Deconvolution Analysis of Dynamic Contrast-Enhanced Data Based on Singular Value Decomposition Optimized by Generalized Cross Validation

A free time point model for dynamic contrast enhanced exploration

Dynamic-Contrast-Enhanced (DCE) Imaging has been widely studied to characterize microcirculatory disorders associated with various diseases. Although numerous studies have demonstrated its diagnostic interest, the physiological interpretation using pharmacokinetic models often remains debatable. Indeed, to be interpretable, a model must provide, at first instance, an accurate description of the DCE data. However, the evaluation and optimization of this accuracy remain rather limited in DCE. Here we established a non-linear Free-Time-Point-Hermite (FTPH) data-description model designed to fit DCE data accurately. Its performance was evaluated on data generated using two contrasting pharmacokinetic microcirculatory hypotheses (MH). The accuracy of data description of the models was evaluated by calculating the mean squared error (QE) from initial and assessed tissue impulse responses. Then, FTPH assessments were provided to blinded observers to evaluate if these assessments allowed observers to identify MH in their data. Regardless of the initial pharmacokinetic model used for data generation, QE was lower than 3% for the noise-free datasets and increased up to 10% for a signal-to-noise-ratio (SNR) of 20. Under SNR = 20, the sensitivity and specificity of the MH identification were over 80%. The performance of the FTPH model was higher than that of the B-Spline model used as a reference. The accuracy of the FTPH model regardless of the initial MH provided an opportunity to have a reference to check the accuracy of other pharmacokinetic models.

A Superfast Super-Resolution Method for Radar Forward-Looking Imaging

The super-resolution method has been widely used for improving azimuth resolution for radar forward-looking imaging. Typically, it can be achieved by solving an undifferentiable L1 regularization problem. The split Bregman algorithm (SBA) is a great tool for solving this undifferentiable problem. However, its real-time imaging ability is limited to matrix inversion and iterations. Although previous studies have used the special structure of the coefficient matrix to reduce the computational complexity of each iteration, the real-time performance is still limited due to the need for hundreds of iterations. In this paper, a superfast SBA (SFSBA) is proposed to overcome this shortcoming. Firstly, the super-resolution problem is transmitted into an L1 regularization problem in the framework of regularization. Then, the proposed SFSBA is used to solve the nondifferentiable L1 regularization problem. Different from the traditional SBA, the proposed SFSBA utilizes the low displacement rank features of Toplitz matrix, along with the Gohberg-Semencul (GS) representation to realize fast inversion of the coefficient matrix, reducing the computational complexity of each iteration from O(N3) to O(N2). It uses a two-order vector extrapolation strategy to reduce the number of iterations. The convergence speed is increased by about 8 times. Finally, the simulation and real data processing results demonstrate that the proposed SFSBA can effectively improve the azimuth resolution of radar forward-looking imaging, and its performance is only slightly lower compared to traditional SBA. The hardware test shows that the computational efficiency of the proposed SFSBA is much higher than that of other traditional super-resolution methods, which would meet the real-time requirements in practice.

Quantitative 3T multiparametric MRI of benign and malignant prostatic tissue in patients with and without local recurrent prostate cancer after external-beam radiation therapy

Background

Post‐radiotherapy locally recurrent prostate cancer (PCa) patients are candidates for focal salvage treatment. Multiparametric MRI (mp‐MRI) is attractive for tumor localization. However, radiotherapy‐induced tissue changes complicate image interpretation. To develop focal salvage strategies, accurate tumor localization and distinction from benign tissue is necessary.

Purpose

To quantitatively characterize radio‐recurrent tumor and benign radiation‐induced changes using mp‐MRI, and investigate which sequences optimize the distinction between tumor and benign surroundings.

Study Type

Prospective case–control.

Subjects

Thirty‐three patients with biochemical failure after external‐beam radiotherapy (cases), 35 patients without post‐radiotherapy recurrent disease (controls), and 13 patients with primary PCa (untreated).

Field Strength/Sequences

3T; quantitative mp‐MRI: T₂‐mapping, ADC, and K^trans and k_ep maps.

Assessment

Quantitative image‐analysis of prostatic regions, within and between cases, controls, and untreated patients.

Statistical Tests

Within‐groups: nonparametric Friedman analysis of variance with post‐hoc Wilcoxon signed‐rank tests; between‐groups: Mann–Whitney tests. All with Bonferroni corrections. Generalized linear mixed modeling to ascertain the contribution of each map and location to tumor likelihood.

Results

Benign imaging values were comparable between cases and controls (P = 0.15 for ADC in the central gland up to 0.91 for k_ep in the peripheral zone), both with similarly high peri‐urethral K^trans and k_ep values (min⁻¹) (median [range]: K^trans = 0.22 [0.14–0.43] and 0.22 [0.14–0.36], P = 0.60, k_ep = 0.43 [0.24–0.57] and 0.48 [0.32–0.67], P = 0.05). After radiotherapy, benign central gland values were significantly decreased for all maps (P ≤ 0.001) as well as T₂, K^trans, and k_ep of benign peripheral zone (all with P ≤ 0.002). All imaging maps distinguished recurrent tumor from benign peripheral zone, but only ADC, K^trans, and k_ep were able to distinguish it from benign central gland. Recurrent tumor and peri‐urethral K^trans values were not significantly different (P = 0.81), but k_ep values were (P < 0.001). Combining all quantitative maps and voxel location resulted in an optimal distinction between tumor and benign voxels.

Data Conclusion

Mp‐MRI can distinguish recurrent tumor from benign tissue.

Level of Evidence: 2

Technical Efficacy Stage: 2

J. Magn. Reson. Imaging 2019;50:269–278.

Modeling Dynamic Contrast-Enhanced MRI Data with a Constrained Local AIF

PURPOSE

This study aims to develop a constrained local arterial input function (cL-AIF) to improve quantitative analysis of dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) data by accounting for the contrast-agent bolus amplitude error in the voxel-specific AIF.

PROCEDURES

Bayesian probability theory-based parameter estimation and model selection were used to compare tracer kinetic modeling employing either the measured remote-AIF (R-AIF, i.e., the traditional approach) or an inferred cL-AIF against both in silico DCE-MRI data and clinical, cervical cancer DCE-MRI data.

RESULTS

When the data model included the cL-AIF, tracer kinetic parameters were correctly estimated from in silico data under contrast-to-noise conditions typical of clinical DCE-MRI experiments. Considering the clinical cervical cancer data, Bayesian model selection was performed for all tumor voxels of the 16 patients (35,602 voxels in total). Among those voxels, a tracer kinetic model that employed the voxel-specific cL-AIF was preferred (i.e., had a higher posterior probability) in 80 % of the voxels compared to the direct use of a single R-AIF. Maps of spatial variation in voxel-specific AIF bolus amplitude and arrival time for heterogeneous tissues, such as cervical cancer, are accessible with the cL-AIF approach.

CONCLUSIONS

The cL-AIF method, which estimates unique local-AIF amplitude and arrival time for each voxel within the tissue of interest, provides better modeling of DCE-MRI data than the use of a single, measured R-AIF. The Bayesian-based data analysis described herein affords estimates of uncertainties for each model parameter, via posterior probability density functions, and voxel-wise comparison across methods/models, via model selection in data modeling.

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.

Model-free quantification of dynamic PET data using nonparametric deconvolution

Dynamic positron emission tomography (PET) data are usually quantified using compartment models (CMs) or derived graphical approaches. Often, however, CMs either do not properly describe the tracer kinetics, or are not identifiable, leading to nonphysiologic estimates of the tracer binding. The PET data are modeled as the convolution of the metabolite-corrected input function and the tracer impulse response function (IRF) in the tissue. Using nonparametric deconvolution methods, it is possible to obtain model-free estimates of the IRF, from which functionals related to tracer volume of distribution and binding may be computed, but this approach has rarely been applied in PET. Here, we apply nonparametric deconvolution using singular value decomposition to simulated and test-retest clinical PET data with four reversible tracers well characterized by CMs ([(11)C]CUMI-101, [(11)C]DASB, [(11)C]PE2I, and [(11)C]WAY-100635), and systematically compare reproducibility, reliability, and identifiability of various IRF-derived functionals with that of traditional CMs outcomes. Results show that nonparametric deconvolution, completely free of any model assumptions, allows for estimates of tracer volume of distribution and binding that are very close to the estimates obtained with CMs and, in some cases, show better test-retest performance than CMs outcomes.

Dynamic contrast-enhanced perfusion processing for neuroradiologists: model-dependent analysis may not be necessary for determining recurrent high-grade glioma versus treatment effect

BACKGROUND AND PURPOSE

Dynamic contrast-enhanced perfusion MR imaging has proved useful in determining whether a contrast-enhancing lesion is secondary to recurrent glial tumor or is treatment-related. In this article, we explore the best method for dynamic contrast-enhanced data analysis.

MATERIALS AND METHODS

We retrospectively reviewed 24 patients who met the following conditions: 1) had at least an initial treatment of a glioma, 2) underwent a half-dose contrast agent (0.05-mmol/kg) diagnostic-quality dynamic contrast-enhanced perfusion study for an enhancing lesion, and 3) had a diagnosis by pathology within 30 days of imaging. The dynamic contrast-enhanced data were processed by using model-dependent analysis (nordicICE) using a 2-compartment model and model-independent signal intensity with time. Multiple methods of determining the vascular input function and numerous perfusion parameters were tested in comparison with a pathologic diagnosis.

RESULTS

The best accuracy (88%) with good correlation compared with pathology (P = .005) was obtained by using a novel, model-independent signal-intensity measurement derived from a brief integration beginning after the initial washout and by using the vascular input function from the superior sagittal sinus for normalization. Modeled parameters, such as mean endothelial transfer constant > 0.05 minutes(-1), correlated (P = .002) but did not reach a diagnostic accuracy equivalent to the model-independent parameter.

CONCLUSIONS

A novel model-independent dynamic contrast-enhanced analysis method showed diagnostic equivalency to more complex model-dependent methods. Having a brief integration after the first pass of contrast may diminish the effects of partial volume macroscopic vessels and slow progressive enhancement characteristic of necrosis. The simple modeling is technique- and observer-dependent but is less time-consuming.

Optimizing the regularization for image reconstruction of cerebral diffuse optical tomography

Functional near-infrared spectroscopy (fNIRS) is an optical method for noninvasively determining brain activation by estimating changes in the absorption of near-infrared light. Diffuse optical tomography (DOT) extends fNIRS by applying overlapping “high density” measurements, and thus providing a three-dimensional imaging with an improved spatial resolution. Reconstructing brain activation images with DOT requires solving an underdetermined inverse problem with far more unknowns in the volume than in the surface measurements. All methods of solving this type of inverse problem rely on regularization and the choice of corresponding regularization or convergence criteria. While several regularization methods are available, it is unclear how well suited they are for cerebral functional DOT in a semi-infinite geometry. Furthermore, the regularization parameter is often chosen without an independent evaluation, and it may be tempting to choose the solution that matches a hypothesis and rejects the other. In this simulation study, we start out by demonstrating how the quality of cerebral DOT reconstructions is altered with the choice of the regularization parameter for different methods. To independently select the regularization parameter, we propose a cross-validation procedure which achieves a reconstruction quality close to the optimum. Additionally, we compare the outcome of seven different image reconstruction methods for cerebral functional DOT. The methods selected include reconstruction procedures that are already widely used for cerebral DOT [minimum l2-norm estimate (l2MNE) and truncated singular value decomposition], recently proposed sparse reconstruction algorithms [minimum l1- and a smooth minimum l0-norm estimate (l1MNE, l0MNE, respectively)] and a depth- and noise-weighted minimum norm (wMNE). Furthermore, we expand the range of algorithms for DOT by adapting two EEG-source localization algorithms [sparse basis field expansions and linearly constrained minimum variance (LCMV) beamforming]. Independent of the applied noise level, we find that the LCMV beamformer is best for single spot activations with perfect location and focality of the results, whereas the minimum l1-norm estimate succeeds with multiple targets.

Assessment of quantitative perfusion parameters by dynamic contrast-enhanced sonography using a deconvolution method: an in vitro and in vivo study

OBJECTIVES

The purpose of this study was to investigate the impact of the arterial input on perfusion parameters measured using dynamic contrast-enhanced sonography combined with a deconvolution method after bolus injections of a contrast agent.

METHODS

The in vitro experiments were conducted using a custom-made setup consisting of pumping a fluid through a phantom made of 3 intertwined silicone pipes, mimicking a complex structure akin to that of vessels in a tumor, combined with their feeding pipe, mimicking the arterial input. In the in vivo experiments, B16F10 melanoma cells were xenografted to 5 nude mice. An ultrasound scanner combined with a linear transducer was used to perform pulse inversion imaging based on linear raw data throughout the experiments. A mathematical model developed by the Gustave Roussy Institute (patent WO/2008/053268) and based on the dye dilution theory was used to evaluate 7 semiquantitative perfusion parameters directly from time-intensity curves and 3 quantitative perfusion parameters from the residue function obtained after a deconvolution process developed in our laboratory based on the Tikhonov regularization method. We evaluated and compared the intraoperator variability values of perfusion parameters determined after these two signal-processing methods.

RESULTS

In vitro, semiquantitative perfusion parameters exhibited intraoperator variability values ranging from 3.39% to 13.60%. Quantitative parameters derived after the deconvolution process ranged from 4.46% to 11.82%. In vivo, tumors exhibited perfusion parameter intraoperator variability values ranging from 3.74% to 29.34%, whereas quantitative ones varied from 5.00% to 12.43%.

CONCLUSIONS

Taking into account the arterial input in evaluating perfusion parameters improves the intraoperator variability and may improve the dynamic contrast-enhanced sonographic technique.

Systems-level modeling of cancer-fibroblast interaction

Cancer cells interact with surrounding stromal fibroblasts during tumorigenesis, but the complex molecular rules that govern these interactions remain poorly understood thus hindering the development of therapeutic strategies to target cancer stroma. We have taken a mathematical approach to begin defining these rules by performing the first large-scale quantitative analysis of fibroblast effects on cancer cell proliferation across more than four hundred heterotypic cell line pairings. Systems-level modeling of this complex dataset using singular value decomposition revealed that normal tissue fibroblasts variably express at least two functionally distinct activities, one which reflects transcriptional programs associated with activated mesenchymal cells, that act either coordinately or at cross-purposes to modulate cancer cell proliferation. These findings suggest that quantitative approaches may prove useful for identifying organizational principles that govern complex heterotypic cell-cell interactions in cancer and other contexts.

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.