Spatial two-tissue compartment model for dynamic contrast-enhanced magnetic resonance imaging

Physics-Informed Autoencoder for Prostate Tissue Microstructure Profiling with Hybrid Multidimensional MRI

Purpose To evaluate the performance of Physics-Informed Autoencoder (PIA), a self-supervised deep learning model, in measuring tissue-based biomarkers for prostate cancer (PCa) using hybrid multidimensional MRI. Materials and Methods This retrospective study introduces PIA, an emerging self-supervised deep learning model that integrates a three-compartment diffusion-relaxation model with hybrid multidimensional MRI. PIA was trained to encode the biophysical model into a deep neural network to predict measurements of tissue-specific biomarkers for PCa without extensive training data requirements. Comprehensive in silico and in vivo experiments, using histopathology measurements as the reference standard, were conducted to validate the model's efficacy in comparison to the traditional nonlinear least squares (NLLS) algorithm. PIA's robustness to noise was tested in in silico experiments with varying signal-to-noise ratio (SNR) conditions, and in vivo performance for estimating volume fractions was evaluated in 21 patients (mean age, 60 years ± 6.6 [SD]; all male) with PCa (71 regions of interest). Evaluation metrics included the intraclass correlation coefficient (ICC) and Pearson correlation coefficient. Results PIA predicted the reference standard tissue parameters with high accuracy, outperforming conventional NLLS methods, especially under noisy conditions (rs = 0.80 vs 0.65, P < .001 for epithelium volume at SNR of 20:1). In in vivo validation, PIA's noninvasive volume fraction estimates matched quantitative histology (ICC, 0.94, 0.85, and 0.92 for epithelium, stroma, and lumen compartments, respectively; P < .001 for all). PIA's measurements strongly correlated with PCa aggressiveness (r = 0.75, P < .001). Furthermore, PIA ran 10 000 faster than NLLS (0.18 second vs 40 minutes per image). Conclusion PIA provided accurate prostate tissue biomarker measurements from MRI data with better robustness to noise and computational efficiency compared with the NLLS algorithm. The results demonstrate the potential of PIA as an accurate, noninvasive, and explainable artificial intelligence method for PCa detection. Keywords: Prostate, Stacked Auto-Encoders, Tissue Characterization, MR-Diffusion-weighted Imaging Supplemental material is available for this article. ©RSNA, 2025 See also commentary by Adams and Bressem in this issue.

Denoising and uncertainty estimation in parameter mapping with approximate Bayesian deep image priors

PURPOSE

To mitigate the problem of noisy parameter maps with high uncertainties by casting parameter mapping as a denoising task based on Deep Image Priors.

METHODS

We extend the concept of denoising with Deep Image Prior (DIP) into parameter mapping by treating the output of an image-generating network as a parametrization of tissue parameter maps. The method implicitly denoises the parameter mapping process by filtering low-level image features with an untrained convolutional neural network (CNN). Our implementation includes uncertainty estimation from Bernoulli approximate variational inference, implemented with MC dropout, which provides model uncertainty in each voxel of the denoised parameter maps. The method is modular, so the specifics of different applications (e.g., T1 mapping) separate into application-specific signal equation blocks. We evaluate the method on variable flip angle T1 mapping, multi-echo T2 mapping, and apparent diffusion coefficient mapping.

RESULTS

We found that deep image prior adapts successfully to several applications in parameter mapping. In all evaluations, the method produces noise-reduced parameter maps with decreased uncertainty compared to conventional methods. The downsides of the proposed method are the long computational time and the introduction of some bias from the denoising prior.

CONCLUSION

DIP successfully denoise the parameter mapping process and applies to several applications with limited hyperparameter tuning. Further, it is easy to implement since DIP methods do not use network training data. Although time-consuming, uncertainty information from MC dropout makes the method more robust and provides useful information when properly calibrated.

Parametric maps of spatial two-tissue compartment model for prostate dynamic contrast enhanced MRI - comparison with the standard tofts model in the diagnosis of prostate cancer

The spatial two-tissue compartment model (2TCM) was used to analyze prostate dynamic contrast enhanced (DCE) MRI data and compared with the standard Tofts model. A total of 29 patients with biopsy-confirmed prostate cancer were included in this IRB-approved study. MRI data were acquired on a Philips Achieva 3T-TX scanner. After T2-weighted and diffusion-weighted imaging, DCE data using 3D T1-FFE mDIXON sequence were acquired pre- and post-contrast media injection (0.1 mmol/kg Multihance) for 60 dynamic scans with temporal resolution of 8.3 s/image. The 2TCM has one fast ([Formula: see text] and [Formula: see text]) and one slow ([Formula: see text] and [Formula: see text]) exchanging compartment, compared with the standard Tofts model parameters (Ktrans and kep). On average, prostate cancer had significantly higher values (p < 0.01) than normal prostate tissue for all calculated parameters. There was a strong correlation (r = 0.94, p < 0.001) between Ktrans and [Formula: see text] for cancer, but weak correlation (r = 0.28, p < 0.05) between kep and [Formula: see text]. Average root-mean-square error (RMSE) in fits from the 2TCM was significantly smaller (p < 0.001) than the RMSE in fits from the Tofts model. Receiver operating characteristic (ROC) analysis showed that fast [Formula: see text] had the highest area under the curve (AUC) than any other individual parameter. The combined four parameters from the 2TCM had a considerably higher AUC value than the combined two parameters from the Tofts model. The 2TCM is useful for quantitative analysis of prostate DCE-MRI data and provides new information in the diagnosis of prostate cancer.

Parametric maps of spatial two-tissue compartment model for prostate dynamic contrast enhanced MRI - comparison with the standard Tofts model in the diagnosis of prostate cancer

The spatial two-tissue compartment model (2TCM) was used to analyze prostate dynamic contrast enhanced (DCE) MRI data and compared with the standard Tofts model. A total of 29 patients with biopsy-confirmed prostate cancer were included in this IRB-approved study. MRI data were acquired on a Philips Achieva 3T-TX scanner. After T2-weighted and diffusion-weighted imaging, DCE data using 3D T1-FFE mDIXON sequence were acquired pre- and post-contrast media injection (0.1 mmol/kg Multihance) for 60 dynamic scans with temporal resolution of 8.3 s/image. The 2TCM has one fast (K 1 trans and k 1 ep ) and one slow (K 2 trans and k 2 ep ) exchanging compartment, compared with the standard Tofts model parameters (K trans and k ep ). On average, prostate cancer had significantly higher values (p < 0.007) than normal prostate tissue for all calculated parameters. There was a strong correlation (r = 0.94, p < 0.0001) between K trans and K 1 trans for cancer, but weak correlation (r = 0.28, p < 0.05) between k ep and k 1 ep . Average root-mean-square error (RMSE) in fits from the 2TCM was significantly smaller (p < 0.001) than the RMSE in fits from the Tofts model. Receiver operating characteristic (ROC) analysis showed that fast K 1 trans had the highest area under the curve (AUC) than any other individual parameter. The combined four parameters from the 2TCM had a considerably higher AUC value than the combined two parameters from the Tofts model. The 2TCM may be useful for quantitative analysis of prostate DCE-MRI data and may provide new information in the diagnosis of prostate cancer.

Bayesian non-linear regression with spatial priors for noise reduction and error estimation in quantitative MRI with an application in T1 estimation

PURPOSE

To develop a method that can reduce and estimate uncertainty in quantitative MR parameter maps without the need for hand-tuning of any hyperparameters.

METHODS

We present an estimation method where uncertainties are reduced by incorporating information on spatial correlations between neighbouring voxels. The method is based on a Bayesian hierarchical non-linear regression model, where the parameters of interest are sampled, using Markov chain Monte Carlo (MCMC), from a high-dimensional posterior distribution with a spatial prior. The degree to which the prior affects the model is determined by an automatic hyperparameter search using an information criterion and is, therefore, free from manual user-dependent tuning. The samples obtained further provide a convenient means to obtain uncertainties in both voxels and regions. The developed method was evaluated on T ₁ estimations based on the variable flip angle method.

RESULTS

The proposed method delivers noise-reduced T ₁ parameter maps with associated error estimates by combining MCMC sampling, the widely applicable information criterion, and total variation-based denoising. The proposed method results in an overall decrease in estimation error when compared to conventional voxel-wise maximum likelihood estimation. However, this comes with an increased bias in some regions, predominately at tissue interfaces, as well as an increase in computational time.

CONCLUSIONS

This study provides a method that generates more precise estimates compared to the conventional method, without incorporating user subjectivity, and with the added benefit of uncertainty estimation.

Hierarchical Bayesian myocardial perfusion quantification

Myocardial blood flow can be quantified from dynamic contrast-enhanced magnetic resonance (MR) images through the fitting of tracer-kinetic models to the observed imaging data. The use of multi-compartment exchange models is desirable as they are physiologically motivated and resolve directly for both blood flow and microvascular function. However, the parameter estimates obtained with such models can be unreliable. This is due to the complexity of the models relative to the observed data which is limited by the low signal-to-noise ratio, the temporal resolution, the length of the acquisitions and other complex imaging artefacts. In this work, a Bayesian inference scheme is proposed which allows the reliable estimation of the parameters of the two-compartment exchange model from myocardial perfusion MR data. The Bayesian scheme allows the incorporation of prior knowledge on the physiological ranges of the model parameters and facilitates the use of the additional information that neighbouring voxels are likely to have similar kinetic parameter values. Hierarchical priors are used to avoid making a priori assumptions on the health of the patients. We provide both a theoretical introduction to Bayesian inference for tracer-kinetic modelling and specific implementation details for this application. This approach is validated in both in silico and in vivo settings. In silico, there was a significant reduction in mean-squared error with the ground-truth parameters using Bayesian inference as compared to using the standard non-linear least squares fitting. When applied to patient data the Bayesian inference scheme returns parameter values that are in-line with those previously reported in the literature, as well as giving parameter maps that match the independant clinical diagnosis of those 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.

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

PURPOSE

In dynamic contrast enhanced (DCE) MRI, separation of signal contributions from perfusion and leakage requires robust estimation of parameters in a pharmacokinetic model. We present and quantify the performance of a method to compute tissue hemodynamic parameters from DCE data using established pharmacokinetic models.

METHODS

We propose a Bayesian scheme to obtain perfusion metrics from DCE MRI data. Initial performance is assessed through digital phantoms of the extended Tofts model (ETM) and the two-compartment exchange model (2CXM), comparing the Bayesian scheme to the standard Levenberg-Marquardt (LM) algorithm. Digital phantoms are also invoked to identify limitations in the pharmacokinetic models related to measurement conditions. Using computed maps of the extra vascular volume (ve) from 19 glioma patients, we analyze differences in the number of un-physiological high-intensity ve values for both ETM and 2CXM, using a one-tailed paired t-test assuming un-equal variance.

RESULTS

The Bayesian parameter estimation scheme demonstrated superior performance over the LM technique in the digital phantom simulations. In addition, we identified limitations in parameter reliability in relation to scan duration for the 2CXM. DCE data for glioma and cervical cancer patients was analyzed with both algorithms and demonstrated improvement in image readability for the Bayesian method. The Bayesian method demonstrated significantly fewer non-physiological high-intensity ve values for the ETM (p<0.0001) and the 2CXM (p<0.0001).

CONCLUSION

We have demonstrated substantial improvement of the perceptive quality of pharmacokinetic parameters from advanced compartment models using the Bayesian parameter estimation scheme as compared to the LM technique.

Bayesian modeling of Dynamic Contrast Enhanced MRI data in cerebral glioma patients improves the diagnostic quality of hemodynamic parameter maps

PURPOSE

The purpose of this work is to investigate if the curve-fitting algorithm in Dynamic Contrast Enhanced (DCE) MRI experiments influences the diagnostic quality of calculated parameter maps.

MATERIAL AND METHODS

We compared the Levenberg-Marquardt (LM) and a Bayesian method (BM) in DCE data of 42 glioma patients, using two compartmental models (extended Toft's and 2-compartment-exchange model). Logistic regression and an ordinal linear mixed model were used to investigate if the image quality differed between the curve-fitting algorithms and to quantify if image quality was affected for different parameters and algorithms. The diagnostic performance to discriminate between high-grade and low-grade gliomas was compared by applying a Wilcoxon signed-rank test (statistical significance p>0.05). Two neuroradiologists assessed different qualitative imaging features.

RESULTS

Parameter maps based on BM, particularly those describing the blood-brain barrier, were superior those based on LM. The image quality was found to be significantly improved (p<0.001) for BM when assessed through independent clinical scores. In addition, given a set of clinical scores, the generating algorithm could be predicted with high accuracy (area under the receiver operating characteristic curve between 0.91 and 1). Using linear mixed models, image quality was found to be improved when applying the 2-compartment-exchange model compared to the extended Toft's model, regardless of the underlying fitting algorithm. Tumor grades were only differentiated reliably on plasma volume maps when applying BM. The curve-fitting algorithm had, however, no influence on grading when using parameter maps describing the blood-brain barrier.

CONCLUSION

The Bayesian method has the potential to increase the diagnostic reliability of Dynamic Contrast Enhanced parameter maps in brain tumors. In our data, images based on the 2-compartment-exchange model were superior to those based on the extended Toft's model.

Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging

BACKGROUND

In the estimation of physiological kinetic parameters from Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data, the determination of the arterial input function (AIF) plays a key role.

OBJECTIVES

This paper proposes a Bayesian method to estimate the physiological parameters of DCE-MRI along with the AIF in situations, where no measurement of the AIF is available.

METHODS

In the proposed algorithm, the maximum entropy method (MEM) is combined with the maximum a posterior approach (MAP). To this end, MEM is used to specify a prior probability distribution of the unknown AIF. The ability of this method to estimate the AIF is validated using the Kullback-Leibler divergence. Subsequently, the kinetic parameters can be estimated with MAP. The proposed algorithm is evaluated with a data set from a breast cancer MRI study.

RESULTS

The application shows that the AIF can reliably be determined from the DCE-MRI data using MEM. Kinetic parameters can be estimated subsequently.

CONCLUSIONS

The maximum entropy method is a powerful tool to reconstructing images from many types of data. This method is useful for generating the probability distribution based on given information. The proposed method gives an alternative way to assess the input function from the existing data. The proposed method allows a good fit of the data and therefore a better estimation of the kinetic parameters. In the end, this allows for a more reliable use of DCE-MRI.

Hyperthermic Laser Ablation of Recurrent Glioblastoma Leads to Temporary Disruption of the Peritumoral Blood Brain Barrier

BACKGROUND

Poor central nervous system penetration of cytotoxic drugs due to the blood brain barrier (BBB) is a major limiting factor in the treatment of brain tumors. Most recurrent glioblastomas (GBM) occur within the peritumoral region. In this study, we describe a hyperthemic method to induce temporary disruption of the peritumoral BBB that can potentially be used to enhance drug delivery.

METHODS

Twenty patients with probable recurrent GBM were enrolled in this study. Fourteen patients were evaluable. MRI-guided laser interstitial thermal therapy was applied to achieve both tumor cytoreduction and disruption of the peritumoral BBB. To determine the degree and timing of peritumoral BBB disruption, dynamic contrast-enhancement brain MRI was used to calculate the vascular transfer constant (Ktrans) in the peritumoral region as direct measures of BBB permeability before and after laser ablation. Serum levels of brain-specific enolase, also known as neuron-specific enolase, were also measured and used as an independent quantification of BBB disruption.

RESULTS

In all 14 evaluable patients, Ktrans levels peaked immediately post laser ablation, followed by a gradual decline over the following 4 weeks. Serum BSE concentrations increased shortly after laser ablation and peaked in 1-3 weeks before decreasing to baseline by 6 weeks.

CONCLUSIONS

The data from our pilot research support that disruption of the peritumoral BBB was induced by hyperthemia with the peak of high permeability occurring within 1-2 weeks after laser ablation and resolving by 4-6 weeks. This provides a therapeutic window of opportunity during which delivery of BBB-impermeant therapeutic agents may be enhanced.

TRIAL REGISTRATION

ClinicalTrials.gov NCT01851733.

Boosting in Nonlinear Regression Models with an Application to DCE-MRI Data

BACKGROUND

For the statistical analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data, compartment models are a commonly used tool. By these models, the observed uptake of contrast agent in some tissue over time is linked to physiologic properties like capillary permeability and blood flow. Up to now, models of different complexity have been used, and it is still unclear which model should be used in which situation. In previous studies, it has been found that for DCE-MRI data, the number of compartments differs for different types of tissue, and that in cancerous tissue, it might actually differ over a region of voxels of one DCE-MR image.

OBJECTIVES

To find the appropriate number of compartments and estimate the parameters of a regression model for each voxel in an DCE-MR image. With that, tumors in an DCE-MR image can be located, and for example therapy success can be assessed.

METHODS

The observed uptake of contrast agent in a voxel of an image of some tissue is described by a concentration time curve. This curve can be modeled using a nonlinear regression model. We present a boosting approach with nonlinear regression as base procedure, which allows us to estimate the number of compartments and the related parameters for each voxel of an DCE-MR image. In addition, a spatially regularized version of this approach is proposed.

RESULTS

With the proposed approach, the number of compartments - and with that the complexity of the model - per voxel is not fixed but data-driven, which allows us to fit models of adequate complexity to the concentration time curves of all voxels. The parameters of the model remain nevertheless interpretable because of the underlying compartment model.

CONCLUSIONS

The proposed boosting approaches outperform all competing methods considered in this paper regarding the correct localization of tumors in DCE-MR images as well as the spatial homogeneity of the estimated number of compartments across the image, and the definition of the tumor edge.

Models and methods for analyzing DCE-MRI: a review

PURPOSE

To present a review of most commonly used techniques to analyze dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), discusses their strengths and weaknesses, and outlines recent clinical applications of findings from these approaches.

METHODS

DCE-MRI allows for noninvasive quantitative analysis of contrast agent (CA) transient in soft tissues. Thus, it is an important and well-established tool to reveal microvasculature and perfusion in various clinical applications. In the last three decades, a host of nonparametric and parametric models and methods have been developed in order to quantify the CA's perfusion into tissue and estimate perfusion-related parameters (indexes) from signal- or concentration-time curves. These indexes are widely used in various clinical applications for the detection, characterization, and therapy monitoring of different diseases.

RESULTS

Promising theoretical findings and experimental results for the reviewed models and techniques in a variety of clinical applications suggest that DCE-MRI is a clinically relevant imaging modality, which can be used for early diagnosis of different diseases, such as breast and prostate cancer, renal rejection, and liver tumors.

CONCLUSIONS

Both nonparametric and parametric approaches for DCE-MRI analysis possess the ability to quantify tissue perfusion.