Issues of discontinuity in the impulse residue function for deconvolution analysis of dynamic contrast-enhanced MRI data

Dual-input tracer kinetic modeling of dynamic contrast-enhanced MRI in thoracic malignancies

Pulmonary perfusion with dynamic contrast‐enhanced (DCE‐) MRI is typically assessed using a single‐input tracer kinetic model. Preliminary studies based on perfusion CT are indicating that dual‐input perfusion modeling of lung tumors may be clinically valuable as lung tumors have a dual blood supply from the pulmonary and aortic system. This study aimed to investigate the feasibility of fitting dual‐input tracer kinetic models to DCE‐MRI datasets of thoracic malignancies, including malignant pleural mesothelioma (MPM) and nonsmall cell lung cancer (NSCLC), by comparing them to single‐input (pulmonary or systemic arterial input) tracer kinetic models for the voxel‐level analysis within the tumor with respect to goodness‐of‐fit statistics. Fifteen patients (five MPM, ten NSCLC) underwent DCE‐MRI prior to radiotherapy. DCE‐MRI data were analyzed using five different single‐ or dual‐input tracer kinetic models: Tofts‐Kety (TK), extended TK (ETK), two compartment exchange (2CX), adiabatic approximation to the tissue homogeneity (AATH) and distributed parameter (DP) models. The pulmonary blood flow (BF), blood volume (BV), mean transit time (MTT), permeability‐surface area product (PS), fractional interstitial volume (v_I), and volume transfer constant (K^Trans) were calculated for both single‐ and dual‐input models. The pulmonary arterial flow fraction (γ), pulmonary arterial blood flow (BF_PA) and systemic arterial blood flow (BF_A) were additionally calculated for only dual‐input models. The competing models were ranked and their Akaike weights were calculated for each voxel according to corrected Akaike information criterion (cAIC). The optimal model was chosen based on the lowest cAIC value. In both types of tumors, all five dual‐input models yielded lower cAIC values than their corresponding single‐input models. The 2CX model was the best‐fitted model and most optimal in describing tracer kinetic behavior to assess microvascular properties in both MPM and NSCLC. The dual‐input 2CX‐model‐derived BF_A was the most significant parameter in differentiating adenocarcinoma from squamous cell carcinoma histology for NSCLC patients.

Spatially regularized estimation of the tissue homogeneity model parameters in DCE-MRI using proximal minimization

PURPOSE

The Tofts and the extended Tofts models are the pharmacokinetic models commonly used in dynamic contrast-enhanced MRI (DCE-MRI) perfusion analysis, although they do not provide two important biological markers, namely, the plasma flow and the permeability-surface area product. Estimates of such markers are possible using advanced pharmacokinetic models describing the vascular distribution phase, such as the tissue homogeneity model. However, the disadvantage of the advanced models lies in biased and uncertain estimates, especially when the estimates are computed voxelwise. The goal of this work is to improve the reliability of the estimates by including information from neighboring voxels.

THEORY AND METHODS

Information from the neighboring voxels is incorporated in the estimation process through spatial regularization in the form of total variation. The spatial regularization is applied on five maps of perfusion parameters estimated using the tissue homogeneity model. Since the total variation is not differentiable, two proximal techniques of convex optimization are used to solve the problem numerically.

RESULTS

The proposed algorithm helps to reduce noise in the estimated perfusion-parameter maps together with improving accuracy of the estimates. These conclusions are proved using a numerical phantom. In addition, experiments on real data show improved spatial consistency and readability of perfusion maps without considerable lowering of the quality of fit.

CONCLUSION

The reliability of the DCE-MRI perfusion analysis using the tissue homogeneity model can be improved by employing spatial regularization. The proposed utilization of modern optimization techniques implies only slightly higher computational costs compared to the standard approach without spatial regularization.

Blind deconvolution estimation of an arterial input function for small animal DCE-MRI

PURPOSE

One of the main obstacles for reliable quantitative dynamic contrast-enhanced (DCE) MRI is the need for accurate knowledge of the arterial input function (AIF). This is a special challenge for preclinical small animal applications where it is very difficult to measure the AIF without partial volume and flow artifacts. Furthermore, using advanced pharmacokinetic models (allowing estimation of blood flow and permeability-surface area product in addition to the classical perfusion parameters) poses stricter requirements on the accuracy and precision of AIF estimation. This paper addresses small animal DCE-MRI with advanced pharmacokinetic models and presents a method for estimation of the AIF based on blind deconvolution.

METHODS

A parametric AIF model designed for small animal physiology and use of advanced pharmacokinetic models is proposed. The parameters of the AIF are estimated using multichannel blind deconvolution.

RESULTS

Evaluation on simulated data show that for realistic signal to noise ratios blind deconvolution AIF estimation leads to comparable results as the use of the true AIF. Evaluation on real data based on DCE-MRI with two contrast agents of different molecular weights showed a consistence with the known effects of the molecular weight.

CONCLUSION

Multi-channel blind deconvolution using the proposed AIF model specific for small animal DCE-MRI provides reliable perfusion parameter estimates under realistic signal to noise conditions.

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints

Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.

Quantitative Myocardial Perfusion with Dynamic Contrast-Enhanced Imaging in MRI and CT: Theoretical Models and Current Implementation

Technological advances in magnetic resonance imaging (MRI) and computed tomography (CT), including higher spatial and temporal resolution, have made the prospect of performing absolute myocardial perfusion quantification possible, previously only achievable with positron emission tomography (PET). This could facilitate integration of myocardial perfusion biomarkers into the current workup for coronary artery disease (CAD), as MRI and CT systems are more widely available than PET scanners. Cardiac PET scanning remains expensive and is restricted by the requirement of a nearby cyclotron. Clinical evidence is needed to demonstrate that MRI and CT have similar accuracy for myocardial perfusion quantification as PET. However, lack of standardization of acquisition protocols and tracer kinetic model selection complicates comparison between different studies and modalities. The aim of this overview is to provide insight into the different tracer kinetic models for quantitative myocardial perfusion analysis and to address typical implementation issues in MRI and CT. We compare different models based on their theoretical derivations and present the respective consequences for MRI and CT acquisition parameters, highlighting the interplay between tracer kinetic modeling and acquisition settings.

Intermodel agreement of myocardial blood flow estimation from stress-rest myocardial perfusion magnetic resonance imaging in patients with coronary artery disease

OBJECTIVES

The aim of this study was to assess the intermodel agreement of different magnetic resonance myocardial perfusion models and evaluate their correspondence to stenosis diameter.

MATERIALS AND METHODS

In total, 260 myocardial segments were analyzed from rest and adenosine stress first-pass myocardial perfusion magnetic resonance images (1.5 T, 0.050 ± 0.005 mmol/kg body weight gadolinium; 122 segments in rest, 138 in stress) in 10 patients with suspected or known coronary artery disease. Signal intensity curves were calculated per myocardial segment, of which the contours were traced with QMASS MR V.7.6 (Medis, Leiden, the Netherlands), and exported to Matlab. Myocardial blood flow quantification was performed with distributed parameter, extended Toft, Patlak, and Fermi parametric models (in-house programs; Matlab R2013a; Mathworks Inc, Natick, MA). Modeling was applied after the signal intensity curves were corrected for spatial magnetic field inhomogeneity and contrast saturation. Overall and grouped perfusion values based on presence of coronary stenosis (>50% diameter reduction) at coronary computed tomography angiography at second generation dual-source computed tomography were compared between the perfusion models.

RESULTS

Rest and stress myocardial perfusion estimates for all models were significantly related to each other (P < 0.001). The highest correlation coefficients were found between the extended Toft and Fermi models (R = 0.89-0.91) and low correlation coefficients between the distributed parameter and Patlak models (R = 0.66-0.68). The models resulted in significantly different perfusion estimates in stress (P = 0.03), but not in rest (P = 0.74). The differences in perfusion estimates in stress were caused by differences between the distributed parameter and Patlak models and between the Patlak and Fermi models (both P < 0.001). Significantly lower perfusion estimates were found for myocardial segments subtended by coronary arteries with versus without significant stenosis, but only for estimations produced by the extended Toft model (P = 0.04) and Fermi model (P = 0.01). There were no significant differences in rest perfusion values between models.

CONCLUSIONS

Quantitative myocardial perfusion values in stress depend on the modeling method used to calculate the perfusion estimate. The difference in myocardial perfusion estimate with or without stenosis in the subtending coronary artery is most pronounced when the extended Toft or Fermi model is used.

Dynamic Contrast-Enhanced MRI Kinetic Parameters as Prognostic Biomarkers for Prediction of Survival of Patient with Advanced Hepatocellular Carcinoma: A Pilot Comparative Study

RATIONALE AND OBJECTIVES

Tracer kinetic model selection for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data analysis influences its use as a prognostic biomarker. Our aim was to find DCE-MRI parameters that predict 1-year survival (1YS) and overall survival (OS) among patients with advanced hepatocellular carcinoma (HCC) treated with antiangiogenic monotherapy by conducting a proof-of-concept comparative study of five different kinetic models.

MATERIALS AND METHODS

Twenty patients with advanced HCC underwent DCE-MRI and subsequently received sunitinib. Pretreatment DCE-MRI data were analyzed retrospectively by using the Tofts-Kety (TK), extended TK, two compartment exchange, adiabatic approximation to the tissue homogeneity (AATH), and distributed parameter (DP) models. Arterial flow fraction (γ), arterial blood flow (BFA), permeability-surface area product (PS), fractional interstitial volume (vI), and other five parameters were calculated for each model. Individual parameters were evaluated for 1YS prediction using cross-validated Kaplan-Meier analysis, and for association with OS using univariate Cox regression analysis, with additional permutation testing.

RESULTS

For 1YS prediction, the TK model-derived γ (P = .007) and vI (P = .029) and the AATH model-derived PS (P = .005) were significant; all these parameters were lower in the high-risk group. Increase in the AATH model-derived PS and the DP model-derived BFA was associated with significant increase in OS with hazard ratios of 0.766 (P = .023) and 0.809 (P = .025), respectively.

CONCLUSIONS

The AATH model-derived PS was an effective prognostic biomarker for both 1YS and OS.

Water-Exchange-Modified Kinetic Parameters from Dynamic Contrast-Enhanced MRI as Prognostic Biomarkers of Survival in Advanced Hepatocellular Carcinoma Treated with Antiangiogenic Monotherapy

BACKGROUND

To find prognostic biomarkers in pretreatment dynamic contrast-enhanced MRI (DCE-MRI) water-exchange-modified (WX) kinetic parameters for advanced hepatocellular carcinoma (HCC) treated with antiangiogenic monotherapy.

METHODS

Twenty patients with advanced HCC underwent DCE-MRI and were subsequently treated with sunitinib. Pretreatment DCE-MRI data on advanced HCC were analyzed using five different WX kinetic models: the Tofts-Kety (WX-TK), extended TK (WX-ETK), two compartment exchange, adiabatic approximation to tissue homogeneity (WX-AATH), and distributed parameter (WX-DP) models. The total hepatic blood flow, arterial flow fraction (γ), arterial blood flow (BFA), portal blood flow, blood volume, mean transit time, permeability-surface area product, fractional interstitial volume (vI), extraction fraction, mean intracellular water molecule lifetime (τC), and fractional intracellular volume (vC) were calculated. After receiver operating characteristic analysis with leave-one-out cross-validation, individual parameters for each model were assessed in terms of 1-year-survival (1YS) discrimination using Kaplan-Meier analysis, and association with overall survival (OS) using univariate Cox regression analysis with permutation testing.

RESULTS

The WX-TK-model-derived γ (P = 0.022) and vI (P = 0.010), and WX-ETK-model-derived τC (P = 0.023) and vC (P = 0.042) were statistically significant prognostic biomarkers for 1YS. Increase in the WX-DP-model-derived BFA (P = 0.025) and decrease in the WX-TK, WX-ETK, WX-AATH, and WX-DP-model-derived vC (P = 0.034, P = 0.038, P = 0.028, P = 0.041, respectively) were significantly associated with an increase in OS.

CONCLUSIONS

The WX-ETK-model-derived vC was an effective prognostic biomarker for advanced HCC treated with sunitinib.

Simulation study of the effect of golden-angle KWIC with generalized kinetic model analysis on diagnostic accuracy for lesion discrimination

PURPOSE

To quantitatively evaluate temporal blurring of dynamic contrast-enhanced MRI data generated using a k-space weighted image contrast (KWIC) image reconstruction technique with golden-angle view-ordering.

METHODS

K-space data were simulated using golden-angle view-ordering and reconstructed using a KWIC algorithm with a Fibonacci number of views enforced for each annulus in k-space. Temporal blurring was evaluated by comparing pharmacokinetic model parameters estimated from the simulated data with the true values. Diagnostic accuracy was quantified using receiver operator characteristic curves (ROC) and the area under the ROC curves (AUC).

RESULTS

Estimation errors of pharmacokinetic model parameters were dependent on the true curve type and the lesion size. For 10mm benign and malignant lesions, estimated AUC values using the true and estimate AIFs were consistent with the true AUC value. For 5mm benign and 20mm malignant lesions, estimated AUC values using the true and estimated AIFs were 0.906±0.020 and 0.905±0.021, respectively, as compared with the true AUC value of 0.896.

CONCLUSIONS

Although the investigated reconstruction algorithm does impose errors in pharmacokinetic model parameter estimation, they are not expected to significantly impact clinical studies of diagnostic accuracy.

Assessment of tumor blood flow distribution by dynamic contrast-enhanced CT

A distinct feature of the tumor vasculature is its tortuosity and irregular branching of vessels, which can translate to a wider dispersion and higher variability of blood flow in the tumor. To enable tumor blood flow variability to be assessed in vivo by imaging, a tracer kinetic model that accounts for flow dispersion is developed for use with dynamic contrast-enhanced (DCE) CT. The proposed model adopts a multiple-pathway approach and allows for the quantification of relative dispersion in the blood flow distribution, which reflects flow variability in the tumor vasculature. Monte Carlo simulation experiments were performed to study the possibility of reducing the number of model parameters based on the Akaike information criterion approach and to explore possible noise and tissue conditions in which the model might be applicable. The model was used for region-of-interest analysis and to generate perfusion parameter maps for three patient DCE CT cases with cerebral tumors, to illustrate clinical applicability.

Measurement of blood-brain barrier permeability with t1-weighted dynamic contrast-enhanced MRI in brain tumors: a comparative study with two different algorithms

The purpose of this study was to assess the feasibility of measuring different permeability parameters with T₁-weighted dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) in order to investigate the blood brain-barrier permeability associated with different brain tumors. The Patlak algorithm and the extended Tofts-Kety model were used to this aim. Twenty-five adult patients with tumors of different histological grades were enrolled in this study. MRI examinations were performed at 1.5 T. Multiflip angle, fast low-angle shot, and axial 3D T₁-weighted images were acquired to calculate T₁ maps, followed by a DCE acquisition. A region of interest was placed within the tumor of each patient to calculate the mean value of different permeability parameters. Differences in permeability measurements were found between different tumor grades, with higher histological grades characterized by higher permeability values. A significant difference in transfer constant (K^trans) values was found between the two methods on high-grade tumors; however, both techniques revealed a significant correlation between the histological grade of tumors and their K^trans values. Our results suggest that DCE acquisition is feasible in patients with brain tumors and that K^trans maps can be easily obtained by these two algorithms, even if the theoretical model adopted could affect the final results.

Quantification of antiangiogenic and antivascular drug activity by kinetic analysis of DCE-MRI data

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can be used to quantify the response of tumors to vascular targeting agents. Tumor response is frequently assessed using mathematical models that describe the distribution of contrast agents over time as a function of fundamental characteristics of vascular physiology. Generally, mathematical models of biological systems are abstractions that attempt to retain fundamental physiologic characteristics, thereby allowing for multiple potential modeling approaches and structures. Various DCE-MRI modeling techniques are discussed in this article.

Tracer kinetic modelling in MRI: estimating perfusion and capillary permeability

The tracer-kinetic models developed in the early 1990s for dynamic contrast-enhanced MRI (DCE-MRI) have since become a standard in numerous applications. At the same time, the development of MRI hardware has led to increases in image quality and temporal resolution that reveal the limitations of the early models. This in turn has stimulated an interest in the development and application of a second generation of modelling approaches. They are designed to overcome these limitations and produce additional and more accurate information on tissue status. In particular, models of the second generation enable separate estimates of perfusion and capillary permeability rather than a single parameter K(trans) that represents a combination of the two. A variety of such models has been proposed in the literature, and development in the field has been constrained by a lack of transparency regarding terminology, notations and physiological assumptions. In this review, we provide an overview of these models in a manner that is both physically intuitive and mathematically rigourous. All are derived from common first principles, using concepts and notations from general tracer-kinetic theory. Explicit links to their historical origins are included to allow for a transfer of experience obtained in other fields (PET, SPECT, CT). A classification is presented that reveals the links between all models, and with the models of the first generation. Detailed formulae for all solutions are provided to facilitate implementation. Our aim is to encourage the application of these tools to DCE-MRI by offering researchers a clearer understanding of their assumptions and requirements.

Fundamentals of tracer kinetics for dynamic contrast-enhanced MRI

Tracer kinetic methods employed for quantitative analysis of dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) share common roots with earlier tracer studies involving arterial-venous sampling and other dynamic imaging modalities. This article reviews the essential foundation concepts and principles in tracer kinetics that are relevant to DCE MRI, including the notions of impulse response and convolution, which are central to the analysis of DCE MRI data. We further examine the formulation and solutions of various compartmental models frequently used in the literature. Topics of recent interest in the processing of DCE MRI data, such as the account of water exchange and the use of reference tissue methods to obviate the measurement of an arterial input, are also discussed. Although the primary focus of this review is on the tracer models and methods for T(1) -weighted DCE MRI, some of these concepts and methods are also applicable for analysis of dynamic susceptibility contrast-enhanced MRI data.