSE

To investigate the influence of the contrast-to-noise ratio (CNR) and temporal resolution of 3D dynamic contrast-enhanced magnetic resonance imaging on the quantification of pulmonary perfusion parameters by means of Monte-Carlo simulations and a volunteer study.

METHODS

Quantification of perfusion parameters such as pulmonary blood flow (PBF) and pulmonary blood volume (PBV) was simulated using synthetic data with varying CNR (noise standard deviations ranging from 0% to 25% of the parenchymal signal maximum) and different temporal resolutions from 1 to 5 seconds. Simulation results were compared with perfusion measurements in 9 healthy volunteers (age: 18-31) using dynamic 3D gradient-echo sequences with different k-space acquisition schemes, resulting in different temporal resolutions of 1.1, 1.3, and 2.0 seconds per volume and varying CNR. Lung parenchyma was segmented using a semiautomatic technique, and PBF, PBV, as well as MTT were determined pixelwise using Tikhonov-regularized deconvolution with an optimized L-curve criterion.

RESULTS

The simulations showed a breakdown of the deconvolution algorithm for temporal resolutions lower than 3 s. PBF was increasingly underestimated with decreasing CNR; the temporal resolution had little influence on PBF estimates in the investigated range. PBV, on the other hand, was more dependent on the temporal resolution and showed less, but noticeable influence of the CNR. For low temporal resolutions, PBV was overestimated.In the volunteer study, no significant differences of PBF between the different sequences were found; however, PBV was underestimated by the slowest sequence, in contrast to the simulation results.

CONCLUSION

Both the mathematical simulations and volunteer measurements showed that the temporal resolution has less influence than the CNR on the quantification of PBF. On the other hand, PBV is more influenced by temporal resolution than by CNR. This indicates that the gain in measurement speed that can be obtained by modern acceleration schemes need not be invested in ultra-high temporal resolution. Instead, sequence optimization should aim for a suitable balance of sufficient CNR on the one hand, and sufficient temporal resolution on the other hand, whereas maintaining a high spatial resolution.

[Magnetic resonance imaging of pulmonary perfusion. Technical requirements and diagnostic impact]

With technical improvements in gradient hardware and the implementation of innovative k-space sampling techniques, such as parallel imaging, the feasibility of pulmonary perfusion MRI could be demonstrated in several studies. Dynamic contrast-enhanced 3D gradient echo sequences as used for time-resolved MR angiography have been established as the preferred pulse sequences for lung perfusion MRI. With these techniques perfusion of the entire lung can be visualized with a sufficiently high temporal and spatial resolution. In several trials in patients with acute pulmonary embolism, pulmonary hypertension and airway diseases, the clinical benefit and good correlation with perfusion scintigraphy have been demonstrated. The following review article describes the technical prerequisites, current post-processing techniques and the clinical indications for MR pulmonary perfusion imaging using MRI.

Nonlinear stochastic regularization to characterize tissue residue function in bolus-tracking MRI: assessment and comparison with SVD, block-circulant SVD, and Tikhonov

An accurate characterization of tissue residue function R(t) in bolus-tracking magnetic resonance imaging is of crucial importance to quantify cerebral hemodynamics. R(t) estimation requires to solve a deconvolution problem. The most popular deconvolution method is singular value decomposition (SVD). However, SVD is known to bear some limitations, e.g., R(t) profiles exhibit nonphysiological oscillations and take on negative values. In addition, SVD estimates are biased in presence of bolus delay and dispersion. Recently, other deconvolution methods have been proposed, in particular block-circulant SVD (cSVD) and Tikhonov regularization (TIKH). Here we propose a new method based on nonlinear stochastic regularization (NSR). NSR is tested on simulated data and compared with SVD, cSVD, and TIKH in presence and absence of bolus dispersion. A clinical case in one patient has also been considered. NSR is shown to perform better than SVD, cSVD, and TIKH in reconstructing both the peak and the residue function, in particular when bolus dispersion is considered. In addition, differently from SVD, cSVD, and TIKH, NSR always provides positive and smooth R(t).

Cerebral blood flow estimation from perfusion-weighted MRI using FT-based MMSE filtering method

INTRODUCTION

Perfusion-weighted MRI can be used for estimating blood flow parameters using bolus tracking technique based on dynamic susceptibility contrast MRI. In order to extract flow parameters, several deconvolution techniques have been proposed, of which the singular value decomposition (SVD) and Fourier transform (FT)-based techniques are more popular and widely used. In this work, an FT-based method has been proposed that involves derivation of an optimal shaped filter (defined as a filter function) estimated using minimum mean-squared error (MMSE) technique in the frequency domain. The proposed technique has been compared with the well-established SVD technique using simulation experiments.

SIMULATION METHODS

Simulation was performed in multiple steps. An arterial input function (AIF) was first defined based on a certain blood flow value. The T2* signal change was then derived from this AIF, and noise was added to the signal. Then, a unique and optimal shaped filter function Phi(f) was derived in order to obtain the best estimate of scaled residue function. One way is by minimizing the mean-squared error between the noiseless and noisy scaled residue function, i.e., using an MMSE method. The effect of low and moderate noise and distorted AIF on cerebral blood flow (CBF) estimates was obtained by using FT-based MMSE method. Results were compared with the SVD technique. In this work, SVD technique was assumed to be the standard reference deconvolution technique.

RESULTS AND DISCUSSION

For low-noise condition, the FT-based technique was more stable than the SVD technique, while for moderate noise, both techniques consistently underestimated CBF. SVD technique was found to be more stable in presence of AIF distortions. However, SVD technique was found to be unstable due to AIF delay compared to the FT-based MMSE method. The shaped filter function was found to be sensitive to effect of AIF distortions.

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.

Error analysis of tumor blood flow measurement using dynamic contrast-enhanced data and model-independent deconvolution analysis

We performed error analysis of tumor blood flow (TBF) measurement using dynamic contrast-enhanced data and model-independent deconvolution analysis, based on computer simulations. For analysis, we generated a time-dependent concentration of the contrast agent in the volume of interest (VOI) from the arterial input function (AIF) consisting of gamma-variate functions using an adiabatic approximation to the tissue homogeneity model under various plasma flow (F(p)), mean capillary transit time (T(c)), permeability-surface area product (PS) and signal-to-noise ratio (SNR) values. Deconvolution analyses based on truncated singular value decomposition with a fixed threshold value (TSVD-F), with an adaptive threshold value (TSVD-A) and with the threshold value determined by generalized cross validation (TSVD-G) were used to estimate F(p) values from the simulated concentration-time curves in the VOI and AIF. First, we investigated the relationship between the optimal threshold value and SNR in TSVD-F, and then derived the equation describing the relationship between the threshold value and SNR for TSVD-A. Second, we investigated the dependences of the estimated F(p) values on T(c), PS, the total duration for data acquisition and the shape of AIF. Although TSVD-F with a threshold value of 0.025, TSVD-A with the threshold value determined by the equation derived in this study and TSVD-G could estimate the F(p) values in a similar manner, the standard deviation of the estimates was the smallest and largest for TSVD-A and TSVD-G, respectively. PS did not largely affect the estimates, while T(c) did in all methods. Increasing the total duration significantly improved the variations in the estimates in all methods. TSVD-G was most sensitive to the shape of AIF, especially when the total duration was short. In conclusion, this study will be useful for understanding the reliability and limitation of model-independent deconvolution analysis when applied to TBF measurement using an extravascular contrast agent.

Assessment of bolus injection protocol with appropriate concentration for quantitative assessment of pulmonary perfusion by dynamic contrast-enhanced MR imaging

PURPOSE

To determine the appropriate concentration for quantitative assessment of dynamic contrast-enhanced pulmonary MR imaging.

MATERIALS AND METHODS

A total of 40 consecutive patients with small bronchioalveolar carcinoma underwent perfusion single-photon emission tomography (SPECT) and three-dimensional (3D) dynamic MR imaging with a 3D radiofrequency spoiled gradient-echo sequence. In each patient, 5 mL of contrast media with 0.1, 0.3, and 0.5 mmol/mL were administered at a rate of 5 mL/second. All patients were divided into two groups (<70 kg and > or =70 kg) for assessment of appropriate concentration to quantitatively assess regional perfusion parameter in routine clinical practice. Pulmonary blood flow (PBF) in each protocol was calculated from a signal intensity (SI)-time course curve. Differences and limits of agreement of PBF between dynamic MR imaging (PBF(MR)) using three different concentrations and perfusion SPECT (PBF(SPECT)) were statistically compared in both patient groups.

RESULTS

PBF(MR) using 0.3 mmol/mL in the <70-kg group and 0.5 mmol/mL in the > or =70-kg group showed no significant difference compared with PBF(SPECT) (P > 0.05). Limits of agreements in 0.3 mmol/mL in the <70-kg group and 0.5 mmol/mL in the > or =70-kg group were smaller than those of the other concentrations and small enough for clinical purposes.

CONCLUSION

Appropriate concentrations provide accurate and reproducible assessments of regional pulmonary perfusion parameters on 3D dynamic MR perfusion imaging. We suggest using 5 mL of contrast media with 0.3 mmol/mL for patients weighing less than 70 kg and 0.5 mmol/mL for patients weighing 70 kg or more.

Primary pulmonary hypertension: 3D dynamic perfusion MRI for quantitative analysis of regional pulmonary perfusion

OBJECTIVE

The purpose of this study was to determine whether quantitative pulmonary perfusion parameters obtained from 3D dynamic contrast-enhanced MR perfusion data can be used to assess the severity of primary pulmonary hypertension (PPH) as indicated by pulmonary vascular resistance (PVR) and mean pulmonary artery pressure (MPAP).

CONCLUSION

Three-dimensional dynamic contrast-enhanced MRI has potential for assessment of disease severity as indicated by PVR and MPAP in patients with PPH.

Pixel-by-pixel deconvolution of bolus-tracking data: optimization and implementation

Quantification of haemodynamic parameters with a deconvolution analysis of bolus-tracking data is an ill-posed problem which requires regularization. In a previous study, simulated data without structural errors were used to validate two methods for a pixel-by-pixel analysis: standard-form Tikhonov regularization with either the L-curve criterion (LCC) or generalized cross validation (GCV) for selecting the regularization parameter. However, problems of image artefacts were reported when the methods were applied to patient data. The aim of this study was to investigate the nature of these problems in more detail and evaluate strategies of optimization for routine application in the clinic. In addition we investigated to which extent the calculation time of the algorithm can be minimized. In order to ensure that the conclusions are relevant for a larger range of clinical applications, we relied on patient data for evaluation of the algorithms. Simulated data were used to validate the conclusions in a more quantitative manner. We conclude that the reported problems with image quality can be removed by appropriate optimization of either LCC or GCV. In all examples this could be achieved with LCC without significant perturbation of the values in pixels where the regularization parameter was originally selected accurately. GCV could not be optimized for the renal data, and in the CT data only at the cost of image resolution. Using the implementations given, calculation times were sufficiently short for routine application in the clinic.

Technical aspects of perfusion-weighted imaging

There is increasing interest in using diffusion-weighted (DWI) MR imaging and perfusion-weighted MR imaging (PWI) to assist clinical decision-making in the management of acute stroke patients. Larger PWI than DWI lesions have been speculated to represent potentially salvageable tissue that is at risk of infarction unless nutritive flow is restored and presence of these mismatches have been proposed as inclusion criteria for identifying patients most likely to benefit from therapeutic intervention. Understanding the technical aspects of PWI may improve comprehension of the capabilities and limitations of this technique.

DSC perfusion MRI—Quantification and reduction of systematic errors arising in areas of reduced cerebral blood flow

Dynamic susceptibility contrast (DSC)-MRI is commonly used to measure cerebral perfusion in acute ischemic stroke. Quantification of perfusion parameters involves deconvolution of the tissue concentration-time curves with an arterial input function (AIF), typically with the use of singular value decomposition (SVD). To mitigate the effects of noise on the estimated cerebral blood flow (CBF), a regularization parameter or threshold is used. Often a single global threshold is applied to every voxel, and its value has a dramatic effect on the CBF values obtained. When a single global threshold was applied to simulated concentration-time curves produced using exponential, triangular, and boxcar residue functions, significant systematic errors were found in the measured perfusion parameters. We estimate the errors obtained for different sampling intervals and signal-to-noise ratios (SNRs), and discuss the source of the systematic error. We present a method that partially corrects for the systematic error in the presence of an exponential residue function by applying a linear fit, which removes underestimates of long mean transit time (MTT) and overestimates of short MTT. For example, the correction reduced the error at a temporal resolution of 2.5 s and an SNR of 30 from 29.1% to 11.7%. However, the error is largest in the presence of noise and at MTTs that are likely to be encountered in areas of hypoperfusion; furthermore, even though it is reduced, it cannot be corrected for exactly.

Effect of x-ray tube current on the accuracy of cerebral perfusion parameters obtained by CT perfusion studies

The purpose of this study was to investigate the effect of x-ray tube current on the accuracy of cerebral perfusion parameters obtained by CT perfusion studies using multi-detector row CT (MDCT). Following the standard CT perfusion study protocol, continuous (cine) scans (1 s/rotation x 60 s) consisting of four 5 mm thick contiguous slices were performed using an MDCT scanner with a tube voltage of 80 kVp and a tube current of 200 mA. We generated the simulated images with tube currents of 50 mA, 100 mA and 150 mA by adding the corresponding noise to the raw scan data of the original image acquired above using a noise simulation tool. From the original and simulated images, we generated the functional images of cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transit time (MTT) in seven patients with cerebrovascular disease, and compared the correlation coefficients (CCs) between the perfusion parameter values obtained from the original and simulated images. The coefficients of variation (CVs) in the white matter were also compared. The CC values deteriorated with decreasing tube current. There was a significant difference between 50 mA and 100 mA for all perfusion parameters. The CV values increased with decreasing tube current. There were significant differences between 50 mA and 100 mA and between 100 mA and 150 mA for CBF. For CBV and MTT, there was also a significant difference between 150 mA and 200 mA. This study will be useful for understanding the effect of x-ray tube current on the accuracy of cerebral perfusion parameters obtained by CT perfusion studies using MDCT, and for selecting the tube current.

Advantages of frequency-domain modeling in dynamic-susceptibility contrast magnetic resonance cerebral blood flow quantification

In dynamic-susceptibility contrast magnetic resonance perfusion imaging, the cerebral blood flow (CBF) is estimated from the tissue residue function obtained through deconvolution of the contrast concentration functions. However, the reliability of CBF estimates obtained by deconvolution is sensitive to various distortions including high-frequency noise amplification. The frequency-domain Fourier transform-based and the time-domain singular-value decomposition-based (SVD) algorithms both have biases introduced into their CBF estimates when noise stability criteria are applied or when contrast recirculation is present. The recovery of the desired signal components from amid these distortions by modeling the residue function in the frequency domain is demonstrated. The basic advantages and applicability of the frequency-domain modeling concept are explored through a simple frequency-domain Lorentzian model (FDLM); with results compared to standard SVD-based approaches. The performance of the FDLM method is model dependent, well representing residue functions in the exponential family while less accurately representing other functions.

Wavelet-based noise reduction for improved deconvolution of time-series data in dynamic susceptibility-contrast MRI

Dynamic susceptibility-contrast (DSC) MRI requires deconvolution to retrieve the tissue residue function R(t) and the cerebral blood flow (CBF). In this study, deconvolution of time-series data was performed by wavelet-transform-based denoising combined with the Fourier transform (FT). Traditional FT-based deconvolution of noisy data requires frequency-domain filtering, often leading to excessive smoothing of the recovered signal. In the present approach, only a low degree of regularisation was employed while the major noise reduction was accomplished by wavelet transformation of data and Wiener-like filtering in the wavelet space. After inverse wavelet transform, the estimate of CBF.R(t) was obtained. DSC-MRI signal-versus-time curves (signal-to-noise ratios 40 and 100) were simulated, corresponding to CBF values in the range 10-60 ml/(min 100 g). Three shapes of the tissue residue function were investigated. The technique was also applied to six volunteers. Simulations showed CBF estimates with acceptable accuracy and precision, as well as independence of any time shift between the arterial input function and the tissue concentration curve. The grey-matter to white-matter CBF ratio in volunteers was 2.4+/-0.2. The proposed wavelet/FT deconvolution is robust and can be implemented into existing perfusion software. CBF maps from healthy volunteers showed high quality.

Reassessing the clinical efficacy of two MR quantitative DSC PWI CBF algorithms following cross-calibration with PET images

Clinical cerebral blood flow (CBF) maps generated through dynamic- susceptibility contrast (DSC) magnetic resonance (MR) perfusion imaging are currently cross-calibrated with PET studies. The cross-calibration is achieved by rescaling the MR CBF values so that normal white matter CBF corresponds to 22 ml/100 g/min. Examples are provided in this paper to show how this rescaling procedure changes both the clinical interpretation of CBF maps and the manner by which the performance of a given deconvolution algorithm should be assessed. (i) Singular-value decomposition-based (SVD) algorithms produce absolute CBF estimates that are inherently under-estimated for all tissue mean transit times (MTT) but, after rescaling, will generate CBF maps that are over-estimated for MTT >4.8 s. (ii) In principle, frequency-domain modelling techniques are expected to be inherently less sensitive to contrast recirculation biases than the time-domain SVD algorithms. However, it is shown that both CBF algorithms become greatly less sensitive to distortions from recirculation after clinical cross-calibration through rescaling has been performed. It is concluded that, when rescaling procedures are employed, it is relatively more important to develop deconvolution algorithms that produce CBF estimates with accuracies that vary little with MTT than to produce algorithms that provide inherently more accurate CBF estimates, but whose relative accuracy varies significantly with MTT.

Tracer delay correction of cerebral blood flow with dynamic susceptibility contrast-enhanced MRI

Cerebral blood flow (CBF) and vascular mean transit time (MTT) can be determined by dynamic susceptibility contrast-enhanced magnetic resonance imaging and deconvolution with an arterial input function. However, deconvolution by a singular value decomposition (SVD) method is sensitive to the tracer delay that often occurs in patients with cerebrovascular disease. We investigated the effect of tracer delay on CBF determined by SVD deconvolution. Simulation study showed that underestimation of CBF due to tracer delay was larger for shorter MTTs. We developed a delay correction method that determines tracer delay by means of least-squares fitting pixel-by-pixel. The corrected CBF was determined by SVD deconvolution after time-shifting of the measured concentration curve. The simulations showed that the corrected CBF was insensitive to tracer delay irrespective of the vascular model, although CBF fluctuation increased slightly. We applied the delay correction to the CBF and MTT images acquired for nine patients with hyperacute stroke and unilateral occlusion of the middle cerebral artery. We found in some patients that the delay correction modulated the contrast of CBF and MTT images. For hyperacute stroke patients, tracer delay correction is essential to obtain reliable perfusion image when SVD deconvolution is used.

Effect of Regional Tracer Delay on CBF in Healthy Subjects Measured with Dynamic Susceptibility Contrast-Enhanced MRI: Comparison with 15O-PET

PURPOSE

Deconvolution based on truncated singular value decomposition (SVD deconvolution) is a promising method for measuring cerebral blood flow (CBF) with dynamic susceptibility contrast-enhanced magnetic resonance imaging (DSC-MRI), but it has proved extremely sensitive to tracer delay. The purpose of this study was to investigate the effect of regional tracer delay on CBF determined by SVD deconvolution (SVD-CBF). SVD-CBFs with and without correction for the delay were compared with CBF measured by positron emission tomography (PET-CBF), which is regarded as the gold standard for quantification of CBF.

METHODS

Perfusion MRI and PET were performed on seven healthy men. In the PET study, the CBF image was obtained with bolus injection of H2(15)O and continuous arterial sampling. In the DSC-MRI study with bolus injection of Gd-based contrast agent, dynamic perfusion data were obtained with a 1.5T scanner at 1-s intervals by means of gradient-echo echo-planar imaging. CBF was determined by the SVD deconvolution method with and without correction for the tracer delay. Region-of-interest measurements were obtained in the gray matter (cerebral cortex in the middle cerebral artery territory) and white matter (centrum semiovale).

RESULTS

Tracer delay was significantly longer in white matter than in gray matter (1.45+/-0.61 s vs. 0.59+/-0.35 s, P<0.01). Correction for the delay increased SVD-CBF in the white matter and consequently reduced the gray-to-white SVD-CBF ratio. The uncorrected gray-to-white SVD-CBF ratio was significantly larger than that of PET-CBF (3.33+/-0.66 vs. 2.54+/-0.49, P<0.01). However, the gray-to-white delay-corrected SVD-CBF ratio did not differ significantly from that of PET-CBF (2.83+/-0.31 vs. 2.54+/-0.49, P=0.10).

CONCLUSION

The tracer delay in DSC-MRI causes errors in CBF estimates, even in healthy persons, and therefore should be corrected for when delay-sensitive deconvolution, such as SVD deconvolution, is used.

Quantitative assessment of regional pulmonary perfusion in the entire lung using three-dimensional ultrafast dynamic contrast-enhanced magnetic resonance imaging: Preliminary experience in 40 subjects

PURPOSE

To assess regional differences in quantitative pulmonary perfusion parameters, i.e., pulmonary blood flow (PBF), mean transit time (MTT), and pulmonary blood volume (PBV) in the entire lung on a pixel-by-pixel basis in normal volunteers and pulmonary hypertension patients.

MATERIALS AND METHODS

Three-dimensional ultrafast dynamic contrast-enhanced MR imaging was performed in 15 normal volunteers and 25 patients with pulmonary hypertension. From the signal intensity-time course curves, PBF, MTT and PBV maps were generated using deconvolution analysis, indicator dilution theories, and the central volume principle, on a pixel-by-pixel basis. From pulmonary perfusion parameter maps of normal volunteers and pulmonary hypertension patients, regional PBF, MTT, and PBV were statistically evaluated.

RESULTS

Regional PBF, MTT, and PBV showed significant differences in the gravitational and isogravitational directions (P < 0.05). The quantitative pulmonary perfusion parameter maps demonstrated significant differences between normal volunteers and pulmonary hypertension patients (P < 0.05).

CONCLUSION

Three-dimensional ultrafast dynamic contrast-enhanced MR imaging is feasible for the assessment of regional quantitative pulmonary perfusion parameters in the entire lung on a pixel-by-pixel basis in normal volunteers and pulmonary hypertension patients.

Assessment of perfusion by dynamic contrast-enhanced imaging using a deconvolution approach based on regression and singular value decomposition

The assessment of tissue perfusion by dynamic contrast-enhanced (DCE) imaging involves a deconvolution process. For analysis of DCE imaging data, we implemented a regression approach to select appropriate regularization parameters for deconvolution using the standard and generalized singular value decomposition methods. Monte Carlo simulation experiments were carried out to study the performance and to compare with other existing methods used for deconvolution analysis of DCE imaging data. The present approach is found to be robust and reliable at the levels of noise commonly encountered in DCE imaging, and for different models of the underlying tissue vasculature. The advantages of the present method, as compared with previous methods, include its efficiency of computation, ability to achieve adequate regularization to reproduce less noisy solutions, and that it does not require prior knowledge of the noise condition. The proposed method is applied on actual patient study cases with brain tumors and ischemic stroke, to illustrate its applicability as a clinical tool for diagnosis and assessment of treatment response.

Defining a local arterial input function for perfusion MRI using independent component analysis

Quantification of cerebral blood flow (CBF) using dynamic-susceptibility contrast MRI relies on the deconvolution of the arterial input function (AIF), which is commonly estimated from the signal changes in a major artery. However, it has been shown that the presence of bolus delay/dispersion between the artery and the tissue of interest can be a significant source of error. These effects could be minimized if a local AIF were used, although the measurement of a local AIF can be problematic. This work describes a new methodology to define a local AIF using independent component analysis (ICA). The methodology was tested on data from patients with various cerebrovascular abnormalities and compared to the conventional approach of using a global AIF. The new methodology produced higher CBF and shorter mean transit time values (compared to the global AIF case) in areas with distorted AIFs, suggesting that the effects of delay/dispersion are minimized. The minimization of these effects using the calculated local AIF should lead to a more accurate quantification of CBF, which can have important implications for diagnosis and management of patients with cerebral ischemia.

Effects of echo time variation on perfusion assessment using dynamic susceptibility contrast MR imaging at 3 tesla

The implications of changing the echo time of a gradient-echo echo planar imaging sequence applied to dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) for perfusion imaging at 3T were investigated. Four echo times in the range of 21 to 45 ms were examined in a total of 17 patients who received a dose of 0.1 mmol/kg bodyweight Gadobutrol (Gadovist, 1.0 mmol/ml). As the primary optimization parameter, the concentration-to-noise ratio (SNRc) was selected as it takes effects of variations in baseline as well as in signal drop into account. In an analysis of gray matter, white matter and arterial regions of interest, SNRc showed the highest values for the shortest applied echo time in all cases. Maps of regional cerebral blood volume (rCBV) and blood flow (rCBF) were calculated using deconvolution based on singular value decomposition. The quality of rCBF and rCBV images was judged to be good or excellent in all cases, independent of the echo time. Calculated gray matter/white matter ratios of rCBF and rCBV displayed no significant dependence on the applied echo time. Considering the better SNRc and arterial signal saturation aspects, we found that the shortest investigated echo time was the superior one. We thus suggest that short echo times should be applied, taking technical limitations and clinical demands into consideration.

Choice of the regularization parameter for perfusion quantification with MRI

Truncated singular value decomposition (TSVD) is an effective method for the deconvolution of dynamic contrast enhanced (DCE) MRI. Two robust methods for the selection of the truncation threshold on a pixel-by-pixel basis--generalized cross validation (GCV) and the L-curve criterion (LCC)--were optimized and compared to paradigms in the literature. GCV and LCC were found to perform optimally when applied with a smooth version of TSVD, known as standard form Tikhonov regularization (SFTR). The methods lead to improvements in the estimate of the residue function and of its maximum, and converge properly with SNR. The oscillations typically observed in the solution vanish entirely, and perfusion is more accurately estimated at small mean transit times. This results in improved image contrast and increased sensitivity to perfusion abnormalities, at the cost of 1-2 min in calculation time and hyperintense clusters in the image. Preliminary experience with clinical data suggests that the latter problem can be resolved using spatial continuity and/or hybrid thresholding methods. In the simulations GCV and LCC are equivalent in terms of performance, but GCV thresholding is faster.

Aspects on the accuracy of cerebral perfusion parameters obtained by dynamic susceptibility contrast MRI: a simulation study

Several studies have indicated that deconvolution based on singular value decomposition (SVD) is a robust concept for retrieval of cerebral blood flow in dynamic susceptibility contrast (DSC) MRI. However, the behavior of the technique under typical experimental conditions has not been completely investigated. In the present study, cerebral perfusion was simulated using different temporal resolutions, different signal-to-noise ratios (S/Ns), different shapes of the arterial input function (AIF), different signal drops, and different cut-off levels in the SVD deconvolution. Using Zierler's area-to-height relationship in combination with the central volume theorem, calculations of regional cerebral blood volume (rCBV), regional cerebral blood flow (rCBF), and regional mean transit time (rMTT) were accomplished, based on simulated DSC-MRI signal curves corresponding to artery, gray matter (GM), white matter (WM), and ischemic tissue. Gaussian noise was added to the noise-free signal curves to generate different S/Ns. We studied image time intervals of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 s, as well as different degrees of signal decrease. The singular-value threshold in the SVD procedure and the shape of the AIF were also varied. Increased rCBF was seen when noise was added, especially for rCBF in WM at the larger image time intervals. The rCBF showed large standard deviations using a low threshold value. A prolonged time interval led to a lower absolute value of rCBF both in GM and WM, and a low/broad AIF also underestimated the rCBF. When a larger maximal signal decrease was assumed, smaller standard deviations were observed. No systematic change of the average rCBV was observed with increasing noise or with increasing image time interval. At S/N = 40, a low cut-off value resulted in an rCBF that was closer to the true value. Furthermore, at low S/N it was difficult to differentiate ischemic tissue from WM.

Cerebral perfusion assessment by bolus tracking using hyperpolarized13C

Cerebral perfusion was assessed with 13C MRI in a rat model after intravenous injections of the 13C-labeled compound bis-1,1-(hydroxymethyl)-1-13C-cyclopropane-D8 in aqueous solutions hyperpolarized by dynamic nuclear polarization (DNP). Since the tracer acted as a direct signal source, several of the problems associated with techniques based on traditional dynamic susceptibility contrast (DSC) MRI contrast agents were avoided. Maps of cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT) were calculated. The MTT was determined to be 2.8 +/- 0.8 sec. However, arterial partial-volume effects in the animal model prevented accurate absolute quantification of CBF and CBV. It was demonstrated that depolarization of the hyperpolarized 13C tracer via relaxation and the imaging sequence had little influence on CBF assessment when the time resolution of the imaging sequence was short compared to the MTT. However, CBV and MTT were increasingly underestimated as MTT or the depolarization rate increased if depolarization was not taken into account. With a modified bolus-tracking theory depolarization could be compensated for, assuming that the depolarization rate was known. Three separate compensation methods were investigated experimentally and by numerical simulations.

Deconvolution of dynamic contrast-enhanced MRI data by linear inversion: Choice of the regularization parameter

Truncated singular value decomposition (TSVD) is an effective method for the deconvolution of dynamic contrast-enhanced MRI. Two robust methods for the selection of the truncation threshold on a pixel-by-pixel basis--generalized cross validation (GCV) and the L-curve criterion (LCC)--were optimized and compared to paradigms in the literature. The methods lead to improvements in the estimate of the residue function and of its maximum and converge properly with SNR. The oscillations typically observed in the solution vanish entirely and perfusion is more accurately estimated at small mean transit times. This results in improved image contrast and increased sensitivity to perfusion abnormalities, at the cost of 1-2 min in calculation time and isolated instabilities in the image. It is argued that the latter problem may be resolved by optimization. Simulated results for GCV and LCC are equivalent in terms of performance, but GCV is faster.