Perfusion quantification using Gaussian process deconvolution

SPINNED: Simulation-based physics-informed neural network for deconvolution of dynamic susceptibility contrast MRI perfusion data

PURPOSE

To propose the simulation-based physics-informed neural network for deconvolution of dynamic susceptibility contrast (DSC) MRI (SPINNED) as an alternative for more robust and accurate deconvolution compared to existing methods.

METHODS

The SPINNED method was developed by generating synthetic tissue residue functions and arterial input functions through mathematical simulations and by using them to create synthetic DSC MRI time series. The SPINNED model was trained using these simulated data to learn the underlying physical relation (deconvolution) between the DSC-MRI time series and the arterial input functions. The accuracy and robustness of the proposed SPINNED method were assessed by comparing it with two common deconvolution methods in DSC MRI data analysis, circulant singular value decomposition, and Volterra singular value decomposition, using both simulation data and real patient data.

RESULTS

The proposed SPINNED method was more accurate than the conventional methods across all SNR levels and showed better robustness against noise in both simulation and real patient data. The SPINNED method also showed much faster processing speed than the conventional methods.

CONCLUSION

These results support that the proposed SPINNED method can be a good alternative to the existing methods for resolving the deconvolution problem in DSC MRI. The proposed method does not require any separate ground-truth measurement for training and offers additional benefits of quick processing time and coverage of diverse clinical scenarios. Consequently, it will contribute to more reliable, accurate, and rapid diagnoses in clinical applications compared with the previous methods including those based on supervised learning.

Applications of artificial intelligence for DWI and PWI data processing in acute ischemic stroke: Current practices and future directions

Multimodal Magnetic Resonance Imaging (MRI) techniques of Perfusion-Weighted Imaging (PWI) and Diffusion-Weighted Imaging (DWI) data are integral parts of the diagnostic workup in the acute stroke setting. The visual interpretation of PWI/DWI data is the most likely procedure to triage Acute Ischemic Stroke (AIS) patients who will access reperfusion therapy, especially in those exceeding 6 h of stroke onset. In fact, this process defines two classes of tissue: the ischemic core, which is presumed to be irreversibly damaged, visualized on DWI data and the penumbra which is the reversibly injured brain tissue around the ischemic tissue, visualized on PWI data. AIS patients with a large ischemic penumbra and limited infarction core have a high probability of benefiting from endovascular treatment. However, it is a tedious and time-consuming procedure. Consequently, it is subject to high inter- and intra-observer variability. Thus, the assessment of the potential risks and benefits of endovascular treatment is uncertain. Fast, accurate and automatic post-processing of PWI and DWI data is important for clinical diagnosis and is necessary to help the decision making for therapy. Therefore, an automated procedure that identifies stroke slices, stroke hemisphere, segments stroke regions in DWI, and measures hypoperfused tissue in PWI enhances considerably the reproducibility and the accuracy of stroke assessment. In this work, we draw an overview of several applications of Artificial Intelligence (AI) for the automation processing and their potential contributions in clinical practices. We compare the current approaches among each other's with respect to some key requirements.

Spatio-temporal multi-task network cascade for accurate assessment of cardiac CT perfusion

The assessment of myocardial perfusion has become increasingly important in the early diagnosis of coronary artery disease. Currently, the process of perfusion assessment is time-consuming and subjective. Although automated methods by threshold processing have been proposed, they cannot obtain an accurate perfusion assessment. Thus, there is a great clinical demand to obtain a rapid and accurate assessment of myocardial perfusion through a standard procedure using an automated algorithm. In this work, we present a spatio-temporal multi-task network cascade (ST-MNC) to provide an accurate and robust assessment of myocardial perfusion. The proposed network captures patch-based spatio-temporal representations for each pixel through a spatio-temporal encoder-decoder network. Then the multi-task network cascade uses spatio-temporal representations as shared features to predict various perfusion parameters and myocardial ischemic regions. Extensive experiments on CT images of 232 subjects demonstrate ST-MNC could produce a good approximation for perfusion parameters and an accurate classification for ischemic regions. These results show that our proposed method can provide a fast and accurate assessment of myocardial perfusion.

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.

A Machine Learning Approach to Perfusion Imaging With Dynamic Susceptibility Contrast MR

Background: Dynamic susceptibility contrast (DSC) MR perfusion is a frequently-used technique for neurovascular imaging. The progress of a bolus of contrast agent through the tissue of the brain is imaged via a series of T2*-weighted MRI scans. Clinically relevant parameters such as blood flow and Tmax can be calculated by deconvolving the contrast-time curves with the bolus shape (arterial input function). In acute stroke, for instance, these parameters may help distinguish between the likely salvageable tissue and irreversibly damaged infarct core. Deconvolution typically relies on singular value decomposition (SVD): however, studies have shown that these algorithms are very sensitive to noise and artifacts present in the image and therefore may introduce distortions that influence the estimated output parameters. Methods: In this work, we present a machine learning approach to the estimation of perfusion parameters in DSC-MRI. Various machine learning models using as input the raw MR source data were trained to reproduce the output of an FDA approved commercial implementation of the SVD deconvolution algorithm. Experiments were conducted to determine the effect of training set size, optimal patch size, and the effect of using different machine-learning models for regression. Results: Model performance increased with training set size, but after 5,000 samples (voxels) this effect was minimal. Models inferring perfusion maps from a 5 by 5 voxel patch outperformed models able to use the information in a single voxel, but larger patches led to worse performance. Random Forest models produced had the lowest root mean squared error, with neural networks performing second best: however, a phantom study revealed that the random forest was highly susceptible to noise levels, while the neural network was more robust. Conclusion: The machine learning-based approach produces estimates of the perfusion parameters invariant to the noise and artifacts that commonly occur as part of MR acquisition. As a result, better robustness to noise is obtained, when evaluated against the FDA approved software on acute stroke patients and simulated phantom data.

Prediction of Hemorrhagic Transformation Severity in Acute Stroke From Source Perfusion MRI

OBJECTIVE

Hemorrhagic transformation (HT) is the most severe complication of reperfusion therapy in acute ischemic stroke (AIS) patients. Management of AIS patients could benefit from accurate prediction of upcoming HT. While prediction of HT occurrence has recently provided encouraging results, the prediction of the severity and territory of the HT could bring valuable insights that are beyond current methods.

METHODS

This study tackles these issues and aims to predict the spatial occurrence of HT in AIS from perfusion-weighted magnetic resonance imaging (PWI) combined with diffusion weighted imaging. In all, 165 patients were included in this study and analyzed retrospectively from a cohort of AIS patients treated with reperfusion therapy in a single stroke center.

RESULTS

Machine learning models are compared within our framework; support vector machines, linear regression, decision trees, neural networks, and kernel spectral regression were applied to the dataset. Kernel spectral regression performed best with an accuracy of $\text{83.7} \pm \text{2.6}\%$.

CONCLUSION

The key contribution of our framework formalize HT prediction as a machine learning problem. Specifically, the model learns to extract imaging markers of HT directly from source PWI images rather than from pre-established metrics.

SIGNIFICANCE

Predictions visualized in terms of spatial likelihood of HT in various territories of the brain were evaluated against follow-up gradient recalled echo and provide novel insights for neurointerventionalists prior to endovascular therapy.

Stable spline deconvolution for dynamic susceptibility contrast MRI

PURPOSE

To present the stable spline (SS) deconvolution method for the quantification of the cerebral blood flow (CBF) from dynamic susceptibility contrast MRI.

METHODS

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.

RESULTS

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.

CONCLUSION

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.

Analysis of perfusion MRI in stroke: To deconvolve, or not to deconvolve

PURPOSE

There is currently controversy regarding the benefits of deconvolution-based parameters in stroke imaging, with studies suggesting a similar infarct prediction using summary parameters. We investigate here the performance of deconvolution-based parameters and summary parameters for dynamic-susceptibility contrast (DSC) MRI analysis, with particular emphasis on precision.

METHODS

Numerical simulations were used to assess the contribution of noise and arterial input function (AIF) variability to measurement precision. A realistic AIF range was defined based on in vivo data from an acute stroke clinical study. The simulated tissue curves were analyzed using two popular singular value decomposition (SVD) based algorithms, as well as using summary parameters.

RESULTS

SVD-based deconvolution methods were found to considerably reduce the AIF-dependency, but a residual AIF bias remained on the calculated parameters. Summary parameters, in turn, show a lower sensitivity to noise. The residual AIF-dependency for deconvolution methods and the large AIF-sensitivity of summary parameters was greatly reduced when normalizing them relative to normal tissue.

CONCLUSION

Consistent with recent studies suggesting high performance of summary parameters in infarct prediction, our results suggest that DSC-MRI analysis using properly normalized summary parameters may have advantages in terms of lower noise and AIF-sensitivity as compared to commonly used deconvolution methods. Magn Reson Med 76:1282-1290, 2016. © 2015 Wiley Periodicals, Inc.

Tissue-specific sparse deconvolution for brain CT perfusion

Enhancing perfusion maps in low-dose computed tomography perfusion (CTP) for cerebrovascular disease diagnosis is a challenging task, especially for low-contrast tissue categories where infarct core and ischemic penumbra usually occur. Sparse perfusion deconvolution has been recently proposed to effectively improve the image quality and diagnostic accuracy of low-dose perfusion CT by extracting the complementary information from the high-dose perfusion maps to restore the low-dose using a joint spatio-temporal model. However the low-contrast tissue classes where infarct core and ischemic penumbra are likely to occur in cerebral perfusion CT tend to be over-smoothed, leading to loss of essential biomarkers. In this paper, we propose a tissue-specific sparse deconvolution approach to preserve the subtle perfusion information in the low-contrast tissue classes. We first build tissue-specific dictionaries from segmentations of high-dose perfusion maps using online dictionary learning, and then perform deconvolution-based hemodynamic parameters estimation for block-wise tissue segments on the low-dose CTP data. Extensive validation on clinical datasets of patients with cerebrovascular disease demonstrates the superior performance of our proposed method compared to state-of-art, and potentially improve diagnostic accuracy by increasing the differentiation between normal and ischemic tissues in the brain.

Biased visualization of hypoperfused tissue by computed tomography due to short imaging duration: improved classification by image down-sampling and vascular models

OBJECTIVES

Lesion detection in acute stroke by computed-tomography perfusion (CTP) can be affected by incomplete bolus coverage in veins and hypoperfused tissue, so-called bolus truncation (BT), and low contrast-to-noise ratio (CNR). We examined the BT-frequency and hypothesized that image down-sampling and a vascular model (VM) for perfusion calculation would improve normo- and hypoperfused tissue classification.

METHODS

CTP datasets from 40 acute stroke patients were retrospectively analysed for BT. In 16 patients with hypoperfused tissue but no BT, repeated 2-by-2 image down-sampling and uniform filtering was performed, comparing CNR to perfusion-MRI levels and tissue classification to that of unprocessed data. By simulating reduced scan duration, the minimum scan-duration at which estimated lesion volumes came within 10% of their true volume was compared for VM and state-of-the-art algorithms.

RESULTS

BT in veins and hypoperfused tissue was observed in 9/40 (22.5%) and 17/40 patients (42.5%), respectively. Down-sampling to 128 × 128 resolution yielded CNR comparable to MR data and improved tissue classification (p = 0.0069). VM reduced minimum scan duration, providing reliable maps of cerebral blood flow and mean transit time: 5 s (p = 0.03) and 7 s (p < 0.0001), respectively).

CONCLUSIONS

BT is not uncommon in stroke CTP with 40-s scan duration. Applying image down-sampling and VM improve tissue classification.

KEY POINTS

• Too-short imaging duration is common in clinical acute stroke CTP imaging. • The consequence is impaired identification of hypoperfused tissue in acute stroke patients. • The vascular model is less sensitive than current algorithms to imaging duration. • Noise reduction by image down-sampling improves identification of hypoperfused tissue by CTP.

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

BACKGROUND AND PURPOSE

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.

MATERIALS AND METHODS

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.

RESULTS

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).

CONCLUSIONS

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.

Reliable estimation of capillary transit time distributions using DSC-MRI

The regional availability of oxygen in brain tissue is traditionally inferred from the magnitude of cerebral blood flow (CBF) and the concentration of oxygen in arterial blood. Measurements of CBF are therefore widely used in the localization of neuronal response to stimulation and in the evaluation of patients suspected of acute ischemic stroke or flow-limiting carotid stenosis. It was recently demonstrated that capillary transit time heterogeneity (CTH) limits maximum oxygen extraction fraction (OEF(max)) that can be achieved for a given CBF. Here we present a statistical approach for determining CTH, mean transit time (MTT), and CBF using dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). Using numerical simulations, we demonstrate that CTH, MTT, and OEF(max) can be estimated with low bias and variance across a wide range of microvascular flow patterns, even at modest signal-to-noise ratios. Mean transit time estimated by singular value decomposition (SVD) deconvolution, however, is confounded by CTH. The proposed technique readily identifies malperfused tissue in acute stroke patients and appears to highlight information not detected by the standard SVD technique. We speculate that this technique permits the non-invasive detection of tissue with impaired oxygen delivery in neurologic disorders such as acute ischemic stroke and Alzheimer's disease during routine diagnostic imaging.

Improving low-dose blood-brain barrier permeability quantification using sparse high-dose induced prior for Patlak model

Blood-brain barrier permeability (BBBP) measurements extracted from the perfusion computed tomography (PCT) using the Patlak model can be a valuable indicator to predict hemorrhagic transformation in patients with acute stroke. Unfortunately, the standard Patlak model based PCT requires excessive radiation exposure, which raised attention on radiation safety. Minimizing radiation dose is of high value in clinical practice but can degrade the image quality due to the introduced severe noise. The purpose of this work is to construct high quality BBBP maps from low-dose PCT data by using the brain structural similarity between different individuals and the relations between the high- and low-dose maps. The proposed sparse high-dose induced (shd-Patlak) model performs by building a high-dose induced prior for the Patlak model with a set of location adaptive dictionaries, followed by an optimized estimation of BBBP map with the prior regularized Patlak model. Evaluation with the simulated low-dose clinical brain PCT datasets clearly demonstrate that the shd-Patlak model can achieve more significant gains than the standard Patlak model with improved visual quality, higher fidelity to the gold standard and more accurate details for clinical analysis.

Arterial input function in perfusion MRI: a comprehensive review

Cerebral perfusion, also referred to as cerebral blood flow (CBF), is one of the most important parameters related to brain physiology and function. The technique of dynamic-susceptibility contrast (DSC) MRI is currently the most commonly used MRI method to measure perfusion. It relies on the intravenous injection of a contrast agent and the rapid measurement of the transient signal changes during the passage of the bolus through the brain. Central to quantification of CBF using this technique is the so-called arterial input function (AIF), which describes the contrast agent input to the tissue of interest. Due to its fundamental role, there has been a lot of progress in recent years regarding how and where to measure the AIF, how it influences DSC-MRI quantification, what artefacts one should avoid, and the design of automatic methods to measure the AIF. The AIF is also directly linked to most of the major sources of artefacts in CBF quantification, including partial volume effect, bolus delay and dispersion, peak truncation effects, contrast agent non-linearity, etc. While there have been a number of good review articles on DSC-MRI over the years, these are often comprehensive but, by necessity, with limited in-depth discussion of the various topics covered. This review article covers in greater depth the issues associated with the AIF and their implications for perfusion quantification using DSC-MRI.

The 39 steps: evading error and deciphering the secrets for accurate dynamic susceptibility contrast MRI

Dynamic susceptibility contrast (DSC) MRI is the most commonly used MRI method to assess cerebral perfusion and other related haemodynamic parameters. Although the technique is well established and used routinely in clinical centres, there are still many problems that impede accurate perfusion quantification. In this review article, we present 39 steps which guide the reader through the theoretical principles, practical decisions, potential problems, current limitations and latest advances in DSC-MRI. The 39 steps span the collection, analysis and interpretation of DSC-MRI data, expounding issues and possibilities relating to the contrast agent, the acquisition of DSC-MRI data, data pre-processing, the contrast concentration-time course, the arterial input function, deconvolution, common perfusion parameters, post-processing possibilities, patient studies, absolute versus relative quantification and automated analysis methods.

Towards robust deconvolution of low-dose perfusion CT: sparse perfusion deconvolution using online dictionary learning

Computed tomography perfusion (CTP) is an important functional imaging modality in the evaluation of cerebrovascular diseases, particularly in acute stroke and vasospasm. However, the post-processed parametric maps of blood flow tend to be noisy, especially in low-dose CTP, due to the noisy contrast enhancement profile and the oscillatory nature of the results generated by the current computational methods. In this paper, we propose a robust sparse perfusion deconvolution method (SPD) to estimate cerebral blood flow in CTP performed at low radiation dose. We first build a dictionary from high-dose perfusion maps using online dictionary learning and then perform deconvolution-based hemodynamic parameters estimation on the low-dose CTP data. Our method is validated on clinical data of patients with normal and pathological CBF maps. The results show that we achieve superior performance than existing methods, and potentially improve the differentiation between normal and ischemic tissue in the brain.

A control point interpolation method for the non-parametric quantification of cerebral haemodynamics from dynamic susceptibility contrast MRI

DSC-MRI analysis is based on tracer kinetic theory and typically involves the deconvolution of the MRI signal in tissue with an arterial input function (AIF), which is an ill-posed inverse problem. The current standard singular value decomposition (SVD) method typically underestimates perfusion and introduces non-physiological oscillations in the resulting residue function. An alternative vascular model (VM) based approach permits only a restricted family of shapes for the residue function, which might not be appropriate in pathologies like stroke. In this work a novel deconvolution algorithm is presented that can estimate both perfusion and residue function shape accurately without requiring the latter to belong to a specific class of functional shapes. A control point interpolation (CPI) method is proposed that represents the residue function by a number of control points (CPs), each having two degrees of freedom (in amplitude and time). A complete residue function shape is then generated from the CPs using a cubic spline interpolation. The CPI method is shown in simulation to be able to estimate cerebral blood flow (CBF) with greater accuracy giving a regression coefficient between true and estimated CBF of 0.96 compared to 0.83 for VM and 0.71 for the circular SVD (oSVD) method. The CPI method was able to accurately estimate the residue function over a wide range of simulated conditions. The CPI method has also been demonstrated on clinical data where a marked difference was observed between the residue function of normally appearing brain parenchyma and infarcted tissue. The CPI method could serve as a viable means to examine the residue function shape under pathological variations.

Bayesian hemodynamic parameter estimation by bolus tracking perfusion weighted imaging

A delay-insensitive probabilistic method for estimating hemodynamic parameters, delays, theoretical residue functions, and concentration time curves by computed tomography (CT) and magnetic resonance (MR) perfusion weighted imaging is presented. Only a mild stationarity hypothesis is made beyond the standard perfusion model. New microvascular parameters with simple hemodynamic interpretation are naturally introduced. Simulations on standard digital phantoms show that the method outperforms the oscillating singular value decomposition (oSVD) method in terms of goodness-of-fit, linearity, statistical and systematic errors on all parameters, especially at low signal-to-noise ratios (SNRs). Delay is always estimated sharply with user-supplied resolution and is purely arterial, by contrast to oSVD time-to-maximum TMAX that is very noisy and biased by mean transit time (MTT), blood volume, and SNR. Residue functions and signals estimates do not suffer overfitting anymore. One CT acute stroke case confirms simulation results and highlights the ability of the method to reliably estimate MTT when SNR is low. Delays look promising for delineating the arterial occlusion territory and collateral circulation.

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.

Deconvolution-Based CT and MR Brain Perfusion Measurement: Theoretical Model Revisited and Practical Implementation Details

Deconvolution-based analysis of CT and MR brain perfusion data is widely used in clinical practice and it is still a topic of ongoing research activities. In this paper, we present a comprehensive derivation and explanation of the underlying physiological model for intravascular tracer systems. We also discuss practical details that are needed to properly implement algorithms for perfusion analysis. Our description of the practical computer implementation is focused on the most frequently employed algebraic deconvolution methods based on the singular value decomposition. In particular, we further discuss the need for regularization in order to obtain physiologically reasonable results. We include an overview of relevant preprocessing steps and provide numerous references to the literature. We cover both CT and MR brain perfusion imaging in this paper because they share many common aspects. The combination of both the theoretical as well as the practical aspects of perfusion analysis explicitly emphasizes the simplifications to the underlying physiological model that are necessary in order to apply it to measured data acquired with current CT and MR scanners.

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.

A spatio-temporal deconvolution method to improve perfusion CT quantification

Perfusion imaging is a useful adjunct to anatomic imaging in numerous diagnostic and therapy-monitoring settings. One approach to perfusion imaging is to assume a convolution relationship between a local arterial input function and the tissue enhancement profile of the region of interest via a "residue function" and subsequently solve for this residue function. This ill-posed problem is generally solved using singular-value decomposition based approaches, and the hemodynamic parameters are solved for each voxel independently. In this paper, we present a formulation which incorporates both spatial and temporal correlations, and show through simulations that this new formulation yields higher accuracy and greater robustness with respect to image noise. We also show using rectal cancer tumor images that this new formulation results in better segregation of normal and cancerous voxels.

A new approach to analysis of the impulse response function (IRF) in dynamic contrast-enhanced MRI (DCEMRI): a simulation study

The purpose of this research was to develop a novel numerical procedure to deconvolute the arterial input function (AIF) from contrast concentration vs. time curves and to obtain the impulse response functions (IRFs) from dynamic contrast-enhanced MRI (DCEMRI) data. Numerical simulations were performed to study variations of contrast concentration vs. time curves and the corresponding IRFs. The simulated contrast media concentration curves were generated by varying the parameters of an empirical mathematical model (EMM) within reasonable ranges based on a previous experimental study. The AIF was calculated from plots of contrast media concentration vs. time in muscle under assumption that they are well approximated by the "two-compartment model" (TCM). A general simple mathematical model of the IRF was developed, and the physiological meaning of the model parameters was determined by comparing them with the widely accepted TCM. The results demonstrate that the deconvolution procedure developed in this research is a simple, robust, and useful technique. In addition, "impulse response analysis" leads to the derivation of novel parameters relating to tumor vascular architecture, and these new parameters may have clinical utility.

Improved residue function and reduced flow dependence in MR perfusion using least-absolute-deviation regularization

Cerebral blood flow (CBF) estimates derived from singular value decomposition (SVD) of time intensity curves from Gadolinium bolus perfusion-weighted imaging are known to underestimate CBF, especially at high flow rates. We report the development of a model-independent delay-invariant deconvolution technique using least-absolute-deviation (LAD) regularization to improve the CBF estimation accuracy. Computer simulations were performed to compare the accuracy of CBF estimates derived from LAD, reformulated SVD (rSVD) and standard SVD (sSVD) techniques. Simulations were performed at image signal-to-noise ratios ranging from 20 to 400, cerebral blood volumes from 1% to 10%, and CBF from 2.5 mL/100 g/min to 176.5 mL/100 g/min to estimate the effect of these parameters on the accuracy of CBF estimation. The LAD method improved the CBF estimation accuracy by up to 32% in gray matter and 23% in white matter compared with rSVD and sSVD methods. LAD method also reduces the systematic bias of rSVD and sSVD methods to baseline SNR while producing more accurate and reproducible residue function calculation than either rSVD or sSVD method. Initial clinical implementation of the method on six representative clinical cases confirm the advantages of the LAD method over rSVD and sSVD methods.

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).

Minimising the effects of bolus dispersion in bolus-tracking MRI

Bolus-tracking perfusion measurements in patients with vascular abnormalities are often unreliable, because delay and/or dispersion of the bolus within the vessels distorts the measured arterial input function (AIF). Erroneous measurements of perfusion can be identified by examining the measured response function, the shape of which is determined by both the tissue and arterial retention. In this work, an accurate response function is extracted by combining maximum-likelihood expectation-maximisation deconvolution, regularised using an oscillation index, with subsequent wavelet thresholding. Simulations show that this method recovers both the smooth-dispersed and the sharp-delayed response functions. This enables regions where the bolus is delayed and/or dispersed to be identified when the methodology is applied to data from patients with vascular abnormalities. Simulations also demonstrate robust and accurate perfusion estimates when there is no bolus delay and/or dispersion. The presence of delay and/or dispersion in the response function suggests that the perfusion measurements are erroneous, and that the global AIF is an inaccurate approximation to the true AIF in these regions. Perfusion measurements are corrected within the affected regions by defining a regional AIF from the independent component analysis of the dynamic susceptibility contrast MRI data. The regional AIF is shown to remove the delay and dispersion, improving the accuracy of the perfusion maps.

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.

Parametric imaging in dynamic susceptibility contrast MRI-phantom and in vivo studies

Possibility of quantitative perfusion imaging with DSC MRI is still under discussion. In this work, the quantitative related parameters are analyzed and DSC-MRI limitations are discussed. It includes investigation of measurement procedures/conditions as well as parametric image synthesis methodology. The set of phantoms was constructed and used to inspect the role of Gd-DTPA concentration estimation by EPI measurements, the influence of partial volume effect on concentration estimation, the role of a phantom and its pipes orientation, etc. Additionally, parametric image synthesis methodology was investigated by analysis of influence of a bolus dispersion, bolus arrival time, and other signal parameters on an image quality. As a conclusion testing software package is proposed.

PerfTool: a software platform for investigating bolus-tracking perfusion imaging quantification strategies

PURPOSE

To develop a software platform, PerfTool (for perfusion tool), for the comprehensive evaluation of bolus-tracking quantitative perfusion imaging methods and algorithms, along with a method to rapidly visualize and evaluate the performance of algorithms.

MATERIALS AND METHODS

Algorithms were evaluated interactively with PerfTool using synthetic DeltaR2* data sets with different perfusion parameter permutations (known as test patterns). Patient data and test patterns were used to evaluate a standard singular value deconvolution (SVD) approach (sSVD) and a reformulated implementation (rSVD) that is insensitive to arterial-tissue delay (ATD), and to explore the effect of the SVD regularization parameter (p(SVD)) on CBF estimates.

RESULTS

The CBF overestimation resulting from sensitivity to ATD in sSVD compared to rSVD was demonstrated with the patient data, and the effect was confirmed using a test pattern. The same test pattern demonstrated the CBF underestimation resulting from high p(SVD) thresholds.

CONCLUSION

PerfTool is an extensible software tool that allows perfusion measurements to be obtained by different methods, and is flexible enough to incorporate new developments and apply them to real patient data and test patterns.

Identification of cardiovascular dilution systems by contrast ultrasound

Indicator dilution techniques permit accurate measurements of important cardiovascular parameters, such as pulmonary blood volume (PBV) and ejection fraction (EF). However, their use is limited by the need for central catheterization. Contrast ultrasonography allows overcoming this problem. PBV and EF can be measured by a dilution system identification algorithm after detection of multiple dilution curves by an ultrasound scanner. In this paper, we present a system identification method that exploits the a priori knowledge on the dilution system and finds the optimum parameters for the parametric model representing the dilution system impulse response. No subsequent model interpolation is needed. Volume measurements show accurate in-vitro results and clinical feasibility, while 50 EF measurements in patients show a 0.88 correlation coefficient with echocardiographic biplane estimates. In conclusion, adding a priori knowledge to the system identification algorithm leads to increased accuracy and robustness of the method for PBV and EF measurements.

Bayesian estimation of cerebral perfusion using a physiological model of microvasculature

Perfusion weighted MRI has proven very useful for deriving hemodynamic parameters such as CBF, CBV and MTT. These quantities are important diagnostically, e.g. in acute stroke, where they are used to delineate ischemic regions. Yet the standard method for estimating CBF based on singular value decomposition (SVD) has been demonstrated to underestimate (especially high) flow components and to be sensitive to delays in the arterial input function (AIF). Furthermore, the estimated residue functions often oscillate. This compromises their physiological interpretation/basis and makes estimation of related measures such as flow heterogeneity difficult. In this study, we estimate perfusion parameters based on a vascular model (VM) which represents heterogeneous capillary flow and explicitly leads to monotonically decreasing residue functions. We use a fully Bayesian approach to obtain posterior probability distributions for all parameters. In simulation studies, we show that the VM method has less bias in CBF estimates than the SVD based method for realistic SNRs. This also applies to cases where the AIF is delayed. We employ our method to estimate perfusion maps using data from (i) a healthy volunteer and (ii) from a stroke patient.

Iterative blind deconvolution in magnetic resonance brain perfusion imaging

In first pass magnetic resonance brain perfusion imaging, arterial input functions are used in the deconvolution of the observed contrast concentrations to obtain quantitative hemodynamic parameters. Ideally, arterial input functions should be measured in each imaged voxel to eliminate the effects of delay and dispersion of the contrast agent from the injection site. An approach based on iterative blind deconvolution with the Richardson-Lucy algorithm is proposed for the simultaneous estimation of voxel-specific arterial input functions and voxel-specific tissue residue functions. An extended contrast concentration model was used to separate the first pass bolus from additional recirculation and leakage signals. The extended model was evaluated using in vivo data. Computer simulations examined the feasibility of iterative blind deconvolution in perfusion imaging. Preliminary in vivo results from a patient with fibromuscular dysplasia showed territories with delayed/dispersed arterial input functions that coincided with the location of territories supplied by collateral circulation as described from the complete radiologic examination. Higher flow values and shorter mean transit times compared to conventional methods were obtained in these areas, suggesting that the effects of dispersion were minimized. The in vivo estimated arterial input functions visualized the patient's blood supply patterns as a function of time.

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.

Principles of cerebral perfusion imaging by bolus tracking

The principles of cerebral perfusion imaging by the method of dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) (bolus tracking) are described. The MRI signals underlying DSC-MRI are discussed. Tracer kinetics procedures are defined to calculate images of cerebral blood volume (CBV), cerebral blood flow (CBF), and mean transit time (MTT). Two general categories of numerical procedures are reviewed for deriving CBF from the residue function. Procedures that involve deconvolution, such as Fourier deconvolution or singular value decomposition (SVD), are classified as model-independent methods because they do not require a model of the microvascular hemodynamics. Those methods in principle also yield a measure of the tissue impulse response function and the residue function, from which microvascular hemodynamics can be characterized. The second category of methods is the model-dependent methods, which use models of tracer transport and retention in the microvasculature. These methods do not yield independent measures of the residue function and may introduce bias when the physiology does not follow the model. Statistical methods are sometimes used, which involve treating the residue function as a deconvolution kernel and optimizing (fitting) the kernel from the experimental data using procedures such as maximum likelihood. Finally, other hemodynamic indices that can be measured from DSC-MRI data are described.

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.

Magnetic resonance brain perfusion imaging with voxel-specific arterial input functions

PURPOSE

To propose an automatic method for estimating voxel-specific arterial input functions (AIFs) in dynamic contrast brain perfusion imaging.

MATERIALS AND METHODS

Voxel-specific AIFs were estimated blindly using the theory of homomorphic transformations and complex cepstrum analysis. Wiener filtering was used in the subsequent deconvolution. The method was verified using simulated data and evaluated in 10 healthy adults.

RESULTS

Computer simulations accurately estimated differently shaped, normalized AIFs. Simple Wiener filtering resulted in underestimation of flow values. Preliminary in vivo results showed comparable cerebral flow value ratios between gray matter (GM) and white matter (WM) when using blindly estimated voxel-specific AIFs or a single manually selected AIF. Significant differences (P < or = 0.0125) in mean transit time (MTT) and time-to-peak (TTP) in GM compared to WM was seen with the new method.

CONCLUSION

Initial results suggest that the proposed method can replace the tedious and difficult task of manually selecting an AIF, while simultaneously providing better differentiation between time-dependent hemodynamic parameters.

New developments in perfusion imaging by bolus tracking

The author describes the theoretical basis of quantification of cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transit time (MTT) by the bolus tracking method: i.e.dynamic susceptibility contrast MRI using very rapid imaging to capture the first pass of intravenously injected paramagnetic contrast agent.

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.

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.