Method and system for generating a four-dimensional angiographic reconstruction

Abstract

A computer-implemented technique for generating a four-dimensional (4D) angiographic reconstruction includes obtaining biplane angiographic data and obtaining a three-dimensional (3D) vascular geometry. 4D angiographic data are reconstructed from the biplane angiographic data using back-projection constrained by the 3D vascular geometry. In some embodiments, each view of the biplane angiographic data is aligned with the 3D vascular geometry to create a registered 3D vascular structure mask, and contrast intensities from the aligned views are back-projected into a common volume that is constrained using the registered 3D vascular structure mask. In some embodiments, intensity profiles are path-length corrected using the 3D vascular geometry. The 4D angiographic data may be processed using a classifier configured to enhance vessel boundaries, reduce artifacts, or improve flow representation. Volumetric angiographic parametric imaging maps may be generated from the angiographic data and the angiographic data may be rendered for viewing from different angles and time points.

Description

Attorney Docket No.: 011520.02035METHOD AND SYSTEM FOR GENERATING A FOUR-DIMENSIONAL ANGIOGRAPHIC RECONSTRUCTIONCross-Reference to Related Applications

[0001] This application claims priority to U.S. Application No. 63 / 778,348, titled Method and System for 3D Temporal Reconstruction of Neurovascular Contrast Flow Using Biplane Angiography and Convolutional Neural Networks, filed March 26. 2025, which is hereby incorporated by reference in its entirety.Statement Regarding Federally Sponsored Research

[0002] This invention was made with government support under grant numbers EB030092 awarded by National Institutes of Health and 2304388 awarded by the National Science Foundation. The government has certain rights in the invention.Field of the Disclosure

[0003] The present disclosure relates to medical imaging and image processing, and more particularly to techniques for generating a four-dimensional angiographic reconstruction from biplane angiographic data and a three-dimensional vascular geometry.Background of the Disclosure

[0004] Angiographic imaging is widely used to visualize vascular anatomy and bloodflow-related behavior during diagnostic and interventional procedures. In neurovascular applications, digital subtraction angiography provides high temporal and spatial resolution and remains a principal imaging modality for assessing aneurysms, arteriovenous malformations, stenoses, and other vascular conditions. However, conventional angiographic image sequences are projection images and therefore do not directly represent the underlying three-dimensional temporal distribution of contrast within the vasculature. As a result, overlapping vascular structures, loss of depth information, foreshortening, and projection-dependent intensity effects may reduce the accuracy with which contrast propagation and associated hemodynamic behavior are assessed.

[0005] Quantitative angiography and angiographic parametric imaging can provide objective information derived from contrast passage, including parameters such as time-to-Attorney Docket No.: 011520.02035arrival, time-to-peak, mean transit time, peak height, and area under a time-density curve.Although such parameters can be useful for evaluating vascular conditions and treatment response, conventional implementations based on two-dimensional projection data may not fully capture the inherently three-dimensional nature of contrast flow. In particular, projection overlap and lack of depth resolution can introduce error and can limit the extent to which underlying volumetric flow behavior is recovered from standard angiographic acquisitions.

[0006] Three-dimensional vascular information may be available from modalities such as computed tomography angiography or cone-beam computed tomography, but such datasets are generally static and do not provide the same time-resolved depiction of contrast transport as angiographic projection sequences. Existing approaches for reconstructing dynamic three-dimensional flow information from projection data may require additional views, specialized acquisition protocols, or computationally intensive processing. Accordingly, there is a need for improved techniques that can generate a four-dimensional angiographic reconstruction from clinically available biplane angiographic data while using a three-dimensional vascular geometry' to improve localization of contrast information and support volumetric quantitative analysis. Brief Summary of the Disclosure

[0007] The present disclosure provides techniques for generating a four-dimensional angiographic reconstruction from biplane angiographic data and a three-dimensional vascular geometry7. In some embodiments, a computer-implemented method includes obtaining biplane angiographic data, obtaining a three-dimensional vascular geometry, and reconstructing fourdimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry. The reconstruction may include aligning each view of the biplane angiographic data with the three-dimensional vascular geometry to create a registered three-dimensional vascular structure mask, back-projecting contrast intensities from the aligned views into a common volume, and constraining the common volume using the registered three-dimensional vascular structure mask. In some embodiments, the reconstruction is repeated for successive time steps so that the resulting data represent time-resolved volumetric contrast propagation through a vasculature.

[0008] In some embodiments, alignment of the biplane angiographic data includes equalizing vascular structures represented in the views by scaling at least one of the views and adjusting fields of view by cropping at least one of the views. In some embodiments, the relativeAttorney Docket No.: 011520.02035scaling is estimated from advancement of contrast represented in the views along a shared axis. In some embodiments, the reconstruction further includes path-length correcting intensity profiles using the three-dimensional vascular geometry, such as by generating a pathlength map from the three-dimensional vascular geometry and using the pathlength map before or during back-projection.

[0009] In some embodiments, reconstruction of the four-dimensional angiographic data further uses acquisition-geometry data associated with the biplane angiographic imaging system that acquired the biplane angiographic data. The acquisition-geometry data may include one or more of gantry7geometry7, detector geometry7, source-to-image distance, source-to-object distance, detector position, synchronization information, orientation information, projection geometry descriptors, or combinations thereof. In some embodiments, the acquisition-geometry data are obtained from metadata associated with angiographic image files, from a communication bus of the angiographic imaging system, from one or more encoders of the angiographic imaging system, or combinations thereof. In some embodiments, projection matrices are determined for a particular acquisition run from the acquisition-geometry data. The projection matrices may be used to register the biplane angiographic data to the three-dimensional vascular geometry7and to define imaging rays for back-projecting contrast intensities from the biplane angiographic data into a common volume so that the reconstructed four-dimensional angiographic data correspond spatially to the three-dimensional vascular geometry for that acquisition run.

[0010] In some embodiments, reconstructing the four-dimensional angiographic data further includes enforcing a continuity condition on the reconstructed contrast distribution. The continuity condition may conserve mass of contrast across space and time and may constrain variation of the reconstructed contrast distribution between adjacent slices, adjacent voxels, adjacent vessel segments, adjacent time points, or combinations thereof. In some embodiments, the continuity7condition is applied after an initial constrained back-projection reconstruction to improve localization of contrast, preserve continuity of reconstructed flow within connected vascular regions, and improve temporal consistency of the reconstructed four-dimensional angiographic data.

[0011] In some embodiments, the four-dimensional angiographic data are further processed using a machine-learning classifier configured to enhance vessel boundaries, reduceAttorney Docket No.: 011520.02035artifacts, or improve accuracy of flow representation. The machine-learning classifier may include a convolutional neural network trained on angiograms having known flow patterns, and may include an encoder-decoder architecture with skip connections. In some embodiments, the four-dimensional angiographic data are used to generate one or more volumetric angiographic parametric imaging maps, such as maps corresponding to mean transit time, peak height, area under a time-density curve, time-to-peak, or time-to-arrival. In some embodiments, the fourdimensional angiographic data are rendered using volume rendering to permit viewing from different angles and time points.

[0012] The present disclosure also provides image-processing apparatuses and non-transitory computer-readable media configured to carry out the foregoing techniques. In some embodiments, an image-processing apparatus includes a memory configured to store biplane angiographic data and a three-dimensional vascular geometry, and a processor configured to reconstruct four-dimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry. In some embodiments, the apparatus is operatively associated with a C-arm biplane angiographic system configured to obtain the biplane angiographic data.Description of the Drawings

[0013] For a fuller understanding of the nature and objects of the disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.

[0014] FIG. 1: Example embodiments of a constrained back-projection algorithm workflow. Gray boxes indicated input data, including biplane angiography and a corresponding 3D vascular structure (know n a priori). Blue boxes represent processing steps within our algorithm. The green 4D angiography box is the raw output of our algorithm, and the orange 3D API analysis box shows our quantitative post-processing step. The 3D structure is used two-fold: first to generate a pathlength map to be used in our pathlength correction processing and second to mask the back-projected angiograms in the constrained back-projection step. All other processes occur linearly and use the biplane angiography data.

[0015] FIG. 2: Constrained back-projection of the same axial slice at three different time points. Each row7represents a different time point. The line in the AP view7of the originalAttorney Docket No.: 011520.02035angiographic acquisition (A) is used to reference a specific slice of the 4D reconstruction (B) at the indicated time.

[0016] FIG. 3: A sample time-density curve, with each API parameter denoted, including time-to-peak (TTP), mean transit time (MTT), time-to-arrival (TTA), peak height (PH) and area under the curve (AUC, shaded region). Temporal parameters are shown in red (MTT, TTP, and TTA), while intensity-based parameters are shown in blue (PH and AUC).

[0017] FIG. 4: Representative time points from each model's reconstructed 4D angiogram are shown across each row. To demonstrate the volumetric nature of the angiograms, the time series is viewed from various angles throughout the sequence.

[0018] FIG. 5: API maps for model Ml at 25 cm / s inlet velocity', generated from the constrained back-projection-reconstructed 4D angiogram. Maps include time-to-arrival (TTA), mean transit time (MTT), time-to-peak (TTP), peak height (PH), and area under the time-density curve (AUC). Temporal parameters are in seconds, while intensity-based parameters are unitless.

[0019] FIG. 6: Cross-sectional comparison of API results within the ICA (at the dashed line) of model Ml at 35 cm / s inlet velocity’. PH and AUC were constant in this cross section due to full filling with contrast media.

[0020] FIG. 7: Cross-sectional comparison of API results within the aneury sm dome (at the dashed line) of model Ml at 35 cm / s inlet velocity. We observe better agreement between intensity-based parameters, with mild spatial disagreement between datasets across the crosssection.

[0021] FIG. 8: A diagram of a sy stem according to an embodiment of the present disclosure.

[0022] FIG. 9: A chart depicting a method according to another embodiment of the present disclosure.

[0023] FIG. 10: A chart depicting a method according to another embodiment of the present disclosure.Attorney Docket No.: 011520.02035Detailed Description of the Disclosure

[0024] The present disclosure relates to image processing for generating a fourdimensional angiographic reconstruction from biplane angiographic data and a three-dimensional vascular geometry. In representative implementations, the four-dimensional angiographic reconstruction is a time-resolved volumetric representation of contrast propagation through a vasculature so that spatial distribution and temporal progression of contrast flow may be visualized and analyzed from a common dataset. Although many examples described herein refer to neurovascular imaging, including cerebral arteries, aneurysms, arteriovenous malformations, and stenotic regions, the same processing may be applied to coronary', peripheral, pulmonary', abdominal, renal, or other vascular territories in which projection angiographic image sequences and a three-dimensional vascular geometry are available.

[0025] With reference to FIG. 8, an image-processing system 100 may include a biplane angiographic system 110, a memory 120, and an image-processing apparatus 130 having one or more processors 132 in electronic communication with the memory 120. The biplane angiographic system 110 may be a C-arm biplane angiographic system having a first x-ray source and detector pair 112 arranged to obtain a first view and a second x-ray source and detector pair 114arranged to obtain a second view. The first view and the second view may be orthogonal views, substantially orthogonal views, or views separated by another known angular relationship. In many clinical implementations, the views are acquired during administration of a contrast agent and stored as time-resolved angiographic image sequences. The memory 120 may store the biplane angiographic data, a three-dimensional vascular geometry, calibration information, registration parameters, pathlength information, intermediate reconstruction data, trained machine-learning models, and output data. The processor 132 may execute instructions that obtain the biplane angiographic data, obtain the three-dimensional vascular geometry, reconstruct four-dimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry, process the reconstructed data using a machine-learning classifier, generate one or more volumetric angiographic parametric imaging maps, and render the reconstructed data for display.

[0026] The first view and the second view need not be limited to anterior-posterior and lateral views and need not be limited to a fixed orthogonal arrangement. In some embodiments, any two views may be used so long as the geometric relationship between the views is known,Attorney Docket No.: 011520.02035determined, or estimated. The angular relationship between the views may be orthogonal, substantially orthogonal, oblique, or otherwise selected for a particular imaging procedure. In some embodiments, the projection geometry for each selected view is determined for a particular acquisition run and is used in registration of the biplane angiographic data to the three-dimensional vascular geometry and in subsequent back-projection of contrast intensities into the common volume to generate the four-dimensional angiographic data.

[0027] The biplane angiographic data may be obtained directly from the biplane angiographic system 110 or may be retrieved from the memory 120 after acquisition. In some embodiments, the biplane angiographic data are digital subtraction angiography image sequences that capture passage of a contrast bolus through the vasculature over a series of time steps. Each view may include a plurality of image frames, and corresponding frames from the two views may represent the same or substantially the same acquisition time. The acquisition rate may be selected to resolve clinically useful contrast-flow behavior, including contrast arrival, inflow, filling, peak opacification, washout, recirculation, and related hemodynamic events. Prior to reconstruction, the processor 132 may apply one or more preprocessing operations to the biplane angiographic data, such as temporal synchronization, background subtraction, denoising, geometric correction, intensity normalization, motion compensation, or segmentation of regions containing vascular structures of interest.

[0028] In some embodiments, the processor obtains acquisition-geometry data associated with the biplane angiographic system and uses the acquisition-geometry data during registration and reconstruction. The acquisition-geometry data may include one or more of gantry geometry, detector geometry, source-to-image distance, source-to-object distance, detector position, orientation information, synchronization information, or other information indicative of the imaging geometry for a given acquisition run. In some embodiments, the acquisition-geometry data are obtained from metadata associated with the acquired angiographic image files, from a communication bus of the angiographic imaging system, from one or more system encoders, or from combinations thereof. In some embodiments, projection matrices corresponding to the acquired views are determined for each acquisition run based on the acquisition-geometry data. The projection matrices may be used to register the acquired views to the three-dimensional vascular geometry7, to define imaging rays corresponding to projected image locations in the acquired views, and to support back-projection of contrast intensities from the acquired viewsAttorney Docket No.: 011520.02035into the common volume so that the reconstructed four-dimensional angiographic data reflect the run-specific imaging configuration of the biplane angiographic system.

[0029] The three-dimensional vascular geometry may be obtained from computed tomography angiography, cone-beam computed tomography, or the memory storing patient imaging data. In some embodiments, the three-dimensional vascular geometry' is obtained from a prior study that is retrieved from a picture archiving and communication system or another data repository. In some embodiments, the three-dimensional vascular geometry is reconstructed from angiographic data using epipolar reconstruction. For example, corresponding vascular points or vessel centerlines identified in multiple projection views may be used to estimate three-dimensional positions along epipolar constraints, thereby yielding a three-dimensional representation of the vasculature. The resulting geometry may be stored as a voxelized volume, a segmented vascular mask, a centerline model with associated vessel radii, a surface model, or another representation suitable for constraining volumetric reconstruction. In many examples, the geometry is further processed to generate a three-dimensional vascular structure mask that identifies vessel lumen regions within a reconstruction volume. The three-dimensional vascular structure mask may be binary, probabilistic, di stance- weighted, radius-weighted, or otherwise encoded to indicate spatial locations in which contrast is expected or more likely to be present.

[0030] Reconstruction of the four-dimensional angiographic data may’ include aligning each view of the biplane angiographic data with the three-dimensional vascular geometry' to create a registered three-dimensional vascular structure mask. Alignment may account for translation, rotation, scale, detector geometry', gantry' geometry7, field-of-view differences, local deformation, and other factors that cause mismatch between the projection images and the three-dimensional geometry. In some embodiments, aligning each view includes applying one or more rigid transformations, affine transformations, deformable transformations, or combinations thereof. A rigid transformation may adjust position and orientation of the three-dimensional vascular geometry or the projection images. An affine transformation may further account for scale differences, anisotropic scaling, shear, or other linear geometric variation. A deformable transformation may account for local mismatch caused by patient motion, physiological motion, segmentation variation, or modality-dependent distortion. Registration may be performed by maximizing similarity’ between projected vessel structures and vascular features present in the biplane views, such as vessel edges, centerlines, bifurcation points, aneurysm contours, contrast-filled regions, or segmented vessel masks.Attorney Docket No.: 011520.02035

[0031] In some embodiments, aligning each view includes equalizing vascular structures represented in the views by scaling at least one of the views. Relative magnification differences may exist between the two views because of differences in source-to-image distance, source-to-object distance, detector position, or acquisition geometry. To reduce those differences, the processor may estimate a relative magnification between the views based on advancement of contrast represented in the views along a shared axis. For example, a vessel segment or anatomical direction visible in both views may be selected, and the apparent advancement of the contrast front through that segment may be measured in each view over corresponding time points. A ratio between the measured advancement values may be used to derive a scale factor for one of the views so that vascular structures in the two views are more closely equalized in size and represented with a more consistent effective pixel scale. In some implementations, the scale factor is estimated from multiple vessel segments, multiple time points, multiple branch points, or combinations thereof to improve robustness.

[0032] In some embodiments, aligning each view also includes adjusting fields of view of the views by cropping at least one of the views. After scaling, the views may still differ in their represented field of view, even when they depict the same vascular territory. The processor may therefore identify overlapping anatomical content between the views and crop one or both views so that corresponding vascular structures occupy more consistent coordinate locations. In one example, the view having the smaller clinically relevant field of view is used as a reference and the other view is cropped to match it. Cropping may also remove collimator borders, detector regions outside the anatomy of interest, areas that do not intersect the registered three-dimensional vascular geometry, or other image content that is not used for reconstruction.

[0033] In some embodiments, after an initial volumetric estimate of contrast distribution is generated, the processor enforces a continuity condition on the reconstructed contrast distribution. The continuity condition may represent conservation of mass of contrast within the reconstructed vasculature and may constrain the reconstructed contrast distribution to vary continuously across connected vessel regions and over successive time points. In some embodiments, the continuity condition constrains slice-to-slice variation within the reconstruction volume and frame-to-frame variation across the time series so that discontinuous or non-physiologic changes in reconstructed contrast distribution are reduced. The continuity condition may be imposed by solving one or more equations, by applying one or more regularization terms, by iteratively updating the reconstructed volumes, or by combinationsAttorney Docket No.: 011520.02035thereof. In some embodiments, enforcing the continuity condition improves localization of contrast within branching vascular structures and improves temporal consistency of the fourdimensional angiographic data.

[0034] Once the views are aligned and the three-dimensional vascular geometry is registered, the processor may reconstruct the four-dimensional angiographic data by back-projecting contrast intensities in each view of the aligned biplane angiographic data into a common volume. The common volume may be defined by a three-dimensional grid of voxels spanning the vascular region of interest. For a selected time step, pixel intensities from the first view may be projected along corresponding imaging rays into the common volume, and pixel intensities from the second view may be projected along corresponding imaging rays into the common volume. The contributions from the two views may be accumulated, averaged, weighted, or otherwise combined to generate a volumetric estimate of contrast distribution for that time step. Because the reconstruction is constrained by the three-dimensional vascular geometry, the back-projected intensities need not be distributed throughout the full reconstruction space. Instead, the volumetric estimate may be confined to the vascular space identified by the three-dimensional vascular structure mask or weighted according to that mask so that localization of contrast is improved.

[0035] In some embodiments, reconstructing the four-dimensional angiographic data further includes multiplying the common volume by the registered three-dimensional vascular structure mask. That multiplication may suppress contrast assignments in nonvascular regions and retain or emphasize data that falls within the registered vascular space. The multiplication may be performed as a binary masking step, a voxel-wise weighting step, or a confidence-based modulation step. The result may be a spatially corrected common volume in which the back-projected contrast intensities are more consistent with the known three-dimensional vascular anatomy. The back-projection may be applied across the volume and repeated for each time step to generate the four-dimensional angiographic data as a time series of reconstructed three-dimensional volumes. As shown in FIG. 2, a selected axial slice may be followed over multiple time points to illustrate changing contrast distribution within the reconstructed vasculature.

[0036] In some embodiments, reconstructing the four-dimensional angiographic data includes path-length correcting intensity profiles using the three-dimensional vascular geometry. Projection-based angiographic intensities may vary not only with contrast concentration, but alsoAttorney Docket No.: 011520.02035with the effective distance through which the imaging beam traverses contrast-filled vascular lumen. A vessel segment oriented along a projection direction may therefore produce a different intensity response than a segment carrying a similar concentration of contrast but extending across a different effective path length. To account for this effect, the processor may generate a pathlength map from the three-dimensional vascular geometry and use the pathlength map to correct intensity profiles before or during back-projection. In one example, the pathlength map assigns to each voxel, local segment, centerline location, or projected image location an estimated lumen thickness or effective traversal distance through the vessel. The measured projection intensities may then be normalized, scaled, compensated, or otherwise corrected so that the reconstructed volumetric values more closely represent underlying contrast distribution rather than projection-dependent geometric bias. Path-length correction may be performed independently for each view, for each time step, or for each subset of the vascular geometry. In some embodiments, path-length correction improves preservation of vessel opacification, especially in regions with substantial foreshortening or overlap.

[0037] In some embodiments, path-length correction is performed in projection space to generate depth-invariant angiographic image data before reconstruction of the four-dimensional angiographic data. For a selected view, the processor may determine, from the three-dimensional vascular geometry7, an effective vessel traversal distance corresponding to each projected image location and may generate a depth map or pathlength map representing the effective distance traversed by imaging rays through contrast-bearing vascular structures. The processor may then correct the projected image data based on the depth map or pathlength map so that measured intensity7more accurately reflects contrast concentration rather than apparent signal variation caused by vessel depth, overlap, or foreshortening. In some embodiments, the corrected projected image data are used for quantitative angiography, for generation of angiographic parametric imaging values, for reconstruction of the four-dimensional angiographic data, or for combinations thereof. In some embodiments, path-length correction is applied in projection space, in reconstruction space, or in both projection space and reconstruction space.

[0038] The four-dimensional angiographic data may be post-processed using a machinelearning classifier configured to enhance vessel boundaries, reduce artifacts, or improve accuracy of flow representation. In this context, the machine-learning classifier may generate a voxelwise, patch-wise, or region-wise output that distinguishes vessel signal from artifact, refines reconstructed intensity values, estimates confidence in local flow representation, identifies vesselAttorney Docket No.: 011520.02035boundaries, or otherwise improves the quality of the reconstructed data. In some embodiments, the machine-learning classifier receives a preliminary four-dimensional angiographic reconstruction and outputs a refined four-dimensional angiographic reconstruction. In some embodiments, the machine-learning classifier processes a three-dimensional volume at one time step and the output volumes are then assembled into a refined time series. In some embodiments, the machine-learning classifier receives a spatiotemporal block of data extending across multiple time steps and jointly refines the spatial and temporal dimensions of the reconstruction.

[0039] The machine-learning classifier may be a convolutional neural network trained on angiograms having known flow patterns. In some embodiments, the training data are generated from computational fluid dynamics simulations performed on patient-specific vascular geometries. In some embodiments, the training data are generated from virtual angiograms, digital phantoms, in silico projection datasets, annotated clinical angiograms, or high-fidelity’ reference reconstructions. The known flow patterns used for training may represent contrast arrival, filling, peak opacification, washout, recirculation, laminar flow behavior, disturbed flow behavior, aneurysmal vortex structures, branch-dependent timing differences, or other spatial and temporal characteristics of contrast transport. By training on such data, the machine-learning classifier may learn to distinguish physiologically plausible contrast propagation from reconstruction artifacts caused by limited-angle ambiguity, projection overlap, noise, local misregistration, or incomplete filling.

[0040] In some embodiments, the machine-learning classifier includes a convolutional neural network having an encoder-decoder architecture with skip connections. One example is a U-Net architecture in which an encoder path extracts multiscale spatial features from the preliminary reconstruction and a decoder path restores spatial resolution while skip connections presen e fine vessel detail. The encoder path may include repeated convolution operations, nonlinear activation functions, normalization layers, and downsampling operations that enable the network to recognize vessel geometry, contrast gradients, temporal transitions, and artifact patterns over progressively larger receptive fields. The decoder path may include interpolation, transposed convolution, or other upsampling operations that reconstruct refined volumetric output while reintroducing high-resolution vessel features carried by the skip connections. This architecture may be useful for preserving thin distal vessels, vessel edges, bifurcation geometry, aneurysm neck structure, and localized contrast features that may otherwise be blurred or lost during coarse feature extraction.Attorney Docket No.: 011520.02035

[0041] In some embodiments, the machine-learning classifier is implemented as a two-dimensional network that processes slices, projections, or maximum-intensity representations derived from the four-dimensional angiographic data. In some embodiments, the machinelearning classifier is implemented as a three-dimensional network that processes local volumetric neighborhoods within a given time step. In some embodiments, the machine-learning classifier is implemented as a spatiotemporal network that processes both spatial and temporal dimensions together. A spatiotemporal implementation may use three-dimensional convolutions applied across space and time, recurrent layers, temporal attention mechanisms, transformer-based layers, or combinations thereof to enforce continuity of contrast propagation from one time step to the next. Such temporal processing may reduce frame-to-frame flicker, suppress temporally inconsistent artifacts, preser e bolus progression through connected vessels, and improve localization of arrival and washout behavior.

[0042] The machine-learning classifier may receive one or more inputs selected from the preliminary four-dimensional angiographic data, one or more aligned biplane views, the registered three-dimensional vascular structure mask, the pathlength map, vessel centerline data, segmentation masks, local geometry descriptors, projection geometry descriptors, or confidence maps generated during registration or back-projection. In one example, the network input includes the preliminary reconstruction and the registered three-dimensional vascular structure mask so that anatomical priors are available during refinement. In another example, the network input includes the preliminary reconstruction, local temporal neighborhoods, and the pathlength map so that the network may better distinguish a true intensity variation caused by contrast-flow behavior from an apparent variation caused by projection geometry7. The output of the machinelearning classifier may be a refined volumetric intensity field, a residual correction volume that is combined with the preliminary7reconstruction, a vessel-boundary enhancement map. an artifact-suppression map, a confidence-weighted reconstruction, or a combination thereof.

[0043] Training of the machine-learning classifier may be supervised, weakly supervised, self-supervised, or hybrid. In a supervised arrangement, the network may be trained using inputoutput pairs in which the input is a preliminary constrained back-projection reconstruction and the target is a known or estimated reference volume. The loss function may include one or more terms directed to voxel-wise intensity7agreement, structural similarity, boundary7preservation, vessel continuity, temporal consistency, topology preservation, confidence calibration, or agreement with the measured biplane projections. In some embodiments, the loss functionAttorney Docket No.: 011520.02035includes a vessel-aware term that places greater weight on voxels near vessel boundaries or in thin distal branches. In some embodiments, the loss function includes a temporal smoothness term that encourages gradual change in local contrast intensity over successive time steps unless the training data indicate a rapid transition. In some embodiments, the loss function includes a projection-consistency term that penalizes refined reconstructions that do not reproduce the measured biplane projection data when forward projected. In some embodiments, the machinelearning classifier is trained on a dataset spanning different anatomies, flow rates, contrast injection conditions, image noise levels, projection angles, and disease states so that the trained model generalizes across varied clinical settings.

[0044] In use, the machine-learning classifier may enhance vessel boundaries by sharpening transitions between opacified lumen and surrounding tissue, reduce artifacts by suppressing streaking, blurring, local discontinuities, or false-positive opacification, and improve accuracy of flow representation by restoring spatial and temporal detail consistent with know n contrast-flow behavior. For example, in regions where vessels overlap in one projection view, the constrained back-projection may localize contrast to the vascular volume but still leave ambiguity as to the precise distribution of intensity within a branching structure. The machinelearning classifier may learn from training data how such ambiguous patterns typically resolve in three-dimensional space and over time, thereby improving the reconstructed dataset. In regions with incomplete filling, low signal, or local foreshortening, the machine-learning classifier may preserve physiologically plausible progression of the contrast bolus through connected vessels and may reduce sensitivity to local underestimation or overestimation of intensity. In this manner, machine-learning processing may supplement the geometry-constrained back-projection while retaining the anatomical guidance supplied by the registered three-dimensional vascular structure mask.

[0045] The four-dimensional angiographic data may be used to generate voxel-based time-density cur es. A voxel-based time-density curve may represent the variation of reconstructed contrast intensity within a given voxel over time. From the voxel-based timedensity curve, the processor may calculate one or more volumetric angiographic parametric imaging maps. The one or more volumetric angiographic parametric imaging maps may be selected from mean transit time, peak height, area under a time-density curve, time-to-peak, and time-to-arrival. Time-to-arrival may indicate the time at which contrast is first detected in a voxel or reaches a selected threshold. Time-to-peak may indicate the time at which the voxelAttorney Docket No.: 011520.02035reaches peak intensity. Mean transit time may indicate an average residence time or temporal spread of the contrast bolus within the voxel. Peak height may indicate the maximum value of the voxel-based time-density curve. Area under the time-density curve may indicate integrated contrast exposure over time. Because these quantities are determined from reconstructed volumetric data, the resulting parametric maps may localize flow-related metrics within the three-dimensional vascular anatomy rather than only in projection space.

[0046] The four-dimensional angiographic data may be rendered using volume rendering to enable viewing from different angles and time points. Volume rendering may assign opacity and color to reconstructed intensity values so that opacified vascular structures can be displayed as a three-dimensional time-resolved representation. A user may view the reconstructed vasculature from different perspectives, scroll through time points, play back a contrast-flow sequence, rotate the volume, interrogate selected vessel segments, or clip the volume to inspect internal structures. In some embodiments, multiplanar reconstruction, maximum-intensity projection, surface rendering, centerline rendering, or combinations thereof are used in addition to volume rendering. The displayed images may be synchronized with the original biplane views so that a user may compare measured projections and reconstructed volumes at corresponding time points.

[0047] In some embodiments, the reconstructed four-dimensional angiographic data and one or more quantitative parameters derived therefrom are displayed to a clinician at a display or workstation in an angiographic suite during or after image acquisition. The displayed information may include the rendered four-dimensional angiographic data, one or more volumetric angiographic parametric imaging maps, one or more synchronized original biplane views, or combinations thereof. In some embodiments, the display is updated on a run-specific basis so that the reconstructed four-dimensional angiographic data and the one or more quantitative parameters correspond to the particular acquisition run from which the biplane angiographic data were obtained.

[0048] The volumetric angiographic parametric imaging maps may be displayed as three-dimensional maps showing distribution of time-to-arrival, mean transit time, time-to-peak, peak height, area under the time-density curve, or other hemodynamic metrics throughout the vascular volume. The maps may be displayed independently or overlaid on a rendering of the vascular geometry. Cross-sectional interrogation may be performed within selected vascular segments.Attorney Docket No.: 011520.02035such as an internal carotid artery segment, an aneurysm dome, a parent vessel, a branch vessel, or another region of interest, so that local hemodynamic parameters derived from the reconstructed four-dimensional angiographic data may be compared across different spatial locations in the volume.

[0049] In some embodiments, the image-processing apparatus is a workstation, a server, a cloud-based processing node, a dedicated reconstruction engine integrated with an angiographic suite, or another computing environment. The processor may include one or more central processing units, graphics processing units, digital signal processors, field-programmable gate arrays, application-specific integrated circuits, neural processing units, or combinations thereof. The memory may include volatile memory, nonvolatile memory, removable storage, network storage, or combinations thereof. Instructions executed by the processor may be stored on a non-transitory computer-readable medium. The non-transitory computer-readable medium may store instructions that, when executed by one or more processors, cause the one or more processors to obtain biplane angiographic data, obtain a three-dimensional vascular geometry, and reconstruct four-dimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry. In some embodiments, the instructions further cause the one or more processors to align each view of the biplane angiographic data with the three-dimensional vascular geometry' to create a registered three-dimensional vascular structure mask, back-project contrast intensities into the common volume, multiply the common volume by the registered three-dimensional vascular structure mask, path-length correct intensity profiles using the three-dimensional vascular geometry, generate one or more volumetric angiographic parametric imaging maps from the four-dimensional angiographic data, and process the four-dimensional angiographic data using the machine-learning classifier.

[0050] Although the foregoing examples frequently refer to orthogonal biplane views, the same reconstruction framework may be used with non-orthogonal views so long as the geometric relationship between views is known or estimated. Likewise, although many examples refer to cerebral vasculature, the disclosed processing may be applied to other anatomies and imaging protocols. The three-dimensional vascular geometry may be obtained before the angiographic acquisition, during the same procedure, or from previously stored patient data. The machine-learning classifier may be omitted in some implementations, or may be used only for selected refinement stages, such as denoising, vessel-boundary enhancement, artifact reduction, temporal smoothing, confidence estimation, or correction of local reconstruction ambiguities.Attorney Docket No.: 011520.02035The volumetric angiographic parametric imaging maps may include additional parameters derived from the voxel-based time-density curves beyond those expressly identified above. These and other variations may be used while generating four-dimensional angiographic data from biplane angiographic data and a three-dimensional vascular geometry using back-projection constrained by the three-dimensional vascular geometry.

[0051] With reference to FIG. 9, a method 900 for generating a four-dimensional angiographic reconstruction may include obtaining 903 biplane angiographic data. The biplane angiographic data may be obtained 903 from a biplane angiographic system or from a memory storing previously acquired data. The biplane angiographic data may include a first view and a second view that are orthogonal, substantially orthogonal, or separated by another known angular relationship. In some embodiments, the biplane angiographic data comprise digital subtraction angiography image sequences capturing passage of a contrast bolus through a vasculature over a series of time steps. The biplane angiographic data may be obtained together with acquisition-geometry data associated with the biplane angiographic system, such as gantry geometry, detector geometry, source-to-image distance, source-to-object distance, detector position, synchronization information, orientation information, or projection geometry descriptors.

[0052] The method includes obtaining 906 a three-dimensional vascular geometry. The obtained 906 three-dimensional vascular geometry may correspond to the vasculature depicted in the biplane angiographic data. The three-dimensional vascular geometry may be obtained from computed tomography angiography, cone-beam computed tomography, a memory storing patient imaging data, or other techniques for obtaining such geometry. In some embodiments, the three-dimensional vascular geometry is reconstructed from angiographic data using epipolar reconstruction. The three-dimensional vascular geometry may be stored as a voxelized volume, a segmented vascular mask, a centerline model with associated vessel radii, a surface model, or another representation suitable for constraining volumetric reconstruction.

[0053] The method includes reconstructing 9094D angiographic data from the biplane angiographic data and the 3D vascular geometry'. Some embodiments may include one or more of aligning 912 each view of the biplane angiographc data with the 3D vascular geometry', back-projecting 915 into a common volume constrained by a three-dimensional mask, path-length correcting 918 intensity profiles, repeating 921 for each time step to generate four-dimensionalAttorney Docket No.: 011520.02035angiographic data, processing 924 the four-dimensional data with a machine-learning classifier, and generating 927 volumetric angiographic parametric imaging maps.

[0054] The method 900 may include aligning 912 each view of the biplane angiographic data with the three-dimensional vascular geometry' to create a registered three-dimensional vascular structure mask. In some embodiments, aligning each view includes equalizing vascular structures represented in the views by scaling at least one of the views. Scaling may include estimating a relative magnification between the views based on advancement of contrast represented in the views along a shared axis. In some embodiments, aligning each view includes adjusting fields of view of the views by cropping at least one of the views. Alignment may include applying one or more affine transformations, deformable transformations, rigid transformations, or combinations thereof.

[0055] The method 900 may include back-projecting 915 contrast intensities in each view of the aligned biplane angiographic data into a common volume. The common volume may¬ be defined by a three-dimensional grid of voxels spanning the vascular region of interest. Pixel intensities from the first view may be projected along corresponding imaging rays into the common volume, and pixel intensities from the second view may be projected along corresponding imaging rays into the common volume. In some embodiments, the method 900 includes multiplying the common volume by the registered three-dimensional vascular structure mask to constrain the back-projection to vascular regions.

[0056] The method 900 may include path-length correcting 918 intensity profiles using the three-dimensional vascular geometry. In some embodiments, a pathlength map is generated from the three-dimensional vascular geometry and used to correct the intensity profiles before or during the back-projection. The pathlength map may assign to each voxel, local segment, centerline location, or projected image location an estimated lumen thickness or effective traversal distance through the vessel. Path-length correction may improve preservation of vessel opacification, especially in regions with substantial foreshortening or overlap.

[0057] The method 900 may include apply ing the back-projection across the volume and repeating 921 for each time step to generate the four-dimensional angiographic data. The fourdimensional angiographic data may represent a time series of reconstructed three-dimensional volumes depicting contrast propagation through the vasculature. In some embodiments, the method includes enforcing a continuity condition on a reconstructed contrast distribution. TheAttorney Docket No.: 011520.02035continuity condition may conserve mass of contrast across space and time within a reconstructed vasculature and may constrain slice-to-slice variation, frame-to-frame variation, or both.

[0058] The method 900 may include processing 924 the four-dimensional angiographic data using a machine-learning classifier configured to enhance vessel boundaries, reduce artifacts, or improve accuracy of flow representation. In some embodiments, the machinelearning classifier comprises a convolutional neural network trained on angiograms having known flow patterns. The convolutional neural network may include an encoder-decoder architecture with skip connections.

[0059] The method 900 may include generating 927 one or more volumetric angiographic parametric imaging maps from the four-dimensional angiographic data. The one or more volumetric angiographic parametric imaging maps may be selected from mean transit time, peak height, area under a time-density curve, time-to-peak, and time-to-arrival. In some embodiments, generating the one or more volumetric angiographic parametric imaging maps includes generating voxel-based time-density curves from the four-dimensional angiographic data. The method may further include rendering the four-dimensional angiographic data using volume rendering to enable viewing from different angles and time points, and may include causing the four-dimensional angiographic data or one or more quantitative parameters derived therefrom to be displayed at a display or workstation in an angiographic suite.

[0060] With reference to FIG. 10, the present disclosure may be embodied as a method 1000 for correcting projection-based angiographic intensities. The method 1000 may include obtaining 1003 one or more angiographic projection images of a vasculature. The angiographic projection images may be obtained from a biplane angiographic system or from a memory storing previously acquired data. The method 1000 may include obtaining 1006 a three-dimensional vascular geometry corresponding to the vasculature depicted in the angiographic projection images.

[0061] The method 1000 may include determining 1009, from the three-dimensional vascular geometry, a pathlength map representing effective traversal distances through vascular structures for projected image locations. In some embodiments, determining the pathlength map includes forward projecting the three-dimensional vascular geometry to one or more projection planes corresponding to the one or more angiographic projection images.Attorney Docket No.: 011520.02035

[0062] The method 1000 may include correcting 1012 intensity values of the one or more angiographic projection images based on the pathlength map to generate depth-invariant angiographic image data. The depth-invariant angiographic image data may be used to generate one or more quantitative angiographic parameters or to reconstruct four-dimensional angiographic data.

[0063] Other embodiments of methods may comprise or consist of one or more of the features described throughout the present disclosure.

[0064] Embodiments of the present disclosure provides a method and system that leverages existing 3D reconstructions and integrates them with biplane DSA projections. By employing epipolar reprojection techniques and using the 3D volume as a spatial constraint, the method fills each slice of the 3D volume with temporally dynamic data derived from the two views. Additionally, in some embodiments, the use of a convolutional neural network (CNN), trained initially on simulated data of virtual angiograms, refines the reconstructed angiogram, enhancing accuracy and visual quality. This results in a comprehensive 3D temporal visualization of contrast flow, providing clinicians with a powerful tool for neurovascular assessment.

[0065] Implications of the Problem:• Diagnostic Limitations: Without accurate 3D flow information, clinicians may miss critical details of vascular abnormalities, potentially leading to suboptimal treatment decisions.• Surgical Planning Challenges: Effective treatment of neurovascular conditions often requires precise knowledge of blood flow patterns to avoid complications during interventions.• Inefficient Workflow: Reliance on multiple imaging modalities and complex reconstruction methods can slow down the diagnostic process and increase the burden on imaging departments.

[0066] The healthcare industry requires advanced imaging solutions that can seamlessly integrate into existing systems while providing enhanced diagnostic information. The presently disclosed techniques meet this need by:Attorney Docket No.: 011520.02035Utilizing Existing Equipment: Leveraging standard biplane angiographic units without the need for additional hardware.• Improving Patient Outcomes: Providing clinicians with better tools to assess and treat neurovascular diseases, potentially reducing the risk of adverse events.• Streamlining Clinical Processes: Enhancing the efficiency of neurovascular imaging workflows by reducing the need for multiple imaging sessions or extensive computational resources.

[0067] The disclosure pertains to a method and system for reconstructing three-dimensional (3D) temporal blood flow dynamics in neurovascular imaging using angiographic units equipped with C-arm biplane configurations. This technology integrates existing 3D volume reconstructions with two-dimensional (2D) biplane Digital Subtraction Angiography (DSA) projections to produce a refined 3D temporal representation of contrast agent propagation through neurovascular structures. Achieving this involves advanced image coregistration techniques, epipolar reprojection, and refinement using a convolutional neural network (CNN).

[0068] In some embodiments, the system includes three main components: the angiographic unit, the 3D reconstruction source, and the image processing unit. The angiographic unit may be, for example, a standard C-arm biplane angiographic system capable of acquiring simultaneous orthogonal 2D DSA projections. The 3D reconstruction source may be, for example, a pre-acquired 3D volume of the neurovascular anatomy obtained from modalities such as Computed Tomography Angiography (CT A) or Cone-Beam Computed Tomography (CBCT). The image processing unit may be, for example, a computational system equipped with software designed for image coregistration, epipolar reprojection, and CNN-based refinement.

[0069] In some embodiments, the method includes the acquisition of a high-resolution 3D reconstruction of the patient’s neurovascular anatomy using, for example, CTA, CBCT, or other suitable imaging modalities. This 3D volume serves as a spatial anatomical reference for subsequent processing steps. Concurrently, a DSA procedure is performed using a biplane angiographic unit to acquire two simultaneous orthogonal 2D projections of the contrast agent flowing through the neurovascular structures. These projections capture the temporal dynamics of the contrast flow in two different planes.Attorney Docket No.: 011520.02035

[0070] The method includes coregistration of the 3D volume and the 2D projections. For example, affine transformations may be applied to align the 3D volume with the coordinate systems of the two 2D projections. Deformable (non-rigid) registration techniques account for patient movement, anatomical variations, and differences between the modalities, providing that the anatomical structures in the 3D volume correspond accurately to those in the 2D projections. Transformation matrices may be computed to map points from the 3D volume to the 2D projection planes and vice versa.

[0071] Following registration, embodiments of the method may utilize the principles of epipolar geometry to establish correspondences between the two 2D projections. For each point in one projection, the corresponding epipolar line in the other projection is identified where the matching point lies. The registered 3D volume acts as a spatial constraint, limiting the possible locations of matching points and reducing ambiguity. The process fills each slice (voxel layer) in the 3D volume by interpolating the intensity values using data from the two projections. This slice-by-slice data filling approximates the flow of the contrast agent through the anatomy, creating a temporally dynamic 3D volume.

[0072] To enhance the quality of the reconstructed volume, a convolutional neural network (CNN) designed for image reconstruction tasks may be implemented. Capable of handling volumetric data, the network may include encoder-decoder structures with skip connections, such as a U-Net architecture, to preserve spatial resolution. Initially, the CNN is trained on simulated datasets of virtual angiograms where ground truth 3D flow patterns are know n. This training data includes a variety of flow dynamics and anatomical variations to generalize the network's performance. The preliminary reconstructed 3D volume is input into the CNN, which refines the volume by enhancing vessel boundaries, reducing artifacts, and improving the accuracy of flow representation. The output is a high-quality 3D temporal reconstruction of the contrast agent propagation.

[0073] Rendering and visualization may be achieved using volume rendering techniques to visualize the 3D temporal flow of the contrast agent. Interactive tools may be provided for clinicians to view the flow dynamics from different angles and time points. The system may enable quantitative analysis by extracting parameters such as flow- velocities, volumes, and patterns, facilitating a comprehensive evaluation of the neurovascular structures.Attorney Docket No.: 011520.02035

[0074] An example operational workflow begins with patient preparation, where the patient is positioned in the angiographic unit and the pre-acquired 3D volume is made available. During data acquisition, the contrast agent is injected, and biplane DSA projections are acquired as the agent flows through the neurovascular structures. In the processing phase, coregistration between the 3D volume and the 2D projections is performed using affine and deformable transformations. The epipolar reprojection and data filling process is executed to generate the preliminary 3D dynamic volume, followed by CNN refinement to enhance the reconstruction. Finally, in the visualization and analysis phase, the refined 3D temporal volume is rendered for clinical evaluation, allowing clinicians to analyze the blood flow dynamics and identify any vascular abnormalities.

[0075] The uti 1 i ty and advantages of this technology are significant. It provides enhanced visualization by offering a comprehensive 3D temporal representation of blood flow, improving the understanding of complex neurovascular conditions. Diagnostic accuracy is improved as it aids in the detection and characterization of aneury sms, arteriovenous malformations, stenoses, and other vascular pathologies. The technology integrates seamlessly with existing imaging equipment and processes, promoting an efficient workflow without the need for additional hardware. Optimized algorithms and CNN refinement enable real-time or near-real-time processing, making it suitable for intraoperative or diagnostic use.

[0076] Materials and methods used in this technology may include software tools such as image registration algorithms capable of affine and deformable transformations (e.g., Elastix, ANTs), epipolar geometry computation modules to establish point correspondences between projections, and deep learning frameworks like TensorFlow or PyTorch to implement and train the CNN. Hardware requirements may involve standard computing resources for image processing, potentially augmented with GPUs for accelerated CNN computation. Data requirements may include access to high-quality' 3D volume reconstructions and synchronized biplane DSA projections to ensure accurate and reliable results.

[0077] In an aspect, the present disclosure may be embodied as a method for generating a 4D angiographic reconstruction. The method may include obtaining biplane angiographic data and obtaining a 3D vascular geometry. For example, the method may include obtaining biplane angiographic data using a medical imaging system, such as. for example, a C-arm imaging system. In another example, the method may include obtaining the biplane angiographic dataAttorney Docket No.: 011520.02035and / or the 3D vascular geometry from a memory (i.e., a storage device) such as, for example, a Picture Archiving and Communication System (PACS). The views of the obtained biplane angiographic data may be orthogonal to each other.

[0078] The method includes reconstructing 4D angiographic data from the obtained biplane angiographic data. For example, 4D angiographic data may be reconstructed using back-projection constrained by the obtained 3D vascular geometry. For example, reconstructing 4D angiographic data may include aligning each view of the biplane angiographic data with the 3D vascular geometry to create a registered 3D vascular structure mask; back-projecting contrast intensities in each view of the aligned biplane angiographic data into a common volume; multiplying the common volume (i.e., back-projection matrix) by the registered 3D vascular structure mask; and applying the back-projection across the entire volume and repeating for each time step to generate the 4D angiographic data (flow profile as a time series of 3D volumes). In some embodiments, aligning each view of the biplane angiographic data with the 3D vascular geometry may include one or more of equalizing vascular structures in each view of the biplane angiographic data (e.g., scaling the views) and adjusting fields of view of each view of the biplane angiographic data (e.g.. cropping).

[0079] In some embodiments, the method further includes processing the 4D angiographic data using a machine learning classifier. The machine learning classifier may be configured to enhance vessel boundaries, reduce artifacts, and improve the accuracy of flow representation. The machine learning classifier may be trained on angiograms with known flow patterns. In some embodiments, the machine learning classifier is a convolutional neural network. In some embodiments, the machine learning classifier includes encoder-decoder structures with skip connections (e.g, a U-Net architecture, etc.)

[0080] The method may further include generating one or more volumetric API maps from the 4D angiographic reconstruction. For example, the API maps may be selected from mean transit time (MTT), peak height (PH), area under time-density curve (AUC), time-to-peak (TTP), and time-to-arrival (TTA).

[0081] In another aspect, the present disclosure may be embodied as an image processing apparatus for generating a 4D angiographic reconstruction. For example. The apparatus may include a memory (i.e., a storage device) for storing biplane angiographic data and a 3D vascular geometry. The apparatus includes a processor in electronic communication with the memory.Attorney Docket No.: 011520.02035The processor is configured to perform any of the methods described herein. For example, the processor may be configured to reconstruct 4D angiographic data from the obtained biplane angiographic data using back-projection constrained by the obtained 3D vascular geometry.

[0082] In some embodiments, the apparatus further includes a C-arm biplane angiographic system capable of simultaneously acquiring more than one 2D DSA projections. The processor is in electronic communication with the C-arm and configured to operate the C-arm biplane angiographic system to capture the biplane angiographic data and store the biplane angiographic data in the memoiy .

[0083] In some instances, the processor includes one or more modules and / or components. Each module / component executed by the processor can be any combination of hardware-based module / component (e.g., a field-programmable gate array (FPGA), an application specific integrated circuit (ASIC), a digital signal processor (DSP)), software-based module (e.g., a module of computer code stored in the memoiy and / or in the database, and / or executed at the processor), and / or a combination of hardware- and software-based modules. Each module / component executed by the processor is capable of performing one or more specific functions / operations as described herein. In some instances, the modules / components included and executed in the processor can be, for example, a process, application, virtual machine, and / or some other hardware or software module / component. The processor can be any suitable processor configured to run and / or execute such modules / components. The processor can be any suitable processing device configured to run and / or execute a set of instructions or code. For example, the processor can be a general purpose processor, a central processing unit (CPU), an accelerated processing unit (APU), a field-programmable gate array (FPGA), an application specific integrated circuit (ASIC), a digital signal processor (DSP), and / or the like.

[0084] In another aspect, the present disclosure may be embodied as a non-transitory computer-readable medium having stored thereon a program for instructing a processor to perform any of the methods disclosed herein.

[0085] Further Description and Example Embodiments

[0086] 1. IntroductionAttorney Docket No.: 011520.02035

[0087] Intracranial aneurysms and related neurovascular diseases in the Circle of Willis currently lack objective diagnostic tools during image-guided interventions. Endovascular treatments — such as coiling or stenting with flow diverters — rely on imaging to evaluate treatment outcomes and disease severity. Digital subtraction angiography (DSA) remains the primary’ modality for these procedures. Although DSA provides high spatial and temporal resolution, its qualitative interpretation depends on operator experience, which may lead to variability in assessing treatment efficacy and disease progression.

[0088] Quantitative angiography (QA) has emerged as a complementary approach to standard imaging, providing objective metrics that quantify contrast flow patterns strongly correlated with underlying hemodynamics. QA has demonstrated utility in analyzing neurovascular diseases and predicting treatment efficacy. A significant advancement in this field is angiographic parametric imaging (API), which extracts discrete hemodynamic parameters from time-density curves (TDCs) at every’ pixel in an angiographic sequence (Sec. 2.4). These parameters enable quantitative mapping of underlying hemodynamics, yielding further insights during aneurysm diagnosis and treatment prognosis. Despite its promise, API's application is constrained by the two-dimensional (2D) nature of DSA, limiting its ability to resolve the inherent three-dimensional (3D) complexify of contrast flow phenomena.

[0089] Errors and artifacts introduced by overlapping vascular structures and the lack of depth information in 2D dynamic imaging emphasize the need for advanced methodologies capable of reconstructing three-dimensional flow dynamics. Recent advancements in computational modeling, particularly the use of computational fluid dynamics (CFD), have provided robust tools for generating high-fidelity, time-resolved datasets that can serve as ground truth for validating new imaging techniques. By leveraging patient-specific vascular geometries, CFD simulations offer a detailed understanding of contrast flow dynamics, paving the way' for innovative approaches to QA.

[0090] The limitations of current quantitative approaches were further evaluated via comparison to quantitative metrics derived using four-dimensional (4D) CFD, where a lack of conservation of mass and spatial delocalization led to inconsistencies between standard API representations and true underlying hemodynamic patterns. An additional investigation revealed that pathlength correction, an approach which uses vessel thickness information and a ray-tracing algorithm to calculate and correct for signal variations arising from depth effects rather thanAttorney Docket No.: 011520.02035contrast media propagation. While this development was a step in the right direction, it still could not account for loss of information along the pathlength axis of projection imaging.

[0091] Building on these developments, this study explores a constrained back-projection reconstruction of 4D angiography — integrating 3D spatial data from CTA with high temporal resolution biplane DSA imaging. This methodology addresses the limitations of 2D imaging while adhering to standard clinical protocols. Using CFD-generated ground truth data, we evaluate the accuracy, preservation of functional information and feasibility of this approach, aiming to improve the quantitative analysis of aneurysmal hemodynamics and enhance decisionmaking in neurovascular interventions.

[0092] 2. Methods

[0093] 2.1 Expei ■imental Setup

[0094] Angiographic imaging data was generated in silico using CTA-derived patientspecific internal carotid artery aneurysm (ICA) phantoms within a computational fluid dynamics (CFD) solver (AN SYS Inc., Canonsburg PA). Simulated angiography was used to both precisely control the flow parameters of our angiographic data, and to ensure direct, quantitative comparison was possible between ground truth and reconstructed angiograms, and to avoid tradeoffs in spatial or temporal fidelity associated with C-arm-based 4D angiography protocols, removing confounding factors from ground truth data. We additionally neglect venous circulation using this approach due to computational cost, however this allows more precise visualization and evaluation of pure arterial flow, yielding an idealized dataset which more precisely demonstrates the effectiveness of our reconstruction algorithm.

[0095] First, patient-specific ICA phantoms were imported into ICEM, a CFD mesh generation software. Inlet and outlet boundaries were defined for each model, and simulation parameters consistent with previously reported CFD-based simulated 4D angiography were applied. These parameters included transient, laminar flow simulations solving the incompressible Navier-Stokes equations with a time step of 1 ms (1000 fps) to resolve all unsteady motions in the flow. The fluid's density and viscosity values, approximating blood (1060 kg / m3, 0.0035 Pa-s) and contrast media (1190 kg / m3, 0.0063 Pa-s), were defined at physiological temperature (37°C). Using the passive scalar method, tracer fluid was labeled at the arterial inlet for 1 second to generate a 4D dynamic angiogram with a one second contrastAttorney Docket No.: 011520.02035injection. This approach allowed 1:1 correlation of underlying hemodynamic conditions to tracer flow profdes. Temporal coverage captured inflow and outflow dynamics within the vessel. This methodology was repeated for three intracranial aneurysm models with inlet velocities of 25 cm / s, 35 cm / s, and 45 cm / s, resulting in nine 4D angiography simulations with a temporal resolution of 1000 fps. Variation in inlet velocity while controlling for vascular anatomy allowed isolated comparison of trends in API metrics to underlying blood flow trends.

[0096] To convert the 4D simulations into 2D biplane, dynamic angiograms, a conebeam projection geometry was simulated in ASTRA. Frontal and lateral views were configured at a 90-degree angle to provide perpendicular projections. To test our ability to align biplane images (Sec. 2.2), the source-to-image distance (SID) was set at 105 cm for the frontal view and 110 cm for the lateral view. The source-to-object distance (SOD) varied between 75 cm in the frontal view and 80 cm in the lateral view to create magnification differences. A pixel pitch of 0.194 mm was used for both views to replicate typical C-arm imaging configurations.

[0097] Once these datasets were generated, we applied our constrained back-projection algorithm to reconstruct 4D angiographic data and assessed its quantitative capabilities with a 3D API analysis. The workflow is algorithm is summarized in FIG. 1 while subsequent sections detail each step.

[0098] 2.2 Data Alignment

[0099] An advantageous step in successful constrained back-projection is alignment of both biplane DSA views with a common 3D vascular mask. This may first include equalization of the representation of vascular structures in both biplane views via standardization of the pixel size in each imager. Though we cannot determine pixel size directly without a calibration object, it is possible to provide that the pixel size of one image is the same as the other by estimating the relative magnification of the vessel in each image.

[0100] To accomplish this relative magnification estimation, we utilize the shared axis between the biplane views to compare transit of contrast in the axial direction, as described in our previous work. Once the respective images are scaled to the same pixel pitch (which is known for each detector), remaining discrepancies in this measurement are due to relative magnification differences. Taking the ratio of these measurements yields a scaling factor that can be applied to the pixels of one image system to effectively equalize pixel sizing (Eq. 1).Attorney Docket No.: 011520.02035Where p' is the pixel pitch of the primed detector matrix, and I and I' are the measured advancement of contrast between two frames from the unprimed and primed image systems, respectively. If needed, the scaling factor could be estimated from a collection of such comparisons, to improve the robustness of the estimation.

[0101] Since single pixels represent the same physical distance in each imager after rescaling, the only remaining discrepancy between the two systems is the FOV. We use another previously developed algorithm to equalize the axial fields of view (FOVs) of both imagers, which ensures the axial position of the vessel is represented by the same coordinates in both systems. The distance between the highest axial point of contrast and the bottom of the image frame is compared and equalized between views at corresponding time points. To ensure all axial points in the image are matched, whichever imager has a smaller FOV is used as the reference, and the other image is cropped accordingly.

[0102] Once biplane imagers are aligned, the 3D volume of the vascular structures of interest is incorporated. This can either be obtained directly from the angiography data via epipolar reconstruction or from a previously acquired CT angiography (CTA). In the latter case, the volume may be registered to both biplane views prior to 4D reconstruction. To test this registration robustly, a cone beam CT (CBCT) acquisition, and subsequent volumetric reconstruction, was simulated for each model using ASTRA. A binary mask of the vasculature is generated from this volumetric reconstruction. Subsequent rigid registration of this 3D mask to 2D masks from both biplane views is facilitated by simpleElastix, following a previously developed protocol for 2D to 3D image registration.

[0103] 2.34D Angiographic Reconstruction

[0104] After geometric correlation of contrast flow information from both views and the known, static 3D vascular structure, it is possible to estimate a 4D angiogram, such that the 3D flow profile originally captured in each projection view is reconstructed into a series of time-resolved 3D volumes.

[0105] Using the techniques described in Section 2.2 to ensure both projections are geometrically equivalent, we first back-project the contrast intensities in each image into aAttorney Docket No.: 011520.02035common volume with the same dimensions as the ground truth CFD data. We then multiply this back-projection matrix by the registered 3D vascular structure mask (also the same size as the ground truth CFD data), spatially correcting the contrast profiles and improving localization of the contrast data.

[0106] Additionally, intensity profiles are pathlength corrected using the 3D mask during this step, which has demonstrated an ability to better preserve true contrast densities in previous studies. This constrained back-projection technique is applied across the entire volume, and repeated for each time step, yielding a 4D angiogram with the same dimensions as the ground truth 4D angiograms generated using CFD, demonstrated in FIG. 2. To determine how closely this reconstructed angiogram aligns with ground truth 4D CFD data, the two datasets were compared via mean squared error (MSE).

[0107] 2.4 Angiographic Parametric Imaging (API)

[0108] Angiographic parametric imaging (API) is a form of quantitative angiography which parameterizes pixelwise time-density curves (TDCs) and reports metrics such as time-to-peak (TTP), mean transit time (MTT), time-to-arrival (TTA), peak height (PH) and area under the time-density' curve (AUC), shown in FIG. 3. Though these metrics are typically calculated for each pixel in projection angiography data, it is also possible to generate voxel-based TDCs, allowing this analysis to be translated to volumetric flow patterns. To assess the functionality' of our reconstructed 4D angiograms to provide quantitative information, we perform an API analysis on both the reconstructed 4D data, and the ground truth 4D CFD-generated data. These resultant, identically-sized volumetric API maps are compared voxel-wise across datasets with such metrics as mean absolute error (MAE), MSE and mean absolute percentage error (MAPE).

[0109] 3. Results

[0110] 3.1 4D Angiographic Reconstruction[OHl] For each model, several volumes throughout the time series are displayed in FIG. 4, which shows the inflow of contrast through each model. To represent the 3D structure effectively in a 2D figure, the volume is shown from several different angles throughout the sequence. The MSE between reconstructed volumes and ground truth 4D CFD data, averagedAttorney Docket No.: 011520.02035across all time-steps and across all velocities, is 0.013, 0.004 and 0.0043 for Ml, M2 and M3, respectively. Table 1 shows the MSE as a function of velocity for each of these models.Table 1: Quantitative comparison between reconstructed 4D angiograms and ground truth CFD simulations. Each MSE measurement represents the error across all time steps for a_ specific inlet velocity _Model Inlet Velocity (cm / s) MSE25 0.016Ml 35 0.01345 0.0125 0.005M2 35 0.00445 0.00325 0.006M3 35 0.00445 0.003

[0112] 3.2 Angiographic Parametric Imaging (API) Analysis

[0113] API maps generated from 4D angiographic reconstructions of model Ml are displayed in FIG. 5. The parameters are quantitatively compared to those generated from ground truth CFD simulations in Table 2. From the table, we observe strong agreement across all parameters, with the intensity-based parameters (PH and AUC) showing the best agreement. To further compare the volumes, FIGS. 6 and 7 show a cross-sectional comparison of API results within the inlet artery and aneurysm in Ml (respectively), generated from the two respective datasets.Table 2: Quantitative comparison between API results generated from 4D reconstructed angiograms and ground truth CFD-simulated angiograms at varying blood velocities, including mean absolute error (MAE), mean square error (MSE), and mean absolute percent error (MAPE). For reference, the average magnitude of _ each parameter in the ground truth API maps is reported (GT Mean). _API Results: 4D Reconstruction vs Ground Truth Simulated Angiograpy Model Velocity7(cm / s) API Parameter MAE MSE MAPE GT Mean TTP 0.094 0.026 9.224 0.029 MTT 0.047 0.005 5.014 0.023 25 TTA 0.056 0.014 14.367 0.007PH 0.047 0.006 6.458 0.024 AUC 0.07 0.013 9.66 0.023 TTP 0.086 0.022 9.471 0.027MTT 0.043 0.004 4.963 0.022Attorney Docket No.: 011520.02035TTA 0.04 0.008 14.367 0.005 Ml 35 PH 0.032 0.003 3.633 0.025AUC 0.052 0.007 7.608 0.024 TTP 0.067 0.015 8.672 0.024 MTT 0.035 0.003 4.43 0.02 45 TTA 0.027 0.003 13.157 0.004PH 0.011 0.001 1.136 0.027 AUC 0.023 0.002 2.602 0.026 TTP 0.076 0.048 2.398 0.022 MTT 0.023 0.001 3.055 0.016 25 TTA 0.018 0.003 10.021 0.004PH 0.001 0 0.072 0.021 AUC 0.006 0 0.64 0.02 TTP 0.051 0.025 2.014 0.016 MTT 0.018 0.001 3.117 0.012 TTA 0.013 0.001 9.783 0.003 M2 35PH 0 0 0.034 0.021 AUC 0 0 0.016 0.015 TTP 0.138 0.072 8.349 0.023 MTT 0.011 0 1.469 0.016 45 TTA 0.011 0.003 9.521 0.003PH 0 0 0 0.021 AUC 0.003 0 0.286 0.025 TTP 0.073 0.029 47.427 0.025 MTT 0.023 0.001 3.02 0.019 25 TTA 0.014 0.001 7.526 0.005PH 0.004 0.001 0.434 0.025 AUC 0.004 0.001 0.42 0.025 TTP 0.051 0.015 4.667 0.018 MTT 0.014 0.001 2.529 0.014 TTA 0.009 0 7.246 0.004 M3 35PH 0.004 0.001 0.401 0.025 AUC 0.003 0.001 0.411 0.019 TTP 0.049 0.014 5.118 0.017 MTT 0.011 0 2.047 0.017 45 TTA 0.007 0.001 7.148 0.003PH 0.004 0.001 0.371 0.025AUC 0.003 0.001 0.386 0.019

[0114] 4. Discussion

[0115] We demonstrate that automatic alignment of biplane angiography (Sec. 2.2) can be applied to 4D reconstruction, provided a 3D vascular mask is also correlated with each view,Attorney Docket No.: 011520.02035to generate 4D contrast flow profiles with high temporal resolution. It should be noted that the illustrated automated alignment protocol may be dependent on temporal synchrony between biplane imagers. Fortunately, with our high temporal resolution biplane data, asynchrony between views is quite minimal, meaning the presently disclosed method is valid. At much lower frame rates, less automated techniques of alignment may still be utilized, such as the use of a calibration object, or manual delineation of correspondent points between views. The accuracy of the alignment protocol is also reliant on the assumption that both image systems share a common axial direction (i.e. no cranial or caudal angulation) in order to correlate the relative displacement of contrast media along the axial direction in each view. Misalignment of this axial direction could result in under or over-approximation of the relative pixel sizes of each imager, leading to inaccurate localization of contrast media in subsequent reconstruction steps. However, this could be mitigated using a rigid registration pre-processing step to retrospectively align the images along their axial direction as needed.

[0116] The presently disclosed constrained back-projection approach was also quite successful, with an average MSE of 0.007 across the nine reconstructed 4D angiograms relative to ground truth. This correct localization of contrast density values, as a function of both space and time, was also facilitated by the temporal synchrony between our angiographic acquisitions. Although the accuracy of contrast density localization may be affected by the frame rate of each biplane imager, lower frame rates were not explored as part of this study. The largest sources of error between 4D reconstructions and CFD data were mild foreshortening effects as contrast entered vascular structures which were perpendicular to one biplane view, and sections of the vasculature with heterogeneous filling of contrast (Fig. 8), however, these errors were still quite minimal, particularly for MTT, PH, and AUC.

[0117] The API analysis confirmed the success of our algorithm at temporally resolving volumetric contrast media flow from our biplane data. Intensity-based API parameters were nearly identical between the datasets, which confirms previous reports regarding the benefits of pathlength correction as a pre-processing step for projection-based imaging. Disagreements in temporal API parameters were caused by similar factors as discussed above; vessel foreshortening and incomplete vascular filling can artificially modulate contrast density values as a function of time. For threshold-based, single-timepoint parameters, such as TTP and TTA, this can alter the point at which contrast density is first detected, or where its peak lies, indicated by the elevated error in these parameters in FIG. 7 relative to those in FIG. 6. This indicates thatAttorney Docket No.: 011520.02035other TDC-based parameters which are more robust to these variations may be desired for future 4D reconstructed angiography-based API analyses. This said, previous studies have indicated that MTT, PH and AUC are the three most predictive API parameters for prognosis of aneurysm occlusion, all of which were accurately represented via 4D reconstruction, and region-of-interest-based averaging of API results during assessment of neurovasculature further compensates for inhomogeneity and outliers. Additionally, the strong correlation between API parameters generated from 4D reconstructions and CFD data across many different blood velocities indicates their utility in assessing vascular flow conditions across longitudinal studies. This is duly indicative of the utility of these 4D reconstructions in the assessment of treatment efficacy of endovascular neurointerventions, where API analysis across longitudinal studies has demonstrated prognostic ability. This technique could be used in more elaborate, gradient-based quantitative angiography, where 2D DSA is inadequate to fully capture the 3D hemodynamic phenomena within neurovascular pathologies of interest, to provide detailed 3D velocity mapping.

[0118] This study utilized CFD-generated angiographic data to provide a ground truth 4D dataset to compare to our 4D angiographic reconstructions. There are factors of real angiographic images which may be considered before applying this technique to such data. First, our simulated angiograms are free of quantum mottle and do not factor crosstalk scatter that may¬ be present in the system due to the high frame rate of both image systems. Although this scatter should not influence the alignment and registration steps used to correlate both biplane views to a common 3D vessel mask, the added variance may influence the constrained back-projection, where quantum mottle effects will be populated across the projection axis of both biplane imagers.

[0119] It is also noted that the lack of venous circulation in our CFD ground truth and simulated biplane data. While this allows much more precise evaluation the presently disclosed reconstruction algorithm’s ability to resolve arterial flow in 4D, it may also ignore confounding distal venous signals. These confounding factors, which are prevalent in standard single plane projection angiography, would be effectively resolved through the inclusion of data from a second planar imager. In the event venous circulation still poses an issue, more advanced constraining volumes could be employed, requiring a more precise dynamic mask rather than a static mask, as was used here.Attorney Docket No.: 011520.02035

[0120] Finally, the experimental embodiment used orthogonal biplane data. In the case non-orthogonal views are utilized, the localization of contrast intensities may be diminished slightly, except in the case where a perfectly orthogonal view is along a projection axis with severe vessel foreshortening. This is because, as the angle between imagers diverges from orthogonality, the mutual information in both images increases.

[0121] 5. Conclusions

[0122] This disclosure presents a novel reconstruction technique to temporally resolve 3D contrast media flow profiles from biplane, angiographic data, generating a 4D high resolution angiography dataset. This data qualitatively provides insight regarding 3D flow phenomena, and can be used quantitatively for 3D API analysis, suggesting potential prognostic capabilities of the method in the future. The technique may be useful in neurointerventional suites, both to reduce the need for repeat CTA protocols, and to reduce the need for patient transfer between imaging suites. Implementation of the method may improve visualization and quantitation of the effects of endovascular treatments, further improving patient specificity and standard of care in the clinical setting.

[0123] Key Challenges Addressed:• Limited 3D Flow Visualization: Overcomes the inability of traditional biplane angiography to represent 3D temporal blood flow dynamics.• Integration of Multimodal Data: Bridges the gap between static 3D reconstructions and dynamic 2D projections to create a coherent 3D temporal model.• Computational Efficiency: Provides a method that is feasible for real-time or near-real-time application in clinical settings.Enhanced Diagnostic Capability: Improves the detection and characterization of neurovascular conditions by providing detailed flow information.Attorney Docket No.: 011520.02035

[0124] The presently disclosed technology enables several innovative products and services.• Advanced neurovascular imaging systems that provide real-time 3D temporal visualization of neurovascular contrast flow using existing C-arm biplane angiographic units. This enhances diagnostic capabilities and surgical planning for hospitals, clinics, radiologists, neurosurgeons, and interventional neuroradiologists by offering detailed visualization of blood flow dynamics.• Creation of 3D flow visualization tools, either standalone or integrated, that visualize 3D flows of contrast agents in real time. Radiologists, cardiologists, vascular surgeons, and medical educators can use these tools to improve understanding of vascular pathologies, aiding in both diagnosis and education.• Interventional planning systems to assist neurosurgeons, interventional radiologists, and surgical planners in simulating the effects of procedures on blood flow, enhancing patient outcomes by allowing clinicians to anticipate and mitigate risks associated with surgical interventions.• Educational and training platforms using interactive software that employs 3D temporal reconstructions to teach neurovascular anatomy and physiology.Medical schools, training hospitals, students, and educators benefit from immersive learning experiences that improve comprehension of complex vascular structures and flow dynamics.• Personalized medicine using patient-specific modeling services to tailor treatments based on individual vascular flow characteristics. This enhances treatment efficacy and reduces adverse effects for personalized medicine clinics, oncologists, and cardiologists.• In pharmaceutical research, the disclosed technology aids in visualizing and quantifying drug delivery and distribution within the vascular system.Pharmaceutical companies and clinical research organizations can use this to gain insights into pharmacokinetics and pharmacodynamics, assisting in drug development.Attorney Docket No.: 011520.02035• Augmented Reality (AR) surgical applications can overlay reconstructed 3D flow data onto the patient's anatomy during surgery, providing real-time guidance for surgeons, surgical teams, and operating room technicians. This increases precision and reduces operative risks during procedures.• Regulatory compliance and quality assurance services to ensure imaging data meets regulatory standards for clinical trials and medical device approval, streamlining the approval process for medical device manufacturers, clinical trial coordinators, and regulatory7affairs professionals.• Al-powered diagnostic assistants can be developed using our enhanced imaging data. These Al systems assist in diagnosing vascular diseases, increasing diagnostic accuracy and reducing clinician workload by automating image analysis. Healthcare providers, diagnostic labs, and Al healthcare companies are the primary beneficiaries.• Advanced research and development tools for studying vascular diseases and testing new treatments. Academic institutions, biotech companies, and government research agencies can accelerate scientific discovery with high- resolution, dynamic imaging data.• Integration with Electronic Health Records (EHRs) Systems that incorporate 3D flow data into patient EHRs enhance patient records with rich imaging data, improving continuity of care for healthcare providers, EHR vendors, and healthcare IT departments.

[0125] In various embodiments, embodiments of the present disclosure may be used in cardiac imaging for assessing coronary artery flow and heart function; in pulmonary imaging for visualizing airflow and blood flow in the lungs; or other applications. Specific applications include, for example:• Aneurysm Detection and Monitoring: Specialized tools for early detection and monitoring of cerebral aneurysms.• Stroke Risk Assessment: Applications focused on identifying patients at high risk of stroke due to vascular abnormalities.Attorney Docket No.: 011520.02035• Pediatric Neuroimaging: Tailoring the technology for use in children, accounting for their unique anatomical and physiological characteristics.• Integration with decision support Al models

[0126] Although the present disclosure has been described with respect to one or more particular embodiments, it will be understood that other embodiments of the present disclosure may be made without departing from the spirit and scope of the present disclosure.

Claims

1. Attorney Docket No.: 011520.02035What is claimed is:

1. A computer-implemented method for generating a four-dimensional angiographic reconstruction, the method comprising:obtaining biplane angiographic data;obtaining a three-dimensional vascular geometry: andreconstructing four-dimensional angiographic data from the obtained biplane angiographic data using back-projection constrained by the obtained three-dimensional vascular geometry.

2. The method of claim 1, wherein reconstructing the four-dimensional angiographic data comprises aligning each view of the biplane angiographic data with the three-dimensional vascular geometry to create a registered three-dimensional vascular structure mask.

3. The method of claim 2, wherein aligning each view of the biplane angiographic data compnses equalizing vascular structures represented in the views by scaling at least one of the views.

4. The method of claim 3, wherein scaling the at least one of the views comprises estimating a relative magnification between the views based on advancement of contrast represented in the views along a shared axis.

5. The method of claim 2, wherein aligning each view of the biplane angiographic data comprises adjusting fields of view of the views by cropping at least one of the views.

6. The method of claim 2, wherein aligning each view of the biplane angiographic data with the three-dimensional vascular geometry comprises applying one or more affine transformations, deformable transformations, or rigid transformations.

7. The method of claim 2, wherein reconstructing the four-dimensional angiographic data comprises back-projecting contrast intensities in each view of the aligned biplane angiographic data into a common volume.

8. The method of claim 7, wherein reconstructing the four-dimensional angiographic data further comprises multiplying the common volume by the registered three-dimensional vascular structure mask.Attorney Docket No.: 011520.020359. The method of claim 8, wherein reconstructing the four-dimensional angiographic data further comprises applying the back-projection across the volume and repeating for each time step to generate the four-dimensional angiographic data.

10. The method of claim 1, wherein reconstructing the four-dimensional angiographic data comprises path-length correcting intensity profdes using the three-dimensional vascular geometry.

11. The method of claim 10, further comprising generating a pathlength map from the three-dimensional vascular geometry and using the pathlength map to correct the intensity profdes before or during the back-projection.

12. The method of claim 1, wherein the biplane angiographic data comprises orthogonal views.

13. The method of claim 1, further comprising obtaining acquisition-geometry data associated with a biplane angiographic imaging system that acquired the biplane angiographic data; and reconstructing four-dimensional angiographic data is further based on the acquisition-geometry data.

14. The method of claim 13, wherein the biplane angiographic data and the acquisition-geometry data are obtained from a C-arm biplane angiographic system.

15. The method of claim 14, wherein the acquisition-geometry data comprise C-arm orientation data and table-position data.

16. The method of claim 13, wherein the acquisition-geometry data comprise one or more of gantry geometry, projection geometry descriptors, detector geometry, source-to-image distance, source-to-object distance, detector position, synchronization information, or orientation information associated with the biplane angiographic imaging system.

17. The method of claim 13, wherein reconstructing the four-dimensional angiographic data comprises using the acquisition-geometry data to register the biplane angiographic data to the three-dimensional vascular geometry.

18. The method of claim 13, wherein reconstructing the four-dimensional angiographic data comprises using the acquisition-geometry data during back-projection of contrast intensities into a common volume.Attorney Docket No.: 011520.0203519. The method of claim 13, further comprising causing the four-dimensional angiographic data or one or more quantitative parameters derived therefrom to be displayed at a display or workstation in an angiographic suite for direct interpretation.

20. The method of claim 13, wherein the acquisition-geometry data are obtained from metadata associated with one or more angiographic image files, from a communication bus of the biplane angiographic imaging system, from one or more encoders of the biplane angiographic imaging system, or combinations thereof.

21. The method of claim 13, wherein reconstructing the four-dimensional angiographic data comprises determining one or more projection matrices for a particular acquisition run from the acquisition-geometry data and using the one or more projection matrices to register the biplane angiographic data to the three-dimensional vascular geometry.

22. The method of claim 1, wherein the biplane angiographic data comprise first and second views separated by a known, determined, or estimated angular relationship.

23. The method of claim 1, wherein reconstructing the four-dimensional angiographic data further comprises enforcing a continuity condition on a reconstructed contrast distribution.

24. The method of claim 23, wherein the continuity condition conserves mass of contrast across space and time within a reconstructed vasculature.

25. The method of claim 23, wherein enforcing the continuity condition comprises constraining slice-to-slice variation, frame-to-frame variation, or both slice-to-slice variation and frame-to-frame variation in the reconstructed contrast distribution.

26. The method of claim 1, wherein the three-dimensional vascular geometry is obtained from computed tomography angiography, cone-beam computed tomography, or a memory storing patient imaging data.

27. The method of claim 26, wherein the three-dimensional vascular geometry is reconstructed from angiographic data using epipolar reconstruction.

28. The method of claim 1, further comprising processing the four-dimensional angiographic data using a machine-learning classifier configured to enhance vessel boundaries, reduce artifacts, or improve accuracy of flow representation.Attorney Docket No.: 011520.0203529. The method of claim 28, wherein the machine-learning classifier comprises a convolutional neural network trained on angiograms having known flow patterns.

30. The method of claim 29, wherein the convolutional neural network comprises an encoderdecoder architecture with skip connections.

31. The method of claim 1, further comprising generating one or more volumetric angiographic parametric imaging maps from the four-dimensional angiographic data, the one or more volumetric angiographic parametric imaging maps comprising quantitative hemodynamic information for direct interpretation or further processing.

32. The method of claim 31, wherein the one or more volumetric angiographic parametric imaging maps are selected from mean transit time, peak height, area under a lime-density curve, time-to-peak, and time-to-arrival.

33. The method of claim 31, wherein generating the one or more volumetric angiographic parametric imaging maps comprises generating voxel-based time-density curves from the fourdimensional angiographic data.

34. The method of claim 1, further comprising rendering the four-dimensional angiographic data using volume rendering to enable viewing from different angles and time points.

35. The method of claim 34, wherein the rendered four-dimensional angiographic data are displayed in synchronization with one or more original biplane views at a display or workstation in the angiographic suite.

36. The method of claim 34, wherein the rendered four-dimensional angiographic data are displayed in synchronization with one or more original biplane views at a display or workstation in an angiographic suite.Attorney Docket No.: 011520.0203537. A computer-implemented method for correcting projection-based angiographic intensities, the method comprising:obtaining one or more angiographic projection images of a vasculature;obtaining a three-dimensional vascular geometry corresponding to the vasculature; determining, from the three-dimensional vascular geometry, a pathlength map representing effective traversal distances through vascular structures for projected image locations; andcorrecting intensity values of the one or more angiographic projection images based on the pathlength map to generate depth-invariant angiographic image data.

38. The method of claim 37, wherein determining the pathlength map comprises forward projecting the three-dimensional vascular geometry to one or more projection planes corresponding to the one or more angiographic projection images.

39. The method of claim 37, wherein the depth-invariant angiographic image data are used to generate one or more quantitative angiographic parameters.

40. The method of claim 37, wherein the depth-invariant angiographic image data are used to reconstruct four-dimensional angiographic data.

41. An image-processing apparatus for generating a four-dimensional angiographic reconstruction, comprising:a memory configured to store biplane angiographic data and a three-dimensional vascular geometry; anda processor in electronic communication with the memory, the processor configured to reconstruct four-dimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry.

42. The image-processing apparatus of claim 41, wherein the processor is further configured to align each view of the biplane angiographic data with the three-dimensional vascular geometry to create a registered three-dimensional vascular structure mask.Attorney Docket No.: 011520.0203543. The image-processing apparatus of claim 42, wherein the processor is configured to:back-project contrast intensities in each view of the aligned biplane angiographic data into a common volume;multiply the common volume by the registered three-dimensional vascular structure mask;andrepeat the back-projection for each time step to generate the four-dimensional angiographic data.

44. The image-processing apparatus of claim 42, wherein the processor is further configured to scale at least one view and crop at least one view to equalize vascular representation and field of view between the views.

45. The image-processing apparatus of claim 41, wherein the processor is further configured to path-length correct intensity profiles using the three-dimensional vascular geometry' during reconstruction of the four-dimensional angiographic data.

46. The image-processing apparatus of claim 41, wherein the processor is further configured to process the four-dimensional angiographic data using a machine-learning classifier configured to enhance vessel boundaries, reduce artifacts, or improve accuracy of flow representation.

47. The image-processing apparatus of claim 41, wherein the processor is further configured to generate one or more volumetric angiographic parametric imaging maps from the fourdimensional angiographic data.

48. The image-processing apparatus of claim 41, further comprising a C-arm biplane angiographic system configured to obtain the biplane angiographic data.

49. The image-processing apparatus of claim 41, wherein the memory’ is further configured to store acquisition-geometry data associated with a biplane angiographic imaging system that acquired the biplane angiographic data, and yvherein the processor is further configured to reconstruct the four-dimensional angiographic data further based on the acquisition-geometry' data.Attorney Docket No.: 011520.0203550. The image-processing apparatus of claim 49, wherein the acquisition-geometry data are obtained from metadata associated with one or more angiographic image files, from a communication bus of the biplane angiographic imaging system, from one or more encoders of the biplane angiographic imaging system, or combinations thereof.

51. The image-processing apparatus of claim 49, wherein the processor is further configured to determine one or more projection matrices for a particular acquisition run from the acquisitiongeometry data and to use the one or more projection matrices to register the biplane angiographic data to the three-dimensional vascular geometry.

52. The image-processing apparatus of claim 41, wherein the processor is further configured to enforce a continuity condition on a reconstructed contrast distribution represented by the fourdimensional angiographic data.

53. The image-processing apparatus of claim 52, wherein the continuity condition conserves mass of contrast across space and time within a reconstructed vasculature.

54. The image-processing apparatus of claim 41, wherein the processor is further configured to cause the four-dimensional angiographic data, one or more volumetric angiographic parametric imaging maps, or both the four-dimensional angiographic data and the one or more volumetric angiographic parametric imaging maps to be displayed at a display or workstation in an angiographic suite.

55. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to:obtain biplane angiographic data;obtain a three-dimensional vascular geometry; andreconstruct four-dimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry.

56. The non-transitory computer-readable medium of claim 55, wherein the instructions further cause the one or more processors to align each view of the biplane angiographic data with the three-dimensional vascular geometry to create a registered three-dimensional vascular structure mask, back-project contrast intensities into a common volume, and multiply the common volume by the registered three-dimensional vascular structure mask.Attorney Docket No.: 011520.0203557. The non-transitory computer-readable medium of claim 55, wherein the instructions further cause the one or more processors to path-length correct intensity profdes using the three-dimensional vascular geometry’.

58. The non-transitory computer-readable medium of claim 55, wherein the instructions further cause the one or more processors to generate one or more volumetric angiographic parametric imaging maps from the four-dimensional angiographic data.

59. The non-transitory computer-readable medium of claim 55, wherein the instructions further cause the one or more processors to process the four-dimensional angiographic data using a machine-learning classifier configured to enhance vessel boundaries, reduce artifacts, or improve accuracy of flow representation.

60. An angiographic imaging system for generating a four-dimensional angiographic reconstruction, comprising:a C-arm biplane angiographic system configured to obtain biplane angiographic data; a memory' configured to store the biplane angiographic data, acquisition-geometry data associated w ith the C-arm biplane angiographic system, and a three-dimensional vascular geometry; anda processor in electronic communication with the memory and the C-arm biplane angiographic system, the processor configured to reconstruct four-dimensional angiographic data from the biplane angiographic data using back-projection constrained by the three-dimensional vascular geometry and based further on the acquisitiongeometry data, and to cause the four-dimensional angiographic data to be displayed at a display or workstation in an angiographic suite.

61. The angiographic imaging system of claim 60, wherein the acquisition-geometry data comprise one or more of gantry geometry, detector geometry, source-to-image distance, source-to-object distance, detector position, synchronization information, orientation information, or projection geometry descriptors associated with the C-arm biplane angiographic system.

62. The angiographic imaging system of claim 60. wherein the acquisition-geometry data are obtained from metadata associated with one or more angiographic image files, from a communication bus of the C-arm biplane angiographic system, from one or more encoders of the C-arm biplane angiographic system, or from combinations thereof.Attorney Docket No.: 011520.0203563. The angiographic imaging system of claim 60, wherein the processor is further configured to determine one or more projection matrices for a particular acquisition run from the acquisitiongeometry data and to use the one or more projection matrices to register the biplane angiographic data to the three-dimensional vascular geometry.

64. The angiographic imaging system of claim 63, wherein the processor is further configured to use the one or more projection matrices to define imaging rays for back-projecting contrast intensities from the biplane angiographic data into a common volume.

65. The angiographic imaging system of claim 60, wherein the processor is further configured to enforce a continuity condition on a reconstructed contrast distribution represented by the fourdimensional angiographic data.

66. The angiographic imaging system of claim 65, wherein the continuity condition conserves mass of contrast across space and time within a reconstructed vasculature and constrains slice-to-slice variation, frame-to-frame variation, or both slice-to-slice variation and frame-to-frame variation in the reconstructed contrast distribution.

67. The angiographic imaging system of claim 60. wherein the processor is further configured to path-length correct intensity profiles using the three-dimensional vascular geometry during reconstruction of the four-dimensional angiographic data.

68. The angiographic imaging system of claim 60. wherein the processor is further configured to generate one or more volumetric angiographic parametric imaging maps from the fourdimensional angiographic data and to cause the one or more volumetric angiographic parametric imaging maps to be displayed at the display or workstation in the angiographic suite.

69. The angiographic imaging system of claim 60. wherein the acquisition-geometry data comprise C-arm orientation data and table-position data.

70. The angiographic imaging system of claim 60. wherein the processor is further configured to cause the four-dimensional angiographic data to be displayed in synchronization with one or more original biplane views obtained by the C-arm biplane angiographic system.

Images