Robust estimation of hemo-dynamic parameters in traditional DCE-MRI models

Improving Microstructural Estimation in Time-Dependent Diffusion MRI With a Bayesian Method

BACKGROUND

Accurately fitting diffusion-time-dependent diffusion MRI (td-dMRI) models poses challenges due to complex and nonlinear formulas, signal noise, and limited clinical data acquisition.

PURPOSE

Introduce a Bayesian methodology to refine microstructural fitting within the IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) model and optimize the prior distribution within the Bayesian framework.

STUDY TYPE

Retrospective.

POPULATION

Involving 69 pediatric patients (median age 6 years, interquartile range [IQR] 3-9 years, 61% male) with 41 low-grade and 28 high-grade gliomas, of which 76.8% were identified within the brainstem or cerebellum.

FIELD STRENGTH/SEQUENCE

3 T, oscillating gradient spin-echo (OGSE) and pulsed gradient spin-echo (PGSE).

ASSESSMENT

The Bayesian method's performance in fitting cell diameter (d $$ d $$ ), intracellular volume fraction (f in $$ {f}_{in} $$ ), and extracellular diffusion coefficient (D ex $$ {D}_{ex} $$ ) was compared against the NLLS method, considering simulated and experimental data. The tumor region-of-interest (ROI) were manually delineated on the b0 images. The diagnostic performance in distinguishing high- and low-grade gliomas was assessed, and fitting accuracy was validated against H&E-stained pathology.

STATISTICAL TESTS

T-test, receiver operating curve (ROC), area under the curve (AUC) and DeLong's test were conducted. Significance considered at P < 0.05.

RESULTS

Bayesian methodology manifested increased accuracy with robust estimates in simulation (RMSE decreased by 29.6%, 40.9%, 13.6%, and STD decreased by 29.2%, 43.5%, and 24.0%, respectively ford $$ d $$ ,f in $$ {f}_{in} $$ , andD ex $$ {D}_{ex} $$ compared to NLLS), indicating fewer outliers and reduced error. Diagnostic performance for tumor grade was similar in both methods, however, Bayesian method generated smoother microstructural maps (outliers ratio decreased by 45.3% ± 19.4%) and a marginal enhancement in correlation with H&E staining result (r = 0.721 forf in $$ {f}_{in} $$ compared to r = 0.698 using NLLS, P = 0.5764).

DATA CONCLUSION

The proposed Bayesian method substantially enhances the accuracy and robustness of IMPULSED model estimation, suggesting its potential clinical utility in characterizing cellular microstructure.

EVIDENCE LEVEL

3 TECHNICAL EFFICACY: Stage 1.

Quantitative DCE Dynamics on Transformed MR Imaging Discriminates Clinically Significant Prostate Cancer

Dynamic contrast enhancement (DCE) imaging is a valuable sequence of multiparametric magnetic resonance imaging (mpMRI). A DCE sequence enhances the vasculature and complements T2-weighted (T2W) and Diffusion-weighted imaging (DWI), allowing early detection of prostate cancer. However, DCE assessment has remained primarily qualitative. The study proposes quantifying DCE characteristics (T1W sequences) using six time-dependent metrics computed on feature transformations (306 radiomic features) of abnormal image regions observed over time. We applied our methodology to prostate cancer patients with the DCE MRI images (n = 25) who underwent prostatectomy with confirmed pathological assessment of the disease using Gleason Score. Regions of abnormality were assessed on the T2W MRI, guided using the whole mount pathology. Preliminary analysis finds over six temporal DCE imaging features obtained on different transformations on the imaging regions showed significant differences compared to the indolent counterpart (P ≤ 0.05, q ≤ 0.01). We find classifier models using logistic regression formed on DCE features after feature-based transformation (Centre of Mass) had an AUC of 0.89-0.94. While using mean feature-based transformation, the AUC was in the range of 0.71-0.76, estimated using the 0.632 bootstrap cross-validation method and after applying sample balancing using the synthetic minority oversampling technique (SMOTE). Our study finds, radiomic transformation of DCE images (T1 sequences) provides better signal standardization. Their temporal characteristics allow improved discrimination of aggressive disease.

Unified Bayesian network for uncertainty quantification of physiological parameters in dynamic contrast enhanced (DCE) MRI of the liver

Objective. Physiological parameter estimation is affected by intrinsic ambiguity in the data such as noise and model inaccuracies. The aim of this work is to provide a deep learning framework for accurate parameter and uncertainty estimates for DCE-MRI in the liver.Approach. Concentration time curves are simulated to train a Bayesian neural network (BNN). Training of the BNN involves minimization of a loss function that jointly minimizes the aleatoric and epistemic uncertainties. Uncertainty estimation is evaluated for different noise levels and for different out of distribution (OD) cases, i.e. where the data during inference differs strongly to the data during training. The accuracy of parameter estimates are compared to a nonlinear least squares (NLLS) fitting in numerical simulations andin vivodata of a patient suffering from hepatic tumor lesions.Main results. BNN achieved lower root-mean-squared-errors (RMSE) than the NLLS for the simulated data. RMSE of BNN was on overage of all noise levels lower by 33% ± 1.9% forktrans, 22% ± 6% forveand 89% ± 5% forvpthan the NLLS. The aleatoric uncertainties of the parameters increased with increasing noise level, whereas the epistemic uncertainty increased when a BNN was evaluated with OD data. For thein vivodata, more robust parameter estimations were obtained by the BNN than the NLLS fit. In addition, the differences between estimated parameters for healthy and tumor regions-of-interest were significant (p< 0.0001).Significance. The proposed framework allowed for accurate parameter estimates for quantitative DCE-MRI. In addition, the BNN provided uncertainty estimates which highlighted cases of high noise and in which the training data did not match the data during inference. This is important for clinical application because it would indicate cases in which the trained model is inadequate and additional training with an adapted training data set is required.

Open source code for the generation of digital reference objects for dynamic contrast-enhanced MRI analysis software validation

OBJECTIVES

Dynamic contrast-enhanced MR images can be analyzed through the application of a wide range of kinetic models. This process is prone to variability and a lack of standardization that can affect the measured metrics. There is a need for customized digital reference objects (DROs) for the validation of DCE-MRI software packages that undertake kinetic model analysis. DROs are currently available only for a small subset of the kinetic models commonly applied to DCE-MRI data. This work aimed to address this gap.

METHODS

Code was written in the MATLAB programming environment to generate customizable DROs. This modular code allows the insertion of a plug-in to describe the kinetic model to be tested. We input our generated DROs into three commercial and open-source analysis packages and assessed the agreement of kinetic model parameter values output with the 'ground-truth' values used in the DRO generation.

RESULTS

For the five kinetic models tested, the concordance correlation coefficient values were >98%, indicating excellent agreement of the results with 'ground-truth'.

CONCLUSIONS

Testing our DROs on three independent software packages produced concordant results, strongly suggesting our DRO generation code is correct. This implies that our DROs can be used to validate other third party software for the kinetic model analysis of DCE-MRI data.

ADVANCES IN KNOWLEDGE

This work extends published work of others to allow customized generation of test objects for any applied kinetic model and allows the incorporation of B1 mapping into the DRO for application at higher field strengths.

An in silico validation framework for quantitative DCE-MRI techniques based on a dynamic digital phantom

Quantitative evaluation of an image processing method to perform as designed is central to both its utility and its ability to guide the data acquisition process. Unfortunately, these tasks can be quite challenging due to the difficulty of experimentally obtaining the "ground truth" data to which the output of a given processing method must be compared. One way to address this issue is via "digital phantoms", which are numerical models that provide known biophysical properties of a particular object of interest.  In this contribution, we propose an in silico validation framework for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) acquisition and analysis methods that employs a novel dynamic digital phantom. The phantom provides a spatiotemporally-resolved representation of blood-interstitial flow and contrast agent delivery, where the former is solved by a 1D-3D coupled computational fluid dynamic system, and the latter described by an advection-diffusion equation. Furthermore, we establish a virtual simulator which takes as input the digital phantom, and produces realistic DCE-MRI data with controllable acquisition parameters. We assess the performance of a simulated standard-of-care acquisition (Protocol A) by its ability to generate contrast-enhanced MR images that separate vasculature from surrounding tissue, as measured by the contrast-to-noise ratio (CNR). We find that the CNR significantly decreases as the spatial resolution (SRA, where the subscript indicates Protocol A) or signal-to-noise ratio (SNRA) decreases. Specifically, with an SNRA / SRA = 75 dB / 30 μm, the median CNR is 77.30, whereas an SNRA / SRA = 5 dB / 300 μm reduces the CNR to 6.40. Additionally, we assess the performance of simulated ultra-fast acquisition (Protocol B) by its ability to generate DCE-MR images that capture contrast agent pharmacokinetics, as measured by error in the signal-enhancement ratio (SER) compared to ground truth (PESER). We find that PESER significantly decreases the as temporal resolution (TRB) increases. Similar results are reported for the effects of spatial resolution and signal-to-noise ratio on PESER. For example, with an SNRB / SRB / TRB = 5 dB / 300 μm / 10 s, the median PESER is 21.00%, whereas an SNRB / SRB / TRB = 75 dB / 60 μm / 1 s, yields a median PESER of 0.90%. These results indicate that our in silico framework can generate virtual MR images that capture effects of acquisition parameters on the ability of generated images to capture morphological or pharmacokinetic features. This validation framework is not only useful for investigations of perfusion-based MRI techniques, but also for the systematic evaluation and optimization new MRI acquisition, reconstruction, and image processing techniques.

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.

Efficient DCE-MRI Parameter and Uncertainty Estimation Using a Neural Network

Quantitative DCE-MRI provides voxel-wise estimates of tracer-kinetic parameters that are valuable in the assessment of health and disease. These maps suffer from many known sources of variability. This variability is expensive to compute using current methods, and is typically not reported. Here, we demonstrate a novel approach for simultaneous estimation of tracer-kinetic parameters and their uncertainty due to intrinsic characteristics of the tracer-kinetic model, with very low computation time. We train and use a neural network to estimate the approximate joint posterior distribution of tracer-kinetic parameters. Uncertainties are estimated for each voxel and are specific to the patient, exam, and lesion. We demonstrate the methods' ability to produce accurate tracer-kinetic maps. We compare predicted parameter ranges with uncertainties introduced by noise and by differences in post-processing in a digital reference object. The predicted parameter ranges correlate well with tracer-kinetic parameter ranges observed across different noise realizations and regression algorithms. We also demonstrate the value of this approach to differentiate significant from insignificant changes in brain tumor pharmacokinetics over time. This is achieved by enforcing consistency in resolving model singularities in the applied tracer-kinetic model.

Bayesian pharmacokinetic modeling of dynamic contrast-enhanced magnetic resonance imaging: validation and application

Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model parameters, uncertainty of these estimates can be assessed e.g. by an additional bootstrapping analysis. Here, we present a Bayesian probabilistic modeling approach for tracer-kinetic analysis with a Tofts model, which yields posterior probability distributions of perfusion parameters and therefore promises a robust and information-enriched alternative based on a framework of probability distributions. In this manuscript, we use the quantitative imaging biomarkers alliance (QIBA) Tofts phantom to evaluate the Bayesian tofts model (BTM) against a bootstrapped NLLS approach. Furthermore, we demonstrate how Bayesian posterior probability distributions can be employed to assess treatment response in a breast cancer DCE-MRI dataset using Cohen's d. Accuracy and precision of the BTM posterior distributions were validated and found to be in good agreement with the NLLS approaches, and assessment of therapy response with respect to uncertainty in parameter estimates was found to be excellent. In conclusion, the Bayesian modeling approach provides an elegant means to determine uncertainty via posterior distributions within a single step and provides honest information about changes in parameter estimates.