Comparison of linear and nonlinear implementation of the compartmental tissue uptake model for dynamic contrast-enhanced MRI

Comparison of Early Contrast Enhancement Models in Ultrafast Dynamic Contrast-Enhanced Magnetic Resonance Imaging of Prostate Cancer

Tofts models have failed to produce reliable quantitative markers for prostate cancer. We examined the differences between prostate zones and lesion PI-RADS categories and grade group (GG) using regions of interest drawn in tumor and normal-appearing tissue for a two-compartment uptake (2CU) model (including plasma volume (vp), plasma flow (Fp), permeability surface area product (PS), plasma mean transit time (MTTp), capillary transit time (Tc), extraction fraction (E), and transfer constant (Ktrans)) and exponential (amplitude (A), arrival time (t0), and enhancement rate (α)), sigmoidal (amplitude (A0), center time relative to arrival time (A1 - T0), and slope (A2)), and empirical mathematical models, and time to peak (TTP) parameters fitted to high temporal resolution (1.695 s) DCE-MRI data. In 25 patients with 35 PI-RADS category 3 or higher tumors, we found Fp and α differed between peripheral and transition zones. Parameters Fp, MTTp, Tc, E, α, A1 - T0, and A2 and TTP all showed associations with PI-RADS categories and with GG in the PZ when normal-appearing regions were included in the non-cancer GG. PS and Ktrans were not associated with any PI-RADS category or GG. This pilot study suggests early enhancement parameters derived from ultrafast DCE-MRI may become markers of prostate cancer.

Prediction of Lung Shunt Fraction for Yttrium-90 Treatment of Hepatic Tumors Using Dynamic Contrast Enhanced MRI with Quantitative Perfusion Processing

There is no noninvasive method to estimate lung shunting fraction (LSF) in patients with liver tumors undergoing Yttrium-90 (Y90) therapy. We propose to predict LSF from noninvasive dynamic contrast enhanced (DCE) MRI using perfusion quantification. Two perfusion quantification methods were used to process DCE MRI in 25 liver tumor patients: Kety's tracer kinetic modeling with a delay-fitted global arterial input function (AIF) and quantitative transport mapping (QTM) based on the inversion of transport equation using spatial deconvolution without AIF. LSF was measured on SPECT following Tc-99m macroaggregated albumin (MAA) administration via hepatic arterial catheter. The patient cohort was partitioned into a low-risk group (LSF ≤ 10%) and a high-risk group (LSF > 10%). Results: In this patient cohort, LSF was positively correlated with QTM velocity |u| (r = 0.61, F = 14.0363, p = 0.0021), and no significant correlation was observed with Kety's parameters, tumor volume, patient age and gender. Between the low LSF and high LSF groups, there was a significant difference for QTM |u| (0.0760 ± 0.0440 vs. 0.1822 ± 0.1225 mm/s, p = 0.0011), and Kety's Ktrans (0.0401 ± 0.0360 vs 0.1198 ± 0.3048, p = 0.0471) and Ve (0.0900 ± 0.0307 vs. 0.1495 ± 0.0485, p = 0.0114). The area under the curve (AUC) for distinguishing between low LSF and high LSF was 0.87 for |u|, 0.80 for Ve and 0.74 for Ktrans. Noninvasive prediction of LSF is feasible from DCE MRI with QTM velocity postprocessing.

Quantitative Analysis of DCE and DSC-MRI: From Kinetic Modeling to Deep Learning

BACKGROUND

 Perfusion MRI is a well-established imaging modality with a multitude of applications in oncological and cardiovascular imaging. Clinically used processing methods, while stable and robust, have remained largely unchanged in recent years. Despite promising results from novel methods, their relatively minimal improvement compared to established methods did not generally warrant significant changes to clinical perfusion processing.

RESULTS AND CONCLUSION

 Machine learning in general and deep learning in particular, which are currently revolutionizing computer-aided diagnosis, may carry the potential to change this situation and truly capture the potential of perfusion imaging. Recent advances in the training of recurrent neural networks make it possible to predict and classify time series data with high accuracy. Combining physics-based tissue models and deep learning, using either physics-informed neural networks or universal differential equations, simplifies the training process and increases the interpretability of the resulting models. Due to their versatility, these methods will potentially be useful in bridging the gap between microvascular architecture and perfusion parameters, akin to MR fingerprinting in structural MR imaging. Still, further research is urgently needed before these methods may be used in clinical practice.

KEY POINTS

· Machine learning offers promising methods for processing of perfusion data.. · Recurrent neural networks can classify time series with high accuracy.. · Data augmentation is essentially especially when using small datasets..

CITATION FORMAT

· Rotkopf LT, Zhang KS, Tavakoli AA et al. Quantitative Analysis of DCE and DSC-MRI: From Kinetic Modeling to Deep Learning. Fortschr Röntgenstr 2022; DOI: 10.1055/a-1762-5854.

Quantitative transport mapping (QTM) for differentiating benign and malignant breast lesion: Comparison with traditional kinetics modeling and semi-quantitative enhancement curve characteristics

PURPOSE

To test the feasibility of using quantitative transport mapping (QTM) method, which is based on the inversion of transport equation using spatial deconvolution without any arterial input function, for automatically postprocessing dynamic contrast enhanced MRI (DCE-MRI) to differentiate malignant and benign breast tumors.

MATERIALS AND METHODS

Breast DCE-MRI data with biopsy confirmed malignant (n = 13) and benign tumors (n = 13) was used to assess QTM velocity (|u|) and diffusion coefficient (D), volume transfer constant (K^trans), volume fraction of extravascular extracellular space (V_e) from kinetics method, and traditional enhancement curve characteristics (ECC: amplitude A, wash-in rate α, wash-out rate β). A Mann-Whitney U test and receiver operating characteristic curve (ROC) analysis were performed to assess the diagnostic performance of these parameters for distinguishing between benign and malignant tumors.

RESULTS

Between malignant and benign tumors, there was a significant difference in |u| and K^trans, (p = 0.0066, 0.0274, respectively), but not in D, V_e, A, α and β (p = 0.1119, 0.2382, 0.4418,0.2592 and 0.9591, respectively). ROC area-under-the-curve was 0.82, 0.75 (95% confidence level 0.60-0.95, 0.51-0.90) for |u| and K^trans, respectively.

CONCLUSION

QTM postprocesses DCE-MRI automatically through deconvolution in space and time to solve the inverse problem of the transport equation. Comparing with traditional kinetics method and ECC, QTM method showed better diagnostic accuracy in differentiating benign from malignant breast tumors in this study.

Convolutional neural network for accelerating the computation of the extended Tofts model in dynamic contrast-enhanced magnetic resonance imaging

Quantitative physiological parameters can be obtained from nonlinear pharmacokinetic models, such as the extended Tofts (eTofts) model, applied to dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). However, the computation of such nonlinear models is time consuming. The aim of this study was to develop a convolutional neural network (CNN) for accelerating the computation of fitting eTofts model without sacrificing agreement with conventional nonlinear-least-square (NLLS) fitting. This was a retrospective study, which included 13 patients with brain glioma for training (75%) and validation (25%), and 11 patients (three glioma, four brain metastases, and four lymphoma) for testing. CAIPIRINHA-Dixon-TWIST DCE-MRI and double flip angle T₁ map acquired at 3 T were used. A CNN with both local pathway and global pathway modules was designed to estimate the eTofts model parameters, the volume transfer constant (K^trans ), blood volume fraction (v_p ), and volume fraction of extracellular extravascular space (v_e ), from DCE-MRI data of tumor and normal-appearing voxels. The CNN was trained on mixed dataset consisting of synthetic and patient data. The CNN result and computation speed were compared with NLLS fitting. The robustness to noise variations and generalization to brain metastases and lymphoma data were also evaluated. Statistical tests used were Student's t test on mean absolute error, concordance correlation coefficient (CCC), and normalized root mean squared error. Including global pathway modules in the CNN and training the network with mixed data significantly (p < 0.05) improved the CNN performance. Compared with NLLS fitting, CNN yields an average CCC greater than 0.986 for K^trans , greater than 0.965 for v_p , and greater than 0.948 for v_e . The CNN accelerated computation speed approximately 2000 times compared to NLLS, showed robustness to noise (signal-to-noise ratio >34.42 dB), and had no significant (p > 0.21) difference applied to brain metastases and lymphoma data. In conclusion, the proposed CNN to estimate eTofts parameters showed comparable result as NLLS fitting while significantly reducing the computation time. LEVEL OF EVIDENCE: 3 TECHNICAL EFFICACY STAGE: 1.

Phantom-based quality assurance for multicenter quantitative MRI in locally advanced cervical cancer

BACKGROUND AND PURPOSE

A wide variation of MRI systems is a challenge in multicenter imaging biomarker studies as it adds variation in quantitative MRI values. The aim of this study was to design and test a quality assurance (QA) framework based on phantom measurements, for the quantitative MRI protocols of a multicenter imaging biomarker trial of locally advanced cervical cancer.

MATERIALS AND METHODS

Fifteen institutes participated (five 1.5 T and ten 3 T scanners). Each institute optimized protocols for T2, diffusion-weighted imaging, T1, and dynamic contrast-enhanced (DCE-)MRI according to system possibilities, institutional preferences and study-specific constraints. Calibration phantoms with known values were used for validation. Benchmark protocols, similar on all systems, were used to investigate whether differences resulted from variations in institutional protocols or from system variations. Bias, repeatability (%RC), and reproducibility (%RDC) were determined. Ratios were used for T2 and T1 values.

RESULTS

The institutional protocols showed a range in bias of 0.88-0.98 for T2 (median %RC = 1%; %RDC = 12%), -0.007 to 0.029 × 10^-3 mm²/s for the apparent diffusion coefficient (median %RC = 3%; %RDC = 18%), and 0.39-1.29 for T1 (median %RC = 1%; %RDC = 33%). For DCE a nonlinear vendor-specific relation was observed between measured and true concentrations with magnitude data, whereas the relation was linear when phase data was used.

CONCLUSION

We designed a QA framework for quantitative MRI protocols and demonstrated for a multicenter trial for cervical cancer that measurement of consistent T2 and apparent diffusion coefficient values is feasible despite protocol differences. For DCE-MRI and T1 mapping with the variable flip angle method, this was more challenging.

Quantifying Perfusion Properties with DCE-MRI Using a Dictionary Matching Approach

Perfusion properties can be estimated from pharmacokinetic models applied to DCE-MRI data using curve fitting algorithms; however, these suffer from drawbacks including the local minimum problem and substantial computational time. Here, a dictionary matching approach is proposed as an alternative. Curve fitting and dictionary matching were applied to simulated data using the dual-input single-compartment model with known perfusion property values and 5 in vivo DCE-MRI datasets. In simulation at SNR 60 dB, the dictionary estimate had a mean percent error of 0.4-1.0% for arterial fraction, 0.5-1.4% for distribution volume, and 0.0% for mean transit time. The curve fitting estimate had a mean percent error of 1.1-2.1% for arterial fraction, 0.5-1.3% for distribution volume, and 0.2-1.8% for mean transit time. In vivo, dictionary matching and curve fitting showed no statistically significant differences in any of the perfusion property measurements in any of the 10 ROIs between the methods. In vivo, the dictionary method performed over 140-fold faster than curve fitting, obtaining whole volume perfusion maps in just over 10 s. This study establishes the feasibility of using a dictionary matching approach as a new and faster way of estimating perfusion properties from pharmacokinetic models in DCE-MRI.

Measurement of blood-brain barrier permeability using dynamic contrast-enhanced magnetic resonance imaging with reduced scan time

PURPOSE

To investigate the feasibility of measuring the subtle disruption of blood-brain barrier (BBB) using DCE-MRI with a scan duration shorter than 10 min.

METHODS

The extended Patlak-model (EPM) was introduced to include the effect of plasma flow (F_p ) in the estimation of vascular permeability-surface area product (PS). Numerical simulation studies were carried out to investigate how the reduction in scan time affects the accuracy in estimating contrast kinetic parameters. DCE-MRI studies of the rat brain were conducted with Fisher rats to confirm the results from the simulation. Intracranial F98 glioblastoma models were used to assess areas with different levels of permeability. In the normal brain tissues, the Patlak model (PM) and EPM were compared, whereas the 2-compartment-exchange-model (TCM) and EPM were assessed in the peri-tumor and the tumor regions.

RESULTS

The simulation study results demonstrated that scan time reduction could lead to larger bias in PS estimated by PM (>2000%) than by EPM (<47%), especially when F_p is low. When F_p was high as in the gray matter, the bias in PM-PS (>900%) were larger than that in EPM-PS (<42%). The animal study also showed similar results, where the PM parameters were more sensitive to the scan duration than the EPM parameters. It was also demonstrated that, in the peri-tumor region, the EPM parameters showed less change by scan duration than the TCM parameters.

CONCLUSION

The results of this study suggest that EPM can be used to measure PS with a scan duration of 10 min or less.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate

PURPOSE

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer.

METHODS

Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time.

RESULTS

The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%.

CONCLUSION

The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method.

Linearization improves the repeatability of quantitative dynamic contrast-enhanced MRI

PURPOSE

The purpose of this study was to compare the repeatabilities of the linear and nonlinear Tofts and reference region models (RRM) for dynamic contrast-enhanced MRI (DCE-MRI).

MATERIALS AND METHODS

Simulated and experimental DCE-MRI data from 12 rats with a flank tumor of C6 glioma acquired over three consecutive days were analyzed using four quantitative and semi-quantitative DCE-MRI metrics. The quantitative methods used were: 1) linear Tofts model (LTM), 2) non-linear Tofts model (NTM), 3) linear RRM (LRRM), and 4) non-linear RRM (NRRM). The following semi-quantitative metrics were used: 1) maximum enhancement ratio (MER), 2) time to peak (TTP), 3) initial area under the curve (iauc64), and 4) slope. LTM and NTM were used to estimate K^trans, while LRRM and NRRM were used to estimate K^trans relative to muscle (R^Ktrans). Repeatability was assessed by calculating the within-subject coefficient of variation (wSCV) and the percent intra-subject variation (iSV) determined with the Gage R&R analysis.

RESULTS

The iSV for R^Ktrans using LRRM was two-fold lower compared to NRRM at all simulated and experimental conditions. A similar trend was observed for the Tofts model, where LTM was at least 50% more repeatable than the NTM under all experimental and simulated conditions. The semi-quantitative metrics iauc64 and MER were as equally repeatable as K^trans and R^Ktrans estimated by LTM and LRRM respectively. The iSV for iauc64 and MER were significantly lower than the iSV for slope and TTP.

CONCLUSION

In simulations and experimental results, linearization improves the repeatability of quantitative DCE-MRI by at least 30%, making it as repeatable as semi-quantitative metrics.

Vastly accelerated linear least-squares fitting with numerical optimization for dual-input delay-compensated quantitative liver perfusion mapping

PURPOSE

To propose an efficient algorithm to perform dual input compartment modeling for generating perfusion maps in the liver.

METHODS

We implemented whole field-of-view linear least squares (LLS) to fit a delay-compensated dual-input single-compartment model to very high temporal resolution (four frames per second) contrast-enhanced 3D liver data, to calculate kinetic parameter maps. Using simulated data and experimental data in healthy subjects and patients, whole-field LLS was compared with the conventional voxel-wise nonlinear least-squares (NLLS) approach in terms of accuracy, performance, and computation time.

RESULTS

Simulations showed good agreement between LLS and NLLS for a range of kinetic parameters. The whole-field LLS method allowed generating liver perfusion maps approximately 160-fold faster than voxel-wise NLLS, while obtaining similar perfusion parameters.

CONCLUSIONS

Delay-compensated dual-input liver perfusion analysis using whole-field LLS allows generating perfusion maps with a considerable speedup compared with conventional voxel-wise NLLS fitting. Magn Reson Med 79:2415-2421, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Parameter estimation using weighted total least squares in the two-compartment exchange model

PURPOSE

The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account.

METHOD

To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator.

RESULTS

The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio.

CONCLUSION

The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med 79:561-567, 2017. © 2017 International Society for Magnetic Resonance in Medicine.