METHOD FOR JOINT ARTERIAL INPUT FUNCTION AND TRACER KINETIC PARAMETER ESTIMATION IN ACCELERATED DCEMRI USING A MODEL CONSISTENCY CONSTRAINT

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First Claim
1. A method for improving dynamic contrast enhanced imaging for joint arterial input function and tracer kinetic parameter estimation, the method comprising:
 a) administering a contrast agent to a subject;
b) collecting imaging data from the subject for a tissue or organ;
c) selecting a tracer kinetic model to be applied to the imaging data, the tracer kinetic model being defined by a plurality of tracer kinetic parameters;
d) reconstructing dynamic images from the imaging data as reconstructed dynamic images, wherein a consistency constraint is applied to the reconstructed dynamic images;
the consistency constraint including a weighted sum of a data consistency component and a model consistency component;
e) applying the tracer kinetic model to the reconstructed dynamic images to estimate tracer kinetic parameter maps as estimated tracer kinetic parameter maps, wherein a model consistency constraint is applied; and
f) alternately performing steps d) and e) until converging on a set of dynamic images and tracer kinetic parameter maps.
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Abstract
Tracer kinetic models are utilized as temporal constraints for highly undersampled reconstruction of DCEMRI data. In one embodiment, a method for improving dynamic contrast enhanced imaging. The method includes steps of administering a magnetic resonance contrast agent to a subject and then collecting magnetic resonance contrast agent from the subject. A tracer kinetic model (i.e. eTofts or Patlak) is selected to be applied to the magnetic resonance imaging data. The tracer kinetic model is applied to the magnetic resonance imaging data. Tracer kinetic maps and dynamic images are simultaneously reconstructed and a consistency constraint is applied. The proposed method allows for easy use of different tracer kinetic models in the formulation and estimation of patientspecific arterial input functions jointly with tracer kinetic maps.
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36 Claims
 1. A method for improving dynamic contrast enhanced imaging for joint arterial input function and tracer kinetic parameter estimation, the method comprising:
a) administering a contrast agent to a subject; b) collecting imaging data from the subject for a tissue or organ; c) selecting a tracer kinetic model to be applied to the imaging data, the tracer kinetic model being defined by a plurality of tracer kinetic parameters; d) reconstructing dynamic images from the imaging data as reconstructed dynamic images, wherein a consistency constraint is applied to the reconstructed dynamic images;
the consistency constraint including a weighted sum of a data consistency component and a model consistency component;e) applying the tracer kinetic model to the reconstructed dynamic images to estimate tracer kinetic parameter maps as estimated tracer kinetic parameter maps, wherein a model consistency constraint is applied; and f) alternately performing steps d) and e) until converging on a set of dynamic images and tracer kinetic parameter maps.  View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
 23. A system for improving dynamic contrast enhanced imaging for joint arterial input function and tracer kinetic parameter estimation, the system comprising:
a magnetic resonance imaging system that generates magnetic resonance imaging data from a subject for a tissue or organ; and a programmable computer operable to execute steps of; a) collecting the magnetic resonance imaging data from the subject; b) reconstructing dynamic images from the magnetic resonance imaging data as reconstructed dynamic images, wherein a consistency constraint is applied to the reconstructed dynamic images;
the consistency constraint including a weighted sum of a data consistency component and a model consistency component;c) applying a tracer kinetic model to the reconstructed dynamic images to estimate tracer kinetic parameter maps as estimated tracer kinetic parameter maps, wherein a model consistency constraint is applied; and d) alternately performing steps b) and c) until converging on a set of dynamic images and tracer kinetic parameter maps.  View Dependent Claims (24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36)
1 Specification
This application claims the benefit of U.S. provisional application Ser. No. 62/657,452 filed Apr. 13, 2018, the disclosure of which is hereby incorporated in its entirety by reference herein.
In at least one embodiment, the present invention relates to methods for improving magnetic resonance imaging.
Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCEMRI) is a time resolved methodology of MRI, which involves intravenous administration of a paramagnetic contrast agent and continuous acquisition of images to track the passage of the contrast through a volume of interest. DCEMRI is used most often to evaluate cancer (tumor vascularity), but can also be applied to other diseases. DCEMRI is a powerful technique for probing subvoxel vascular properties of tissue including fractional plasma volume, fractional extracellularextravascular volume, and clinically important transfer constants. DCEMRI involves capturing a series of images before, during, and after administration of a Tishortening contrast agent.
Tracerkinetic (TK) modeling of the enhancement kinetics of the contrast agent enables quantification of TK parameters such as K^{trans}: a volume transfer coefficient across the capillary endothelium, and fractional volumes such as V_{e }(fractional volume of the extravascular extracellular space), and v_{p }(fractional plasma volume). These parameters provide a means as functional biomarkers in diagnosis and treatment planning of cancer in several body parts including the brain, breast, liver, and prostate. In the brain, DCEMRI characterizes the bloodbrain barrier leakiness, which has important implications as a potential early biomarker in the evaluation of neurodegenerative diseases such as Alzheimer'"'"'s disease, multiple sclerosis, and vascular dementia.
DCEMRI is a 4dimensional (x, y, z, time) imaging task, and is challenged by slow MRI acquisition speed. Tracerkinetic (TK) parameter maps are then computed from the dynamic images, and provide information for diagnosis and monitoring treatment response (13). DCEMRI is used throughout the body, most commonly in the prostate, breast, liver, and brain. In the brain, DCEMRI has shown value in the assessment of brain tumor, multiple sclerosis, and Alzheimer disease (46).
With conventional Nyquist sampling, DCEMRI is often unable to simultaneously provide adequate spatiotemporal resolution and spatial coverage. A typical brain DCEMRI provides 5s temporal resolution, which is a minimum requirement for accurate TK modeling (7,8). Using Cartesian sampling at the Nyquist rate, only 510 slices are achievable. This is typically inadequate in large glioblastoma cases and cases with scattered metastatic disease that may be spread throughout the brain (9). It is possible to coarsen spatial resolution to achieve greater spatial coverage, but this compromises the ability to evaluate the narrow (12 mm) enhancing margin of glioblastomas and the ability to evaluate small lesions.
Thus, techniques involving undersampling and constrained reconstruction have been proposed to simultaneously provide high spatial resolution and wholebrain coverage. Early work used compressed sensing and parallel imaging to reconstruct dynamic images from undersampled k,tspace data (1012). Standard TK modeling software was then used to generate highresolution wholebrain TK maps based on the reconstructed images (9,13). A more recent proposed approach was to enforce the TK model and directly estimate TK parameters from undersampled k,tspace data (14). Similar modelbased reconstruction approaches have been used for MRI relaxometry (15,16), PET kinetic parameter estimation (17,18), and recently, DCEMRI kinetic parameter estimation (14,1921). Compared with conventional compressed sensing techniques that reconstruct dynamic images first, the modelbased approach provides superior results and allows higher undersampling rates (14,21). Direct kinetic parameter estimation makes the most efficient use of acquired information; however, it is sensitive to inaccuracy of the forward model. Two major issues with this are variations in the arterial input function (22) and prior knowledge of the appropriate TK model (2325).
In conventional DCEMRI, images are reconstructed for each time point. Patientspecific arterial input functions (AIF) can be identified from vessel voxels using either manual region of interest (ROI) selection or automatic clusterbased ROI selection (26). Some centers use a fixed populationaveraged AIF (27), an institutionally derived population AIF, or a delay and dispersioncorrected version of these (9). The use of a patientspecific AIF (patAIF) is generally preferred because it is known to provide more accurate TK mapping (22). The estimation of patAIF from undersampled data is extremely challenging due to undersampling artifacts. Current modelbased TK reconstruction approaches rely on the use of a populationaveraged AIF (popAIF) (14,21). This is considered a major limitation of these approaches because the use of a popAIF can lead to significant errors in the resulting TK maps (22).
Accordingly, there is a need for improved methods implementing dynamic contrast enhanced magnetic resonance imaging.
The present invention solves one or more problems of the prior art by providing in at least one embodiment, a flexible framework for direct modelbased reconstruction of accelerated DCEMRI.
In at least one aspect, the present invention involves a DCEMRI reconstruction approach that allows for integration of different TK models and/or different TK solvers as well as joint estimation of the patientspecific AIF and TK parameter maps. The performance of the present invention was evaluated using simulated DCEMRI data from a physiologically realistic digital reference object (DRO) and in vivo DCEMRI data from brain tumor patients. The application of the present invention was tested on prospectively undersampled highresolution wholebrain DCEMRI data.
In another aspect, the present invention provides simultaneous reconstruction of TK maps and dynamic images, where TK model consistency is applied as a penalized reconstruction constraint and the patAIF can be iteratively estimated from the dynamic images. This approach is inspired by recent studies of accelerated quantitative MR relaxometry (28,29), where physical or physiological model consistency was applied as a penalized reconstruction constraint (not strictly enforced). This consistency constraint allowed for the data fit to deviate from the model, which made the scheme robust to scenarios with model inconsistencies (e.g., motion). For DCEMRI, TK model is applied as a consistency constraint with a regularization parameter that balances the tradeoff between data consistency and model consistency.
In another aspect, a method for improving dynamic contrast enhanced imaging for joint arterial input function and tracer kinetic parameter estimation is provided. The method includes steps of administering a contrast agent (e.g., a magnetic resonance contrast agent) to a subject and then collecting imaging data (e.g., magnetic resonance imaging data) from the subject for a tissue or organ. A tracer kinetic model (e.g., eTofts or Patlak) is selected to be applied to the magnetic resonance imaging data. The tracer kinetic model is defined by a plurality of tracer kinetic parameters. The tracer kinetic model is applied to the magnetic resonance imaging data to estimate the tracer kinetic parameter map. Tracer kinetic maps and dynamic images are reconstructed by alternating between the reconstruction for tracer kinetic maps and dynamic images until data and model consistency are met simultaneously. In a refinement, the tracer kinetic model is automatically selected from estimated contrast concentration versus time images and estimated patient specific AIF.
In another aspect, a method for improving dynamic contrast enhanced imaging for joint arterial input function and tracer kinetic parameter estimation is provided. The method includes steps of administering a contrast agent (e.g., a magnetic resonance contrast agent) to a subject; collecting imaging data (e.g., a magnetic resonance imaging data) from the subject for a tissue or organ; selecting a tracer kinetic model to be applied to the imaging data, the tracer kinetic model being defined by a plurality of tracer kinetic parameters; and reconstructing dynamic images from the imaging data as reconstructed dynamic images. The method further includes a step of applying the tracer kinetic model to the reconstructed dynamic images to estimate tracer kinetic parameter maps as estimated tracer kinetic parameter maps. Reconstructed dynamic images and estimated tracer kinetic parameter maps are jointly forced to be consistent with the measurement data and the selected tracer kinetic model. Characteristically, this simultaneous consistency is enforce in form of a weighted sum of a data consistency component and a model consistency component. Finally, the steps of reconstructing dynamic images and applying the tracer kinetic model are alternately performed until converging on a set of dynamic images and tracer kinetic parameter maps.
In still another aspect, a system for improving dynamic contrast enhanced imaging for joint arterial input function and tracer kinetic parameter estimation is provided. The system is a magnetic resonance imaging system that generates magnetic resonance imaging data from a subject for a tissue or organ and a programmable computer. The programmable computer is operable to execute steps of: collecting the magnetic resonance imaging data from the subject and reconstructing dynamic images from the magnetic resonance imaging data as reconstructed dynamic images. The programmable computer is further operable to apply a tracer kinetic model to the reconstructed dynamic images to estimated tracer kinetic parameter maps. The computer is operable to apply a consistency constraint to the reconstructed dynamic images and the estimated tracer kinetic parameter maps. Characteristically, the consistency constraint includes a weighted sum of a data consistency component and a model consistency component; The programmable computer is further operable to alternately perform the steps of reconstructing dynamic images and applying the tracer kinetic model until converging on a set of dynamic images and tracer kinetic parameter maps.
Reference will now be made in detail to presently preferred compositions, embodiments and methods of the present invention which constitute the best modes of practicing the invention presently known to the inventors. The Figures are not necessarily to scale. However, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various and alternative forms. Therefore, specific details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for any aspect of the invention and/or as a representative basis for teaching one skilled in the art to variously employ the present invention.
Except in the examples, or where otherwise expressly indicated, all numerical quantities in this description indicating amounts of material or conditions of reaction and/or use are to be understood as modified by the word “about” in describing the broadest scope of the invention. Practice within the numerical limits stated is generally preferred. Also, unless expressly stated to the contrary: the first definition of an acronym or other abbreviation applies to all subsequent uses herein of the same abbreviation and applies mutatis mutandis to normal grammatical variations of the initially defined abbreviation; and, unless expressly stated to the contrary, measurement of a property is determined by the same technique as previously or later referenced for the same property.
It is also to be understood that this invention is not limited to the specific embodiments and methods described below, as specific components and/or conditions may, of course, vary. Furthermore, the terminology used herein is used only for the purpose of describing particular embodiments of the present invention and is not intended to be limiting in any way.
When a computer is described as performing an action or method step, it is understood that the computing devices is operable to perform the action or method step typically by executing one or more line of source code. The actions or method steps can be encoded onto nontransitory memory (e.g., hard drives, optical drive, flash drives, and the like).
It must also be noted that, as used in the specification and the appended claims, the singular form “a,” “an,” and “the” comprise plural referents unless the context clearly indicates otherwise. For example, reference to a component in the singular is intended to comprise a plurality of components.
Throughout this application, where publications are referenced, the disclosures of these publications in their entireties are hereby incorporated by reference into this application to more fully describe the state of the art to which this invention pertains.
Abbreviations:
“AIF” means arterial input function.
“DCEMRI” means dynamic contrast enhanced magnetic resonance imaging.
“ETK” means extended ToftsKety.
“MRI” means magnetic resonance imaging.
“TK” means tracerkinetic.
“ROI” region of interest.
In at least one embodiment, a method for improving dynamic contrast enhanced imaging is provided. The method includes steps of administering a contrast agent (e.g., a magnetic resonance) to a subject and then collecting imaging data (e.g., a magnetic resonance imaging data) from the subject for a tissue or organ. A tracer kinetic model (e.g., ETK or Patlak) is selected to be applied to the imaging data. In a refinement, the tracer kinetic model is selected from a library of tracer kinetic models such that one or more tracer kinetic model from the library are applied to find an optimal tracer kinetic model. The tracer kinetic model is defined by a plurality of tracer kinetic parameters. The tracer kinetic model is applied to the imaging data to estimate the tracer kinetic parameter map. Dynamic images and tracer kinetic parameter maps are reconstructed from the imaging data. A consistency constraint is applied to dynamic images and estimated tracer kinetic parameter maps. Reconstructed dynamic images and estimated tracer kinetic parameter maps are jointly forced to be consistent with the measurement data and the selected tracer kinetic model. Characteristically, this simultaneous consistency is enforced in form of a weighted sum of a data consistency component and a model consistency component. The tracer kinetic model is applied to the reconstructed dynamic images to estimate tracer kinetic parameter maps. The steps of reconstructing dynamic images with consistency constraint and of applying the tracer kinetic model are alternatively performed (e.g. in an alternating fashion) until converging on a set of dynamic images and tracer kinetic parameter maps. In a refinement, the consistency constraint is iteratively enforced to the dynamic images first followed by the tracer kinetic maps. In another refinement, the tracer kinetic model is selected automatically from during estimation of contrast concentration versus time images and patientspecific AIF from undersampled data.
The methods of the present embodiment are advantageously used for determining an arterial input function (AIF) sometimes referred to as vascular input function (VIP) from the imaging data (e.g., magnetic resonance imaging data or other dynamic contrast imaging techniques such as positron dynamic contrast positron emission tomography data), wherein the arterial input function includes a time variation of the contrast agent concentration at one or more predetermined locations in an artery of the subject. The arterial input function is taken as surrogate for the vascular input function. Typically, the arterial input function is determined as a function of time. In other variation, the tissue or organ to which the method is applied can be selected from the group consisting of brain, breast, prostate, liver, kidney, lung, heart, thyroid, pancreas, spleen, intestine, uterus, ovary, limbs, spleen, spine,bones, and eyes.
In one variation, the tracer kinetic model can be preselected (e.g., by a user) as depicted in the flow chart of
With reference to
With reference to
In one variation, a manually selected reference tissue mask for extraction of patient specific AIF/VIF from MRI data is used. In another variation, reference tissue and vessels for data extraction is automatically determined (e.g., in each iteration) based on the current image series. This can be done with a variety of criteria: choosing voxels of peak enhancement (e.g., relative or absolute peak enhancement), comparison to reference (population based) AIF, model order estimation methods like information criteria, goodness of fit criteria like Balvay'"'"'s criterion/Chisquare criterion, and the like. The candidate voxels are ranked based on the selected criteria from best to worst. The AIF/VIF is extracted from the voxels with highest ranking.
As set forth above, the present embodiment applies a tracer kinetic model. Examples of suitable tracer models are the Patlak and extended ToftsKety (ETK) model as set forth in P. S. Tofts, G. Brix, D. L. Buckley, J. L. Evelhoch, E. Henderson, M. V Knopp, H. B. Larsson, T. Y. Lee, N. a Mayr, G. J. Parker, R. E. Port, J. Taylor, and R. M. Weisskoff, “Estimating kinetic parameters from dynamic contrastenhanced T(1)weighted MRI of a diffusable tracer: standardized quantities and symbols. ”J. Magn. Reson. Imaging, vol. 10, no. 3, pp. 22332, Sep. 1999; and Parker, G. J. and Buckley, D. L., 2005. Tracer kinetic modelling for T1weighted DCEMRI. In Dynamic contrastenhanced magnetic resonance imaging in oncology (pp. 8192). Springer Berlin Heidelberg; the entire disclosures of these publications is hereby incorporated by reference. In general, the Patlak and ETK having kinetic parameters: K^{trans }which is a transfer constant from blood plasma into extracellular extravascular space (EES) and v_{p }which is fractional plasma volume. The ETK model also has kinetic parameters K^{ep }which is a transfer constant from EES back to the blood plasma and v_{e }which is a fractional EES volume (v_{e}=K^{trans}/K^{ep}). The concentration for the contrast agent in this model is calculated from:
where
 C_{t }is the equilibrium concentration of contrast agent in whole tissue;
 C_{p }is the equilibrium concentration of contrast agent in plasma;
 C_{e }is the equilibrium concentration of contrast agent in extracellular extravascular space.
 In the simple Toft model, the contrast concentration in the whole tissue can be determined from:
C_{t}(t)=K^{trans}∫_{0}^{t}C_{p}(τ)e^{−(K}^{trans}^{/v}^{e})(tτ)dτ
When v_{p }is considered such as in the ETK model, the contrast concentration in whole tissue can be determined from:
C_{t}(t)=v_{p}C_{p}(t)+K^{trans}∫_{0}^{t}C_{p}(τ)e^{−(K}^{trans}^{/v}^{e}^{)(tτ)}dτ
When the time dependent concentrations, ie, C_{t }and C_{p}, are known, these equations can be inverted to estimate the kinetic parameters. Additional details for converting TK parameter (e.g., K^{trans}, v_{p}) maps to contrast concentration over time using the Patlak model is provided by P. S. Tofts, G. Brix, D. L. Buckley, J. L. Evelhoch, E. Henderson, M. V Knopp, H. B. Larsson, T. Y. Lee, N. a Mayr, G. J. Parker, R. E. Port, J. Taylor, and R. M. Weisskoff, “Estimating kinetic parameters from dynamic contrastenhanced T(1)weighted MRI of a diffusable tracer: standardized quantities and symbols. ”J. Magn. Reson. Imaging, vol. 10, no. 3, pp. 22332, Sep. 1999 and Patlak C. S., Blasberg R. G., Fenstermacher J. D. Graphical evaluation of bloodtobrain transfer constants from multipletime uptake data. J. Cereb. Blood Flow Metab. 1983; 3:17; the entire disclosures of these publications is hereby incorporated by reference.
As set forth above, the dynamic images and the tracer kinetic parameter maps are estimated jointly by enforcing a consistency constraint. The consistency constraint includes a weighted sum of a data consistency component and a model consistency component. The data consistency component assesses how well the acquired imaging data (e.g., raw or Fourier transformed magnetic resonance data) for each voxel in a Field Of View is approximated by the dynamic images calculated from the estimate of concentrationtime curves of the contrast agent for each voxel in a Field Of View. Therefore, a first difference can be between the acquired imaging data for each voxel in a Field Of View and data calculated from the estimated concentrationtime curves for each voxel in a Field Of View. Similarly, the model consistency component assesses how well the concentrationtime curves calculated from the estimate of the tracer kinetic model and its plurality of parameters approximate measured concentrationtime curves of the contrast agent for each voxel in a Field Of View. Therefore, a second difference can be determined between the measured concentrationtime curves for each voxel in a Field Of View and concentrationtime curves calculated from the tracer kinetic model for each voxel in a Field Of View. The consistency constraint seeks to minimize the combination of both differences (e.g., see the β parameter below).
In a variation, the consistency constraint is provided by the minimization (i.e., a a least squares optimization) represented by Equation 1:
where:
 ψ is a signal operator which converts concentrationtimecurves (per voxel) C of a contrast agent to an image intensity time series;
 U is an undersampling mask;
 F is a Fourier transform, and in particular, the discrete Fourier transform matrix or a FastFourierTransform (FFT) algorithm;
 E is a sensitivity encoding matrix providing the spatial relative sensitivities of the pickup coils;
 S_{0 }is image intensity for each voxel prior to contrast agent arrival;
 y is undersampled magnetic resonance imaging data:
 C is a measured concentrationtime curves of the contrast agent for each voxel in the Field Of View;
 P(θ) is a predicted concentration distribution of the contrast agent from the selected tracer kinetic model;
 β is a penalty or weight factor for the model consistency component; and
 θ are tracer kinetic parameters such K^{trans }and v_{p }for the Patlak and ETK models and K^{ep }and v_{e }for the ETK as described below.
 It should be noted that U, F, and E are linear operators which can be expressed as matrices, while ψ can be either a linear or nonlinear operator. So is expressed as matrix with each matrix entry being a value for a spatial point or voxel. C is expressed as matrix with each matrix entry being a value for a spatial point or voxel and time point. In equation 1, the first 12 norm represents the data consistency component and the second 12 norm represents model consistency component.
In another variation, the arterial input function is smoothed or forced to fit a model. In this regard, smoothing, regularization, and regression include any form of variation penalty, e.g., constraints applied to temporal derivatives and frequency spectra of the input function and its epochs, spatial smoothing filters, e.g., (weighted) averaging over or preferential selection from multiple ROI voxels, and regression to a prespecified, parameterized functional form for the input function, e.g., sum of exponentials, sum of gammavariates, sum of sigmoids, or a mixture thereof.
In most applications, all steps of the method set forth above are repeated for multiple slices through said object being imaged and threedimensional image data are reconstructed.
It should also be appreciated that the methods set forth herein can be applied to any dynamic contrast imaging technique such dynamic contrast magnetic resonance imaging and dynamic contrast positron emission tomography.
In another embodiment, a magnetic resonance system, and in particular, an MRI system for improving dynamic contrast enhanced imaging is provided. The system advantageously implements the methods set forth herein. With reference to
Computer 18, and in particular, CPU 20 in conjunction with magnetic resonance imaging system 14 implements the methods set forth above as follows. Computer 18 send control signals to pulse sequencer 34 to control gradient system 46 to apply a gradient magnetic field pulse from polarizing magnetic coil 42 to a subject 56 along a first direct. A subject who has been administered a contract agent is placed in this gradient magnetic field. Computer 18 also sends control signals to pulse sequencer 34 to RF system 46 to apply an excitation radiofrequency pulse to the subject during the first gradient magnetic field pulse where the excitation radiofrequency pulse is resonant with a region in the subject. Computer 18 also sends control signals to pulse sequencer 34 to control gradient system 46 to apply gradient magnetic field pulses to the subject after the first gradient magnetic field pulse in order to provide spatial encoding. RF system 46 receives an output signal from the subject 56 during the second gradient magnetic field pulse such that magnetic resonance imaging data is collected from the subject for a tissue or organ. This output signal is ultimately transferred to computer 18 for processing. Computer 18, and in particular CPU, applies a selected tracer kinetic model to the magnetic resonance imaging data to estimate tracer kinetic parameter maps; and applying the tracer kinetic model to the magnetic resonance imaging data to estimate tracer kinetic parameter maps; and reconstructing tracer kinetic maps and dynamic images from the tracer kinetic parameter maps, wherein a consistency constraint is applied to reconstruct the tracer kinetic maps and dynamic images, the consistency constraint including a sum of a data consistency component and a model consistency component. The tracer kinetic model can be user selected in advance or automatically selected or determined by computer 18. Additional details regarding all of the steps implemented the system and in particular computer 18 are set forth above.
In a variation, magnetic resonance imaging system 14 generates magnetic resonance imaging data from a subject for a tissue or organ. As set forth above, a magnetic resonance contrast agent is administered prior to the generation and collection of the imaging data. Programmable computer 18 is operable to execute steps of collecting the magnetic resonance imaging data from the subject and reconstructing dynamic images and tracer kinetic maps from the magnetic resonance imaging data as set forth above. Computer 18 is further operable to apply a consistency constraint as set forth above. Finally, the steps of reconstructing dynamic images, applying the tracer kinetic model, and applying the consistency constraint are alternately performed until converging on a set of dynamic images and tracer kinetic parameter maps. Computer 18 can be further operable to select a tracer kinetic model to be applied to the magnetic resonance imaging data where the tracer kinetic model being defined by a plurality of tracer kinetic parameters. Advantageously, the programmable computer is also operable to determine an arterial input function or vascular input function from the magnetic resonance imaging data, wherein the arterial input function includes a time variation of a magnetic resonance contrast agent at one or more predetermined locations in an artery of the subject. Characteristically, the arterial input function is taken as surrogate for the vascular input function with the arterial input function being determined as a function of time. In some variations, reference tissue and vessels for AIF extraction are automatically selected in each iteration based on a current image series. In this regard, reference tissue and vessels for AIF extraction can be automatically selected from voxels of peak enhancement or by comparison to reference (population based) AIF or by a model order estimation method. In another refinement, the programmable computer is operable to identify and select a tracer kinetic model from a library of tracer kinetic models. In still other refinement, computer 18 is operable to automatically selected a tracer kinetic model by specifying a collection of possible models (nested or not nested) from which a model identification method is applied to select a model for each voxel or region. In some variation, computer 18 is operable to simultaneously reconstruct tracer kinetic parameter maps and the dynamic images. As set forth above, the tracer kinetic model can be a Patlak model or an extended Tofts model.
Additional details of the present invention can be found in Y Guo, S G Lingala, Y Bliesener, R M Lebel, Y Zhu, K S Nayak. Joint arterial input function and tracker kinetic parameter estimation from undersampled DCEMRI using a model consistency constraint. Magnetic Resonance in Medicine. 79(5):28042815. May 2018; the entire disclosure of which is hereby incorporated by reference.
The following examples illustrate the various embodiments of the present invention. Those skilled in the art will recognize many variations that are within the spirit of the present invention and scope of the claims.
Theory
Model Consistency Constraint
This method jointly estimates contrast concentration versus time images (C) and TK parameter maps (θ) from the undersampled data (y) by solving the following leastsquares problem:
The first I_{2 }norm represents data consistency, where C should be consistent with the measured data y by Ψ (signal equation), U (undersampling mask), F (Fourier transform), and E (sensitivity encoding). S_{0 }is the first temporal frame images that are fully sampled. The second I_{2 }norm represents model consistency, where C is consistent to the forward modeling (P) of TK parameter maps (Patlak, eTofts etc.). This formulation can be simplified to:
where A=UFEΨ represents data consistency modeling, b=(yUFES_{0}) is the known data. To solve the leastsquare optimization problem in Equation [2], we alternatively solve for each variable while keeping others constant. For each iteration n,
Note that Equation [3] is regularized SENSE reconstruction with an I_{2 }norm constraint that can be solved efficiently using conjugate gradients (30). Equation [4] is backward TK modeling that can be solved using any DCEMRI modeling toolbox. Because forward modeling (P) and backward modeling (P^{−1}) are used iteratively, the modeling solver should not utilize linearization or other forms of approximation. For example, ROCKETSHIP (31) and TOPPCAT (32) are two suitable solvers. Detailed sub steps and variants of Equations [3] and [4] are provided in the Appendix.
Joint AIF and TK Parameter Estimation
The proposed formulation allows for joint estimation of the patientspecific AIF. Equation [2] can be modified to estimate C, θ, and AIF from undersampled data by solving the following leastsquares problem:
Similar to the above, we solve each variable alternatively as follows (n^{th }iteration):
Equation [7] is backward TK modeling from contrast concentration including patAIF estimation. This can be performed by identifying an arterial ROI once, using the timeaveraged image or postcontrast image. Within each iteration, it is then possible to: 1) apply this ROI to C to estimate the AIF (averaging the pixels) and 2) use the updated AIF during TK modeling. This is a common procedure in TK modeling for DCEMRI. The only difference is identification of the arterial ROI before the reconstruction of the dynamic images.
Theoretical Benefits
The proposed method formulates model consistency as a constraint with a penalty β and decouples it from data consistency. There are multiple benefits of this formulation: 1) algorithm complexity is reduced compared to recently proposed direct reconstruction techniques that require complex cost function gradient evaluations (14,20,33); 2) different TK models can easily be included in this formulation, as described above; 3) patientspecific AIFs can be estimated jointly with TK maps, as described above; and 4) the penalty β can allow for TK model deviation, reducing errors that may be caused by strict model enforcement (29). This study specifically demonstrates items #2 and #3.
Methods
Data Sources
Digital Reference Object
Anatomically realistic brain tumor DCEMRI DRO was generated based on the method and data provided by Bosca and Jackson (34). The extended Tofts (eTofts) model was used to generate contrast concentration curves with known TK parameter maps and popAIF (27). Coil sensitivity maps measured on our MRI scanner (3T, eightchannel head coil) were coregistered to the DRO and used to generate realistic MRI kspace data (35). Gaussian noise was added to the image space to simulate noise levels typical of DCEMRI at 3T and 1.5T.
Retrospective
Nine anonymized fully sampled brain tumor DCEMRI raw data sets were obtained from patients who had undergone routine brain MRI examinations with contrast (including DCEMRI) at our institution. The study protocol was approved by our Institutional Review Board. The acquisition was based on a 3D Cartesian fast spoiled gradient echo (SPGR) sequence using the following parameters: field of view=22×22×4.2 cm^{3}, spatial resolution=0.9×1.3×7.0 mm^{3}, temporal resolution=5 s, 50 time frames, eight receiver coils, flip angle=15°, echo time =1.3 ms, repetition time=6 ms. DESPOT1 was performed before DCEMRI, with a flip angle of 2°, 5°, and 10° to estimate precontrast T_{1 }and M0 maps. The contrast agent, gadobenate dimeglumine [MultiHance Bracco Inc.; relaxivity r_{1}=4.39 s^{−1}·mM^{−1 }at 37° C. at 3T (36)] was administered with a dose of 0.05 mmol/kg, followed by a 20mL saline flush in the left arm via intravenous injection.
Prospective
Prospectively undersampled data were acquired in one brain tumor patient (male, age 65 years, glioblastoma) with Cartesian goldenangle radial kspace sampling (9,37). 3D SPGR data were acquired continuously for 5 min. Wholebrain coverage was achieved with a field of view of 22*22*20 cm^{3 }and spatial resolution of 0.9*0.9*1.9 mm^{3}. The prospective study protocol was approved by our Institutional Review Board. Written informed consent was provided by the participant.
Demonstration of TK Solver Flexibility
To demonstrate TK solver flexibility, DRO data was retrospectively undersampled using a randomized goldenangle sampling pattern at R=60× (37). Gaussian noise was added to the image space, creating signaltonoise ratio (SNR) levels of 20 and 10 (white matter based) for simulation of DCEMRI image quality at 3T and 1.5T. The proposed method with eTofts modeling was used to reconstruct TK parameter maps at R=60 × and SNR=20 and 10, respectively. An inhouse gradientbased algorithm and an opensource TK modeling toolbox, ROCKETSHIP (31), were used for the eTofts solver in the proposed algorithm (Eq. [4]). Tumor ROIK^{trans }correlation coefficient, R^{2 }and normalized root meansquarederror (nRMSE, normalized by the 90th percentile value within the tumor ROI) between the estimated and true values were calculated and compared. Note that tumor ROI 90th percentile K^{trans }value has been found to be a sensitive and clinically valuable DCEMRI biomarker (38,39), hence normalization of RMSE by this value. TK maps estimated from the noisy fully sampled images (SNR=20, R=1×) were also compared with the true TK maps to evaluate the performance of the proposed method with respect to errors found in conventional DCEMRI.
Demonstration of TK Model Flexibility
The nine fully sampled patient data were fitted to the Patlak and eTofts models to calculate the model fitting error, and an Ftest was performed in the tumor ROI to determine whether the Patlak or eTofts model is the most appropriate fit (2325). In the Ftest (40,41), the null hypothesis is that the two samples of sumofsquared modeling errors were drawn from the same pool. The failure of this hypothesis leads to acceptance of the higherorder model. Thus, for each pixel, the Ftest will reveal whether a higherorder model (eTofts model) should be used (2325). If more than 50% of the tumor pixels were appropriately fitted for a certain model, this model was selected for the data set. We reconstructed the corresponding TK parameter maps for fully sampled data (used as reference) and at undersampling rates of 20×, 60×, and 100 × for all nine cases. A randomized goldenangle sampling pattern (37) was used in the k_{x}k_{y }plane, simulating _{kykz }phase encoding in a 3D wholebrain acquisition. Images were reconstructed using a popAIF (27) with patientspecific delay corrected by the delay estimated from kspace center (42). ROIbased K^{trans }nRMSE and K^{trans }histograms were calculated based on the reference K^{trans }maps. K^{trans }histogram skewness and 90th percentile K^{trans }values were also measured for evaluation, as they have been shown to be valuable in the clinical assessment of brain tumors by DCEMRI (38,39,43).
Demonstration of Joint AIF and TK Estimation
The cases following the Patlak model were reviewed with special attention to vessel signal. Cases that showed significant precontrast inflow enhancement were identified and subsequently excluded. With the remaining cases, we performed joint estimation of AIF and Patlak parameter maps from undersampled data across sampling rates of 20×, 60×, and 100×. For each undersampling rate, 15 realizations were generated by varying the initial angle of the goldenangle radial sampling pattern (37). The goldenangle radial sampling with different initial angle will create mostly nonoverlapped kspace coverage, effectively providing different noise realizations with the same noise level (white matter SNR=20). Reconstructed patientspecific AIFs were compared with the fully sampled reference using nRMSE (normalized to the 90th percentile AIF value over time) and bolus peak difference. ROIbased K^{trans }nRMSE (normalized to the 90th percentile K^{trans }value over the tumor ROI) were also calculated for evaluation.
Demonstration with Prospectively UnderSampled Data
We tested the application of the proposed method for joint AIF and TK parameter estimation on prospectively 30× undersampled highresolution wholebrain DCEMRI data. Fivesecond temporal resolution was achieved by grouping raw (k,t)space data acquired within consecutive 5s intervals, effectively 30× undersampling compared with Nyquist sampling (44). patAIF and TK maps were jointly reconstructed using the proposed model consistency constraint approach. patAIF ROI was selected based on timeaveraged images. Threeplane of K^{trans }and vp maps and patAIF are presented for visual assessment.
Results
Based on the tumor ROI Ftest, the Patlak model was appropriate for six in vivo cases, whereas the eTofts model was appropriate for three in vivo cases.
We have described, demonstrated, and evaluated a novel modelbased reconstruction approach for DCEMRI in which the TK model is posed as a penalized consistency constraint. By this formulation, we decoupled the TK model consistency from the k,t space data consistency. The two subproblems can be solved using existing techniques, namely TK modeling (including AIF estimation) and regularized SENSE reconstruction. The proposed approach allows for easy inclusion of different TK solvers, including thirdparty solvers, and also allows for joint estimation of the patientspecific AIF. We have demonstrated the robustness of the proposed method in one anatomically realistic brain tumor DRO, and a retrospective study of nine brain tumor DCEMRI datasets. The DRO study demonstrated that the proposed method provides performance comparable to conventional TK modeling results from fully sampled noisy images, with only a 2% higher error at 60fold undersampling. The retrospective study shows that the proposed method is robust to noise across different cases, and can provide accurate TK maps with less than 32% error, and AIF with less than 8% error up to 100fold undersampling.
We also demonstrated the application of the proposed method to prospectively undersampled data, where wholebrain highresolution TK maps can be jointly reconstructed with patAIF. The proposed method has a few important limitations. First, the alternating algorithm proposed is a twoloop iteration, where an iterative solver is needed for each subproblem. Compared with a gradientbased direct reconstruction (14), this formulation takes longer computing time. This issue can be addressed by using more powerful computers, implementing in C, and/or using GPU acceleration.
Second, although we demonstrate that the proposed method is compatible with a thirdparty solver, it requires that the solver not use any approximation for the modeling. This is because the proposed approach requires the backward and forward modeling operators to be exact inverses of each other, otherwise error will accumulate during the iteration process. For higherorder TK models, a few linearized approximation approaches have been proposed for fast computation (46,47). Unfortunately, those approximation methods are not compatible with this framework.
Third, although we have shown that this method can include different TK solver, it may be difficult to use a nested model that selects between several different local models based on local fitting errors (2325). This type of approach has been shown in the literature to be advantageous. The quality of intermediate anatomic images in the proposed method, especially in the first few iterations, may make it challenging to generate a modeling mask needed for nested models.
Fourth, we have not accounted for phase that can be induced by the contrast agent (primarily in vessels). Many centers, including ours, use a half dose for DCEMRI, which makes this effect negligible. If a full dose is used, the potential phase effects on the AIF signal can and should be modeled using the closedform solution by Simonis et al. (48).
In conclusion, we have demonstrated a novel modelbased reconstruction approach for accelerated DCEMRI. Posing the TK model as a model consistency constraint, this formulation provides flexible use of different TK solvers, joint estimation of patAIF, and straightforward implementation. In anatomically realistic brain tumor DRO studies, the proposed method provides TK maps with low error that are comparable to fully sampled data. In retrospective undersampling studies, this method provides TK maps with nRMSE less than 32% and patAIF with nRMSE less than 8% at undersampling rates up to 100×.
The proposed method uses an alternating approach to solve for C and θ from undersampled k,tspace data. This appendix details the steps involved in solving the two subproblems shown in Eqn [4] and Eqn [5].
In Eqn [4], we solve for the contrast concentration vs time from the measured data using the following equation:
where A=UFEΨ. We first solve for the image difference (ΔS) from b (since the precontrast signal S_{0 }is included in b) by solving the following leastsquare problems using CG (or another iterative algorithm for leastsquare problems). We use the result from the previous iteration as an initial guess for faster convergence.
where first term represents SENSE, and the second term is an identity constraint to ΨP(θ^{n}) that is constant in this step. P is the forward modeling from TK maps to contrast concentration vs time C, and Ψ is the conversion from contrast concentration C to signal difference ΔS following the steadystate SPGR signal equation:
where TR is the repetition time, a is the flip angle, r_{1 }is the contrast agent relaxivity. R_{0 }and M_{0 }are the precontrast R_{1 }(reciprocal of T_{1}) and the equilibrium longitudinal magnetization that are estimated from a T_{1 }mapping sequence. In this work, we used DESPOT1 (49) prior to the DCEMRI scan.
Note that Ψ is a onetoone mapping for each voxel, and its inversion (C=Ψ^{−1}(ΔS)) is:
Eqn [A.3] is used to compute C after solving for ΔS using Eqn [A.1], this completes the detailed algorithm for solving Eqn [4].
After C is estimated, Eqn [5] represents backward TK modelling. C(t) is used in the equation below to avoid confusion. For the Patlak model, Eqn [4] is expressed as:
Where C_{p}(t) is the arterial input function (AIF). The Patlak model is linear, and a pseudoinverse can be used to solve θ=P^{−1}(C).
For the extendedTofts (eTofts) model, Eqn [4] is expressed as:
where an extra TK parameter K_{ep }is modeled for better fitting. eTofts is nonlinear, and an iterative algorithm can be used to solve this model fitting:
We use a gradientbased 1BFGS algorithm to solve Eqn [A.6], where we derive the gradient for each TK parameter. In this study, we also used an opensource DCEMRI TK modeling toolbox, Rocketship (31), for comparison.
The code and examples of the proposed algorithm are publicly available at “github.com/uscmrel/DCE_MOCCO;” the entire disclosure of which is hereby incorporated by reference.
While exemplary embodiments are described above, it is not intended that these embodiments describe all possible forms of the invention. Rather, the words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention. Additionally, the features of various implementing embodiments may be combined to form further embodiments of the invention.
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