Block-circulant Singular Value Decomposition Research Articles

Investigating cerebral perfusion with high resolution hyperpolarized [1-13 C]pyruvate MRI.

To investigate high-resolution hyperpolarized (HP) 13 C pyruvate MRI for measuring cerebral perfusion in the human brain. HP [1-13 C]pyruvate MRI was acquired in five healthy volunteers with a multi-resolution EPI sequence with 7.5 × 7.5 mm2 resolution for pyruvate. Perfusion parameters were calculated from pyruvate MRI using block-circulant singular value decomposition and compared to relative cerebral blood flow calculated from arterial spin labeling (ASL). To examine regional perfusion patterns, correlations between pyruvate and ASL perfusion were performed for whole brain, gray matter, and white matter voxels. High resolution 7.5 × 7.5 mm2 pyruvate images were used to obtain relative cerebral blood flow (rCBF) values that were significantly positively correlated with ASL rCBF values (r = 0.48, 0.20, 0.28 for whole brain, gray matter, and white matter voxels respectively). Whole brain voxels exhibited the highest correlation between pyruvate and ASL perfusion, and there were distinct regional patterns of relatively high ASL and low pyruvate normalized rCBF found across subjects. Acquiring HP 13 C pyruvate metabolic images at higher resolution allows for finer spatial delineation of brain structures and can be used to obtain cerebral perfusion parameters. Pyruvate perfusion parameters were positively correlated to proton ASL perfusion values, indicating a relationship between the two perfusion measures. This HP 13 C study demonstrated that hyperpolarized pyruvate MRI can assess cerebral metabolism and perfusion within the same study.

Probability maps classify ischemic stroke regions more accurately than CT perfusion summary maps

ObjectivesTo compare single parameter thresholding with multivariable probabilistic classification of ischemic stroke regions in the analysis of computed tomography perfusion (CTP) parameter maps.MethodsPatients were included from two multicenter trials and were divided into two groups based on their modified arterial occlusive lesion grade. CTP parameter maps were generated with three methods—a commercial method (ISP), block-circulant singular value decomposition (bSVD), and non-linear regression (NLR). Follow-up non-contrast CT defined the follow-up infarct region. Conventional thresholds for individual parameter maps were established with a receiver operating characteristic curve analysis. Probabilistic classification was carried out with a logistic regression model combining the available CTP parameters into a single probability.ResultsA total of 225 CTP data sets were included, divided into a group of 166 patients with successful recanalization and 59 with persistent occlusion. The precision and recall of the CTP parameters were lower individually than when combined into a probability. The median difference [interquartile range] in mL between the estimated and follow-up infarct volume was 29/23/23 [52/50/52] (ISP/bSVD/NLR) for conventional thresholding and was 4/6/11 [31/25/30] (ISP/bSVD/NLR) for the probabilistic classification.ConclusionsMultivariable probability maps outperform thresholded CTP parameter maps in estimating the infarct lesion as observed on follow-up non-contrast CT. A multivariable probabilistic approach may harmonize the classification of ischemic stroke regions.Key Points• Combining CTP parameters with a logistic regression model increases the precision and recall in estimating ischemic stroke regions.• Volumes following from a probabilistic analysis predict follow-up infarct volumes better than volumes following from a threshold-based analysis.• A multivariable probabilistic approach may harmonize the classification of ischemic stroke regions.

Non-parametric deconvolution using Bézier curves for quantification of cerebral perfusion in dynamic susceptibility contrast MRI

ObjectiveDeconvolution is an ill-posed inverse problem that tends to yield non-physiological residue functions R(t) in dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). In this study, the use of Bézier curves is proposed for obtaining physiologically reasonable residue functions in perfusion MRI.Materials and methodsCubic Bézier curves were employed, ensuring R(0) = 1, bounded-input, bounded-output stability and a non-negative monotonically decreasing solution, resulting in 5 parameters to be optimized. Bézier deconvolution (BzD), implemented in a Bayesian framework, was tested by simulation under realistic conditions, including effects of arterial delay and dispersion. BzD was also applied to DSC-MRI data from a healthy volunteer.ResultsBézier deconvolution showed robustness to different underlying residue function shapes. Accurate perfusion estimates were observed, except for boxcar residue functions at low signal-to-noise ratio. BzD involving corrections for delay, dispersion, and delay with dispersion generally returned accurate results, except for some degree of cerebral blood flow (CBF) overestimation at low levels of each effect. Maps of mean transit time and delay were markedly different between BzD and block-circulant singular value decomposition (oSVD) deconvolution.DiscussionA novel DSC-MRI deconvolution method based on Bézier curves was implemented and evaluated. BzD produced physiologically plausible impulse response, without spurious oscillations, with generally less CBF underestimation than oSVD.

Variation in arterial input function in a large multicenter computed tomography perfusion study

ObjectivesTo report the variation in computed tomography perfusion (CTP) arterial input function (AIF) in a multicenter stroke study and to assess the impact this has on CTP results.MethodsCTP datasets from 14 different centers were included from the DUtch acute STroke (DUST) study. The AIF was taken as a direct measure to characterize contrast bolus injection. Statistical analysis was applied to evaluate differences in amplitude, area under the curve (AUC), bolus arrival time (BAT), and time to peak (TTP). To assess the clinical relevance of differences in AIF, CTP acquisitions were simulated with a realistic anthropomorphic digital phantom. Perfusion parameters were extracted by CTP analysis using commercial software (IntelliSpace Portal (ISP), version 10.1) as well as an in-house method based on block-circulant singular value decomposition (bSVD).ResultsA total of 1422 CTP datasets were included, ranging from 6 to 322 included patients per center. The measured values of the parameters used to characterize the AIF differed significantly with approximate interquartile ranges of 200–750 HU for the amplitude, 2500–10,000 HU·s for the AUC, 0–17 s for the BAT, and 10–26 s for the TTP. Mean infarct volumes of the phantom were significantly different between centers for both methods of perfusion analysis.ConclusionsAlthough guidelines for the acquisition protocol are often provided for centers participating in a multicenter study, contrast medium injection protocols still vary. The resulting volumetric differences in infarct core and penumbra may impact clinical decision making in stroke diagnosis.Key Points• The contrast medium injection protocol may be different between stroke centers participating in a harmonized multicenter study.• The contrast medium injection protocol influences the results of X-ray computed tomography perfusion imaging.• The contrast medium injection protocol can impact stroke diagnosis and patient selection for treatment.

Stable spline deconvolution for dynamic susceptibility contrast MRI.

To present the stable spline (SS) deconvolution method for the quantification of the cerebral blood flow (CBF) from dynamic susceptibility contrast MRI. The SS method was compared with both the block-circulant singular value decomposition (oSVD) and nonlinear stochastic regularization (NSR) methods. oSVD is one of the most popular deconvolution methods in dynamic susceptibility contrast MRI (DSC-MRI). NSR is an alternative approach that we proposed previously. The three methods were compared using simulated data and two clinical data sets. The SS method correctly reconstructed the dispersed residue function and its peak in presence of dispersion, regardless of the delay. In absence of dispersion, SS performs similarly to oSVD and does not correctly reconstruct the residue function and its peak. SS and NSR better differentiate healthy and pathologic CBF values compared with oSVD in all simulated conditions. Using acquired data, SS and NSR provide more clinically plausible and physiological estimates of the residue function and CBF maps compared with oSVD. The SS method overcomes some of the limitations of oSVD, such as unphysiological estimates of the residue function and NSR, the latter of which is too computationally expensive to be applied to large data sets. Thus, the SS method is a valuable alternative for CBF quantification using DSC-MRI data. Magn Reson Med 78:1801-1811, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Fast nonlinear regression method for CT brain perfusion analysis

Although computed tomography (CT) perfusion (CTP) imaging enables rapid diagnosis and prognosis of ischemic stroke, current CTP analysis methods have several shortcomings. We propose a fast nonlinear regression method with a box-shaped model (boxNLR) that has important advantages over the current state-of-the-art method, block-circulant singular value decomposition (bSVD). These advantages include improved robustness to attenuation curve truncation, extensibility, and unified estimation of perfusion parameters. The method is compared with bSVD and with a commercial SVD-based method. The three methods were quantitatively evaluated by means of a digital perfusion phantom, described by Kudo etal. and qualitatively with the aid of 50 clinical CTP scans. All three methods yielded high Pearson correlation coefficients ([Formula: see text]) with the ground truth in the phantom. The boxNLR perfusion maps of the clinical scans showed higher correlation with bSVD than the perfusion maps from the commercial method. Furthermore, it was shown that boxNLR estimates are robust to noise, truncation, and tracer delay. The proposed method provides a fast and reliable way of estimating perfusion parameters from CTP scans. This suggests it could be a viable alternative to current commercial and academic methods.

Bayesian estimation of cerebral perfusion using reduced-contrast-dose dynamic susceptibility contrast perfusion at 3T.

DSC perfusion has been increasingly used in conjunction with other contrast-enhanced MR applications and therefore there is need for contrast-dose reduction when feasible. The purpose of this study was to establish the feasibility of reduced-contrast-dose brain DSC perfusion by using a probabilistic Bayesian method and to compare the results with the commonly used singular value decomposition technique. Half-dose (0.05-mmol/kg) and full-dose (0.1-mmol/kg) DSC perfusion studies were prospectively performed in 20 patients (12 men; 34-70 years of age) by using a 3T MR imaging scanner and a gradient-EPI sequence (TR/TE, 1450/22 ms; flip angle, 90°). All DSC scans were processed with block circulant singular value decomposition and Bayesian probabilistic methods. SNR analysis was performed in both half-dose and full-dose groups. The CBF, CBV, and MTT maps from both full-dose and half-dose scans were evaluated qualitatively and quantitatively in both WM and GM on coregistered perfusion maps. Statistical analysis was performed by using a t test, regression, and Bland-Altman analysis. The SNR was significantly (P < .0001) lower in the half-dose group with 32% and 40% reduction in GM and WM, respectively. In the half-dose group, the image-quality scores were significantly higher in Bayesian-derived CBV (P = .02) and MTT (P = .004) maps in comparison with block circulant singular value decomposition. Quantitative values of CBF, CBV, and MTT in Bayesian-processed data were comparable and without a statistically significant difference between the half-dose and full-dose groups. The block circulant singular value decomposition-derived half-dose perfusion values were significantly different from those of the full-dose group both in GM (CBF, P < .001; CBV, P = .02; MTT, P = .02) and WM (CBF, P < .001; CBV, P = .003; MTT, P = .01). Reduced-contrast-dose (0.05-mmol/kg) DSC perfusion of the brain is feasible at 3T by using the Bayesian probabilistic method with quantitative results comparable with those of the full-dose protocol.

Perfusion quantification by model-free arterial spin labeling using nonlinear stochastic regularization deconvolution

Quantification of cerebral blood flow can be accomplished by model-free arterial spin labeling using the quantitative STAR labeling of arterial regions (QUASAR) sequence. The required deconvolution is normally based on block-circulant singular value decomposition (cSVD)/oscillation SVD (oSVD), an algorithm associated with nonphysiological residue functions and potential effects of arterial dispersion. The aim of this work was to amend this by implementing nonlinear stochastic regularization (NSR) deconvolution, previously used to retrieve realistic residue functions in dynamic susceptibility contrast MRI. To characterize the residue function in model-free arterial spin labeling, and possibly to improve absolute cerebral blood flow quantification, NSR was applied to deconvolution of QUASAR data. For comparison, SVD-based deconvolution was also employed. Residue function characteristics and cerebral blood flow values from 10 volunteers were obtained. Simulations were performed to support the in vivo results. NSR was able to resolve realistic residue functions in contrast to the SVD-based methods. Mean cerebral blood flow estimates in gray matter were 36.6 ± 2.6, 28.6 ± 3.3, 40.9 ± 3.6, and 42.9 ± 3.9 mL/100 g/min for cSVD, oSVD, NSR, and NSR with correction for arterial dispersion, respectively. In simulations, the NSR-based perfusion estimates showed better accuracy than the SVD-based approaches. Perfusion quantification by model-free arterial spin labeling is evidently dependent on the selected deconvolution method, and NSR is a feasible alternative to SVD-based methods.

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.

Cerebellar and lobar blood flow in schizophrenia: A perfusion weighted imaging study

It is still not clear whether brain hemodynamics plays a role in the functional and structural alterations in schizophrenia, since prior imaging studies showed conflicting findings. In this study we non-invasively explored cerebral and cerebellar lobe perfusion in the largest population of participants with schizophrenia thus far studied with perfusion-weighted imaging (PWI). Forty-seven participants affected by schizophrenia and 29 normal controls were recruited. PWI images were acquired following the intravenous injection of a paramagnetic contrast agent. Regional cerebral blood volume (CBV), blood flow (rCBF), and mean transit time (MTT) were obtained with the block-Circulant Singular Value Decomposition (cSVD) for frontal, temporal, parietal, occipital, and cerebellar lobes, bilaterally. Perfusion parameters were separately obtained for both gray and white matter in each lobe. Subjects with schizophrenia showed no significant differences in perfusion parameters when compared with controls. Interestingly, inverse correlations between age at onset and occipital, frontal and cerebellar MTT and between length of illness and frontal CBV were found. Preserved cerebral and cerebellar perfusion in our chronic population may in part be due to the effects of antipsychotic treatment which may have normalized blood volume and flow. Hypoperfusion in relation to chronicity, particularly in the frontal lobe, has been observed in accordance with earlier studies using positron emission tomography.

Susceptibility of Tmax to Tracer Delay on Perfusion Analysis: Quantitative Evaluation of Various Deconvolution Algorithms Using Digital Phantoms

The time-to-maximum of the tissue residue function (T(max)) perfusion index has proven very predictive of infarct growth in large clinical trials, yet its dependency on simple tracer delays remains unknown. Here, we determine the dependency of computed tomography (CT) perfusion (CTP) T(max) estimates on tracer delay using a range of deconvolution techniques and digital phantoms. Digital phantom data sets simulating the tracer delay were created from CTP data of six healthy individuals, in which time frames of the left cerebral hemisphere were shifted forward and backward by up to ±5 seconds. These phantoms were postprocessed with three common singular value decomposition (SVD) deconvolution algorithms-standard SVD (sSVD), block-circulant SVD (bSVD), and delay-corrected SVD (dSVD)-with an arterial input function (AIF) obtained from the right middle cerebral artery (MCA). The T(max) values of the left hemisphere were compared among different tracer delays and algorithms by a region of interest-based analysis. The T(max) values by sSVD were positively correlated with 'positive shifts' but unchanged with 'negative shifts,' those by bSVD had an excellent positive linear correlation with both positive and negative shifts, and those by dSVD were relatively constant, although slightly increased with the positive shifts. The T(max) is a parameter highly dependent on tracer delays and deconvolution algorithm.

Difference in Tracer Delay–induced Effect among Deconvolution Algorithms in CT Perfusion Analysis: Quantitative Evaluation with Digital Phantoms

Institutional review board approval and informed consent were obtained. The purpose was to evaluate the differences in tracer delay-induced effects of various deconvolution algorithms for computed tomographic (CT) perfusion imaging by using digital phantoms created from actual source data. Three methods of singular value decomposition (SVD) were evaluated. For standard SVD (sSVD), the delays induced significant errors in cerebral blood flow and mean transit time. In contrast, for block-circulant SVD (bSVD), these values remained virtually unchanged, whereas for delay-corrected SVD (dSVD), mild changes were observed. bSVD was superior to sSVD and dSVD for avoiding the tracer delay-induced effects in CT perfusion imaging.

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).

Reference-based Maximum Upslope: A CBF Quantification Method without Using Arterial Input Function in Dynamic Susceptibility Contrast MRI

We assessed errors in cerebral blood flow (CBF) obtained from our proposed reference-based method without using arterial input function (AIF) indices in dynamic susceptibility contrast (DSC) magnetic resonance imaging (MRI). We calculated CBF and the referential tissue-related ratio (CBFratio) using numerical simulation and 3 nondeconvolution methods and a deconvolution method of block-circulant singular value decomposition (cSVD). We compared errors with and without simulated noise as parameters of mean transit time (MTT), AIF delay and temporal resolution, and clinical DSC-MRI maps. The errors in CBF obtained using maximum upslope (US) were smallest among the nondeconvolution methods and almost equivalent to errors in the cSVD method under practical imaging conditions. In addition, errors in the CBFratio obtained using reference-based US (Ref-US) referring to white matter were smallest, even compared to all errors in CBF and CBFratio. The Ref-US method introduced less error than the cSVD method, especially at low flow rates, was further robust against AIF noise and coarse temporal resolution, and was comparably robust against transit delay. In pixel-by-pixel correlations between absolute value maps for US and for cSVD-CBF in clinical DSC-MRI, those correlation coefficients (r) between the 2 maps were stable, r > 0.9, despite variation in the slopes of the linear regression line, so the 2 CBFratio maps were visually well correlated in any case. The Ref-US technique without AIF measurement can become a practical perfusion methodology for DSC-MRI in patients even with acute stroke because it balances robustness with systematic and random errors and it is simply performed.

Tracer Delay–Insensitive Algorithm Can Improve Reliability of CT Perfusion Imaging for Cerebrovascular Steno-Occlusive Disease: Comparison with Quantitative Single-Photon Emission CT

Reliability of CT perfusion (CTP) algorithms has not been fully validated. We investigated whether the cerebral blood flow (CBF) values obtained by using a dynamic CTP technique with a tracer delay-insensitive deconvolution algorithm are more accurate than those obtained by using CTP with delay-sensitive algorithms in unilateral cerebrovascular steno-occlusive disease, when compared with those generated by quantitative single-photon emission CT (SPECT). Using CTP and iodine-123-N-isopropyl-p-iodoamphetamine SPECT with an autoradiographic quantification technique, we examined 20 patients with suggested hemodynamic ischemia due to stenosis or occlusion of the unilateral internal carotid or middle cerebral artery. The algorithms used for CTP included delay-insensitive block-circulant singular value decomposition (SVD) (bSVD) and delay-sensitive standard SVD (sSVD) and box-modulation transfer function (bMTF). Absolute CBF values obtained by using CTP with bSVD were significantly lower than those obtained with SPECT, but the ratios to the nonaffected side were significantly correlated to the quantitative SPECT values with significant agreements, particularly when the arterial input function was obtained from the unaffected side. Contrastingly, CBF ratios with sSVD and bMTF were significantly underestimated, and no significant agreement was determined between CTP with sSVD or bMTF and SPECT, though there were substantial correlations between them in some parameters. With the CTP technique, the insensitivity of the deconvolution algorithm to the tracer-delay effect appears to be essential for estimating semiquantitative CBF values in patients with unilateral steno-occlusive lesions.

Evaluation of an AIF correction algorithm for dynamic susceptibility contrast‐enhanced perfusion MRI

For longitudinal studies in patients suffering from cerebrovascular diseases the poor reproducibility of perfusion measurements via dynamic susceptibility-weighted contrast-enhanced MRI (DSC-MRI) is a relevant concern. We evaluate a novel algorithm capable of overcoming limitations in DSC-MRI caused by partial volume and saturation issues in the arterial input function (AIF) by a blood flow stimulation-study. In 21 subjects, perfusion parameters before and after administration of blood flow stimulating L-arginine were calculated utilizing a block-circulant singular value decomposition (cSVD). A total of two different raters and three different rater conditions were employed to select AIFs: Besides 1) an AIF selection by an experienced rater, a beginner rater applied a steady state-oriented strategy, returning; 2) raw; and 3) corrected AIFs. Highly significant changes in regional cerebral blood flow (rCBF) by 9.0% (P < 0.01) could only be found when the AIF correction was performed. To further test for improved reproducibility, in a subgroup of seven subjects the baseline measurement was repeated 6 weeks after the first examination. In this group as well, using the correction algorithm decreased the SD of the difference between the two baseline measurements by 42%.

Effect of vascular stenosis on perfusion‐weighted imaging; differences between calculation algorithms

To determine the most suitable postprocessing technique for magnetic resonance (MR) perfusion imaging in patients with vascular stenosis, by comparing the cerebral blood flow (CBF) maps of single photon emission tomography (SPECT) and perfusion MR imaging (MRI). In 15 consecutive patients (14 men and one woman, mean age 73.9 +/- 6.0 years) with stenosis of common carotid artery (CCA) or internal carotid artery (ICA) of more than 75%, both brain perfusion MRI and brain perfusion SPECT were performed. From perfusion MR images, CBF maps were calculated with the first moment, singular value decomposition (SVD), and block circulant SVD (b-SVD) methods, and CBF maps from each algorithm were compared with those from SPECT. The b-SVD method had the best correlation with SPECT (R = 0.814), followed by the first moment method (R = 0.776) and the SVD method (R = 0.723). The b-SVD method has the least mean difference with SPECT (0.118), the first moment method also had less difference (0.121), and the SVD had greatest mean difference (0.164). Our results suggest that in patients with vascular impairment the b-SVD method will be the technique of choice rather than SVD or first moment method.