Fitting the two-compartment model in DCE-MRI by linear inversion

Identifiability of spatiotemporal tissue perfusion models

Objective.Standard models for perfusion quantification in DCE-MRI produce a bias by treating voxels as isolated systems. Spatiotemporal models can remove this bias, but it is unknown whether they are fundamentally identifiable. The aim of this study is to investigate this question in silico using one-dimensional toy systems with a one-compartment blood flow model and a two-compartment perfusion model.Approach.For each of the two models, identifiability is explored theoretically and in-silico for three systems. Concentrations over space and time are simulated by forward propagation. Different levels of noise and temporal undersampling are added to investigate sensitivity to measurement error. Model parameters are fitted using a standard gradient descent algorithm, applied iteratively with a stepwise increasing time window. Model fitting is repeated with different initial values to probe uniqueness of the solution. Reconstruction accuracy is quantified for each parameter by comparison to the ground truth.Main results.Theoretical analysis shows that flows and volume fractions are only identifiable up to a constant, and that this degeneracy can be removed by proper choice of parameters. Simulations show that in all cases, the tissue concentrations can be reconstructed accurately. The one-compartment model shows accurate reconstruction of blood velocities and arterial input functions, independent of the initial values and robust to measurement error. The two-compartmental perfusion model was not fully identifiable, showing good reconstruction of arterial velocities and input functions, but multiple valid solutions for the perfusion parameters and venous velocities, and a strong sensitivity to measurement error in these parameters.Significance.These results support the use of one-compartment spatiotemporal flow models, but two-compartment perfusion models were not sufficiently identifiable. Future studies should investigate whether this degeneracy is resolved in more realistic 2D and 3D systems, by adding physically justified constraints, or by optimizing experimental parameters such as injection duration or temporal resolution.

Unpaired deep learning for pharmacokinetic parameter estimation from dynamic contrast-enhanced MRI without AIF measurements

DCE-MRI provides information about vascular permeability and tissue perfusion through the acquisition of pharmacokinetic parameters. However, traditional methods for estimating these pharmacokinetic parameters involve fitting tracer kinetic models, which often suffer from computational complexity and low accuracy due to noisy arterial input function (AIF) measurements. Although some deep learning approaches have been proposed to tackle these challenges, most existing methods rely on supervised learning that requires paired input DCE-MRI and labeled pharmacokinetic parameter maps. This dependency on labeled data introduces significant time and resource constraints and potential noise in the labels, making supervised learning methods often impractical. To address these limitations, we present a novel unpaired deep learning method for estimating pharmacokinetic parameters and the AIF using a physics-driven CycleGAN approach. Our proposed CycleGAN framework is designed based on the underlying physics model, resulting in a simpler architecture with a single generator and discriminator pair. Crucially, our experimental results indicate that our method does not necessitate separate AIF measurements and produces more reliable pharmacokinetic parameters than other techniques.

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.

Motion correction of free-breathing magnetic resonance renography using model-driven registration

INTRODUCTION

Model-driven registration (MDR) is a general approach to remove patient motion in quantitative imaging. In this study, we investigate whether MDR can effectively correct the motion in free-breathing MR renography (MRR).

MATERIALS AND METHODS

MDR was generalised to linear tracer-kinetic models and implemented using 2D or 3D free-form deformations (FFD) with multi-resolution and gradient descent optimization. MDR was evaluated using a kidney-mimicking digital reference object (DRO) and free-breathing patient data acquired at high temporal resolution in multi-slice 2D (5 patients) and 3D acquisitions (8 patients). Registration accuracy was assessed using comparison to ground truth DRO, calculating the Hausdorff distance (HD) between ground truth masks with segmentations and visual evaluation of dynamic images, signal-time courses and parametric maps (all data).

RESULTS

DRO data showed that the bias and precision of parameter maps after MDR are indistinguishable from motion-free data. MDR led to reduction in HD (HDunregistered = 9.98 ± 9.76, HDregistered = 1.63 ± 0.49). Visual inspection showed that MDR effectively removed motion effects in the dynamic data, leading to a clear improvement in anatomical delineation on parametric maps and a reduction in motion-induced oscillations on signal-time courses.

DISCUSSION

MDR provides effective motion correction of MRR in synthetic and patient data. Future work is needed to compare the performance against other more established methods.

On the use of multicompartment models of diffusion and relaxation for placental imaging

Multi-compartment models of diffusion and relaxation are ubiquitous in magnetic resonance research especially applied to neuroimaging applications. These models are increasingly making their way into the world of placental imaging. This review provides a framework for their motivation and implementation and describes some of the outstanding questions that need to be answered before they can be routinely adopted.

Assessment of metastatic lymph nodes in head and neck squamous cell carcinomas using simultaneous 18F-FDG-PET and MRI

In this study, we investigate the feasibility of using dynamic contrast enhanced magnetic resonance imaging (DCE-MRI), diffusion weighted imaging (DWI), and dynamic positron emission tomography (PET) for detection of metastatic lymph nodes in head and neck squamous cell carcinoma (HNSCC) cases. Twenty HNSCC patients scheduled for lymph node dissection underwent DCE-MRI, dynamic PET, and DWI using a PET-MR scanner within one week prior to their planned surgery. During surgery, resected nodes were labeled to identify their nodal levels and sent for routine clinical pathology evaluation. Quantitative parameters of metastatic and normal nodes were calculated from DCE-MRI (v_e, v_p, PS, F_p, K^trans), DWI (ADC) and PET (K_i, K₁, k₂, k₃) to assess if an individual or a combination of parameters can classify normal and metastatic lymph nodes accurately. There were 38 normal and 11 metastatic nodes covered by all three imaging methods and confirmed by pathology. 34% of all normal nodes had volumes greater than or equal to the smallest metastatic node while 4 normal nodes had SUV > 4.5. Among the MRI parameters, the median v_p, F_p, PS, and K^trans values of the metastatic lymph nodes were significantly lower (p = <0.05) than those of normal nodes. v_e and ADC did not show any statistical significance. For the dynamic PET parameters, the metastatic nodes had significantly higher k₃ (p value = 8.8 × 10^-8) and K_i (p value = 5.3 × 10^-8) than normal nodes. K₁ and k₂ did not show any statistically significant difference. K_i had the best separation with accuracy = 0.96 (sensitivity = 1, specificity = 0.95) using a cutoff of K_i = 5.3 × 10^-3 mL/cm³/min, while k₃ and volume had accuracy of 0.94 (sensitivity = 0.82, specificity = 0.97) and 0.90 (sensitivity = 0.64, specificity = 0.97) respectively. 100% accuracy can be achieved using a multivariate logistic regression model of MRI parameters after thresholding the data with K_i < 5.3 × 10^-3 mL/cm³/min. The results of this preliminary study suggest that quantitative MRI may provide additional value in distinguishing metastatic nodes, particularly among small nodes, when used together with FDG-PET.

APRICOT: Advanced Platform for Reproducible Infrastructures in the Cloud via Open Tools

Background  Scientific publications are meant to exchange knowledge among researchers but the inability to properly reproduce computational experiments limits the quality of scientific research. Furthermore, bibliography shows that irreproducible preclinical research exceeds 50%, which produces a huge waste of resources on nonprofitable research at Life Sciences field. As a consequence, scientific reproducibility is being fostered to promote Open Science through open databases and software tools that are typically deployed on existing computational resources. However, some computational experiments require complex virtual infrastructures, such as elastic clusters of PCs, that can be dynamically provided from multiple clouds. Obtaining these infrastructures requires not only an infrastructure provider, but also advanced knowledge in the cloud computing field.

Objectives  The main aim of this paper is to improve reproducibility in life sciences to produce better and more cost-effective research. For that purpose, our intention is to simplify the infrastructure usage and deployment for researchers.

Methods  This paper introduces Advanced Platform for Reproducible Infrastructures in the Cloud via Open Tools (APRICOT), an open source extension for Jupyter to deploy deterministic virtual infrastructures across multiclouds for reproducible scientific computational experiments. To exemplify its utilization and how APRICOT can improve the reproduction of experiments with complex computation requirements, two examples in the field of life sciences are provided. All requirements to reproduce both experiments are disclosed within APRICOT and, therefore, can be reproduced by the users.

Results  To show the capabilities of APRICOT, we have processed a real magnetic resonance image to accurately characterize a prostate cancer using a Message Passing Interface cluster deployed automatically with APRICOT. In addition, the second example shows how APRICOT scales the deployed infrastructure, according to the workload, using a batch cluster. This example consists of a multiparametric study of a positron emission tomography image reconstruction.

Conclusion  APRICOT's benefits are the integration of specific infrastructure deployment, the management and usage for Open Science, making experiments that involve specific computational infrastructures reproducible. All the experiment steps and details can be documented at the same Jupyter notebook which includes infrastructure specifications, data storage, experimentation execution, results gathering, and infrastructure termination. Thus, distributing the experimentation notebook and needed data should be enough to reproduce the experiment.

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.

Improved fetal blood oxygenation and placental estimated measurements of diffusion-weighted MRI using data-driven Bayesian modeling

PURPOSE

Motion correction in placental DW-MRI is challenging due to maternal breathing motion, maternal movements, and rapid intensity changes. Parameter estimates are usually obtained using least-squares methods for voxel-wise fitting; however, they typically give noisy estimates due to low signal-to-noise ratio. We introduce a model-driven registration (MDR) technique which incorporates a placenta-specific signal model into the registration process, and we present a Bayesian approach for Diffusion-rElaxation Combined Imaging for Detailed placental Evaluation model to obtain individual and population trends in estimated parameters.

METHODS

MDR exploits the fact that a placenta signal model is available and thus we incorporate it into the registration to generate a series of target images. The proposed registration method is compared to a pre-existing method used for DCE-MRI data making use of principal components analysis. The Bayesian shrinkage prior (BSP) method has no user-defined parameters and therefore measures of parameter variation in a region of interest are determined by the data alone. The MDR method and the Bayesian approach were evaluated on 10 control 4D DW-MRI singleton placental data.

RESULTS

MDR method improves the alignment of placenta data compared to the pre-existing method. It also shows a further reduction of the residual error between the data and the fit. BSP approach showed higher precision leading to more clearly apparent spatial features in the parameter maps. Placental fetal oxygen saturation (FO₂ ) showed a negative linear correlation with gestational age.

CONCLUSIONS

The proposed pipeline provides a robust framework for registering DW-MRI data and analyzing longitudinal changes of placental function.

Pharmacokinetic modeling of dynamic contrast-enhanced MRI using a reference region and input function tail

PURPOSE

Quantitative analysis of dynamic contrast-enhanced MRI (DCE-MRI) requires an arterial input function (AIF) which is difficult to measure. We propose the reference region and input function tail (RRIFT) approach which uses a reference tissue and the washout portion of the AIF.

METHODS

RRIFT was evaluated in simulations with 100 parameter combinations at various temporal resolutions (5-30 s) and noise levels (σ = 0.01-0.05 mM). RRIFT was compared against the extended Tofts model (ETM) in 8 studies from patients with glioblastoma multiforme. Two versions of RRIFT were evaluated: one using measured patient-specific AIF tails, and another assuming a literature-based AIF tail.

RESULTS

RRIFT estimated the transfer constant K trans and interstitial volume v e with median errors within 20% across all simulations. RRIFT was more accurate and precise than the ETM at temporal resolutions slower than 10 s. The percentage error of K trans had a median and interquartile range of -9 ± 45% with the ETM and -2 ± 17% with RRIFT at a temporal resolution of 30 s under noiseless conditions. RRIFT was in excellent agreement with the ETM in vivo, with concordance correlation coefficients (CCC) of 0.95 for K trans , 0.96 for v e , and 0.73 for the plasma volume v p using a measured AIF tail. With the literature-based AIF tail, the CCC was 0.89 for K trans , 0.93 for v e and 0.78 for v p .

CONCLUSIONS

Quantitative DCE-MRI analysis using the input function tail and a reference tissue yields absolute kinetic parameters with the RRIFT method. This approach was viable in simulation and in vivo for temporal resolutions as low as 30 s.

An extended reference region model for DCE-MRI that accounts for plasma volume

The reference region model (RRM) for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides pharmacokinetic parameters without requiring the arterial input function. A limitation of the RRM is that it assumes that the blood plasma volume in the tissue of interest is zero, but this is often not true in highly vascularized tissues, such as some tumours. This study proposes an extended reference region model (ERRM) to account for tissue plasma volume. Furthermore, ERRM was combined with a two-fit approach to reduce the number of fitting parameters, and this was named the constrained ERRM (CERRM). The accuracy and precision of RRM, ERRM and CERRM were evaluated in simulations covering a range of parameters, noise and temporal resolutions. These models were also compared with the extended Tofts model (ETM) on in vivo glioblastoma multiforme data. In simulations, RRM overestimated K^trans by over 10% at v_p  = 0.01 under noiseless conditions. In comparison, ERRM and CERRM were both accurate, with CERRM showing better precision when noise was included. On in vivo data, CERRM provided maps that had the highest agreement with ETM, whilst also being robust at temporal resolutions as poor as 30 s. ERRM can provide pharmacokinetic parameters without an arterial input function in tissues with non-negligible v_p where RRM provides inaccurate estimates. The two-fit approach, named CERRM, further improves on the accuracy and precision of ERRM.

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.

Joint arterial input function and tracer kinetic parameter estimation from undersampled dynamic contrast-enhanced MRI using a model consistency constraint

PURPOSE

To develop and evaluate a model-based reconstruction framework for joint arterial input function (AIF) and kinetic parameter estimation from undersampled brain tumor dynamic contrast-enhanced MRI (DCE-MRI) data.

METHODS

The proposed method poses the tracer-kinetic (TK) model as a model consistency constraint, enabling the flexible inclusion of different TK models and TK solvers, and the joint estimation of the AIF. The proposed method is evaluated using an anatomic realistic digital reference object (DRO), and nine retrospectively down-sampled brain tumor DCE-MRI datasets. We also demonstrate application to 30-fold prospectively undersampled brain tumor DCE-MRI.

RESULTS

In DRO studies with up to 60-fold undersampling, the proposed method provided TK maps with low error that were comparable to fully sampled data and were demonstrated to be compatible with a third-party TK solver. In retrospective undersampling studies, this method provided patient-specific AIF with normalized root mean-squared-error (normalized by the 90th percentile value) less than 8% at up to 100-fold undersampling. In the 30-fold undersampled prospective study, the proposed method provided high-resolution whole-brain TK maps and patient-specific AIF.

CONCLUSION

The proposed model-based DCE-MRI reconstruction enables the use of different TK solvers with a model consistency constraint and enables joint estimation of patient-specific AIF. TK maps and patient-specific AIF with high fidelity can be reconstructed at up to 100-fold undersampling in k,t-space. Magn Reson Med 79:2804-2815, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

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

Purpose

Fitting tracer kinetic models using linear methods is much faster than using their nonlinear counterparts, although this comes often at the expense of reduced accuracy and precision. The aim of this study was to derive and compare the performance of the linear compartmental tissue uptake (CTU) model with its nonlinear version with respect to their percentage error and precision.

Theory and Methods

The linear and nonlinear CTU models were initially compared using simulations with varying noise and temporal sampling. Subsequently, the clinical applicability of the linear model was demonstrated on 14 patients with locally advanced cervical cancer examined with dynamic contrast‐enhanced magnetic resonance imaging.

Results

Simulations revealed equal percentage error and precision when noise was within clinical achievable ranges (contrast‐to‐noise ratio >10). The linear method was significantly faster than the nonlinear method, with a minimum speedup of around 230 across all tested sampling rates. Clinical analysis revealed that parameters estimated using the linear and nonlinear CTU model were highly correlated (ρ ≥ 0.95).

Conclusion

The linear CTU model is computationally more efficient and more stable against temporal downsampling, whereas the nonlinear method is more robust to variations in noise. The two methods may be used interchangeably within clinical achievable ranges of temporal sampling and noise. Magn Reson Med 77:2414–2423, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

An open source software for analysis of dynamic contrast enhanced magnetic resonance images: UMMPerfusion revisited

Background

Perfusion imaging has become an important image based tool to derive the physiological information in various applications, like tumor diagnostics and therapy, stroke, (cardio-) vascular diseases, or functional assessment of organs. However, even after 20 years of intense research in this field, perfusion imaging still remains a research tool without a broad clinical usage. One problem is the lack of standardization in technical aspects which have to be considered for successful quantitative evaluation; the second problem is a lack of tools that allow a direct integration into the diagnostic workflow in radiology.

Results

Five compartment models, namely, a one compartment model (1CP), a two compartment exchange (2CXM), a two compartment uptake model (2CUM), a two compartment filtration model (2FM) and eventually the extended Toft’s model (ETM) were implemented as plugin for the DICOM workstation OsiriX. Moreover, the plugin has a clean graphical user interface and provides means for quality management during the perfusion data analysis. Based on reference test data, the implementation was validated against a reference implementation. No differences were found in the calculated parameters.

Conclusion

We developed open source software to analyse DCE-MRI perfusion data. The software is designed as plugin for the DICOM Workstation OsiriX. It features a clean GUI and provides a simple workflow for data analysis while it could also be seen as a toolbox providing an implementation of several recent compartment models to be applied in research tasks. Integration into the infrastructure of a radiology department is given via OsiriX. Results can be saved automatically and reports generated automatically during data analysis ensure certain quality control.