Bedside two-dimensional cardiac ultrasound three-dimensional reconstruction and cardiac function parameter calculation method

Abstract

The present application relates to a kind of bedside two-dimensional heart super three-dimensional reconstruction and cardiac function parameter calculation method.The method obtains high-quality effective frame by multi-strategy quality control, based on left ventricular segmentation and area curve identification ED / ES phase candidate frame;"shared implicit three-dimensional shape-weak pose-geometric prior body-plane constraint three-dimensional Gaussian explicit model" closed loop is constructed, first pose optimization obtains free weak pose, is regularized and is accumulated as geometric prior body, and then train explicit three-dimensional Gaussian model;Explicit model is projected to two-dimensional ultrasound plane in reverse, according to weak label consistency second pose optimization is carried out, and weak pose and geometric prior body are iteratively updated;ED / ES three-dimensional body is finally output, and EDV, ESV, SV, EF, HR and CO are automatically calculated under unified physical grid.The present application enables ordinary bedside two-dimensional heart super video to form three-dimensional modeling and functional parameter calculation link of iterative correction under the condition of no external positioning equipment.

Description

Technical Field

[0001] This invention belongs to the field of medical image processing, specifically relating to a method and system for automatically generating three-dimensional structures of end-diastolic and end-systolic phases from bedside two-dimensional echocardiogram videos and calculating cardiac function parameters. Background Technology

[0002] Bedside transthoracic echocardiography typically outputs two-dimensional grayscale video. Clinicians observe apical four-chamber, apical two-chamber, apical five-chamber, or other commonly used sections, combining this with their experience to determine left ventricular size, wall motion, ejection fraction, and volume status. The two-dimensional Simpson dual-plane method requires obtaining standard A4C and A2C sections as closely as possible and relies on manual or semi-automatic endocardial boundary marking. This method is mature and easily interpreted, but its accuracy is significantly affected by the standard section, apical truncation, section skewness, endocardial boundary clarity, and ED / ES frame selection.

[0003] Existing automated methods mainly include 2D segmentation and area curve methods, geometric assumption methods based on single frames or dual planes, deep learning methods that directly predict EF from 2D video, 3D ultrasound reconstruction methods that rely on 3D probes or external positioning devices, and general 3D reconstruction or 3D Gaussian representation methods based on multi-view images and camera poses. While these methods are valuable in their respective scenarios, they share common difficulties when dealing with bedside 2D echocardiogram videos: ordinary bedside videos typically lack the probe's true six-DOF pose, stable external calibration trajectories, and are affected by factors such as breathing, probe jitter, acoustic window changes, speckle noise, occlusion, and the intrusion of non-target sections between frames.

[0004] Conventional 3D Gaussian splatting typically relies on multi-view images, relatively accurate camera pose, and relatively stable texture observation. Bedside echocardiography, however, involves weak pose sweeps of a limited fan-shaped section within the cardiac region. The images are ultrasound intensity responses rather than ordinary RGB textures, and the morphologies of the ED and ES cardiac chambers differ significantly within the same video. Therefore, directly applying conventional multi-view 3D reconstruction or conventional 3DGS workflows can easily lead to problems such as pose instability, Gaussian float, localized holes, bridging artifacts, responses in non-cardiac regions, and incomparable ED / ES volumes.

[0005] Existing technologies suffer from at least the following drawbacks: First, bedside 2D echocardiography videos lack realistic spatial pose, and each frame's 2D slice cannot be directly placed into a unified 3D coordinate system. Second, the quality of the original frames and the consistency of the slices are insufficient; empty frames, blurred frames, occluded frames, probe drift frames, and non-target slice frames affect subsequent segmentation, phase separation, and reconstruction. Third, while 2D area curves can reflect some changes in cardiac chamber cycles, they cannot directly provide 3D EDV, ESV, and spatial structural differences. Fourth, ordinary 3D Gaussian reconstruction relies on accurate camera models and multi-view textures, making it unsuitable for ultrasound fan-shaped slices, beam directions, and weak pose input. Fifth, randomly initialized 3D Gaussians are prone to producing floating Gaussians, local voids, and incorrectly connected structures under sparse ultrasound slices, narrow-angle sweeps, and strong noise conditions. Sixth, if the reconstruction results of ED and ES are not unified to the same physical grid, volume statistics will be affected by differences in spatial extent, voxel spacing, threshold aperture, and support region. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for bedside two-dimensional echocardiography video three-dimensional reconstruction and automatic calculation of cardiac function parameters without relying on external positioning equipment. By constructing a closed-loop alternating optimization framework of "shared implicit three-dimensional shape - weak pose - geometric prior body - planar constrained three-dimensional Gaussian explicit model", it solves the problems of lack of pose information, large frame quality fluctuation, ED / ES dependence on manual selection, and the incompatibility of ordinary 3DGS with ultrasound characteristics in the prior art.

[0007] This invention provides a method for 3D reconstruction of 2D echocardiogram video and automatic calculation of cardiac function parameters without relying on external positioning equipment. This method ensures input frame availability through multi-strategy quality control, achieves automatic ED / ES phase separation through left ventricular segmentation and area curves, establishes relative sectional spatial relationships through alternating weak pose optimization within the phase, constrains 3D Gaussian initialization and optimization through geometric prior 3D volumes, and achieves comparison of ED / ES 3D structure and functional indicators through a unified physical mesh. Furthermore, the upgraded technical logic of this invention uses weak pose as the core variable of the entire scheme: first, it establishes mutual verification relationships between 2D sections by sharing implicit 3D shapes to obtain weak poses within the phase; then, it constructs geometric prior 3D volumes based on the weak poses and trains an explicit 3D Gaussian model; subsequently, it uses the explicit 3D model to reslice the 2D ultrasound plane for feedback, correcting the weak poses and geometric priors. Thus, the geometric prior is no longer just a one-time initialization result, but an intermediate bridge connecting implicit reconstruction and explicit 3DGS reconstruction; the explicit model is no longer just the output endpoint, but a feedback source for reverse optimization of implicit weak poses.

[0008] The technical solution of the present invention: A method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters includes the following steps: S1: Acquire bedside 2D echocardiogram video and perform basic preprocessing, remove low-quality image frames to obtain retained frames, perform left ventricular segmentation and ED / ES phase separation on the retained frames to obtain a set of in-phase candidate frames; S2: The first alternating optimization is performed using the shared implicit 3D shape function and weak pose to obtain the free weak pose within the phase; S3: Normalize the free weak pose into a continuous planar sweep pose, and construct a geometric prior 3D volume based on the pose; S4: Initialize and train a planar constrained 3D Gaussian explicit model based on the aforementioned geometric prior 3D volume; S5: Back-project the trained explicit model onto the in-phase two-dimensional ultrasound plane, perform a second pose optimization based on weak label consistency, and update the weak pose and geometric prior three-dimensional volume. S6: Repeat steps S2 to S5 until the iteration termination condition is met, output the three-dimensional volumes of end-diastolic (ED) and end-systolic (ES), and calculate cardiac function parameters.

[0009] Further in step S2: the first alternating optimization includes: optimizing the shared implicit 3D shape function Fφ(X) while fixing the pose, so that multiple 2D weak labels remain consistent on the same 3D shape; optimizing the weak pose matrix T(t) of each frame while fixing the shared implicit 3D shape function, so that the 2D cross-section of each frame is aligned with the shared implicit shape; its objective function is... in the formula The loss function represents the two-dimensional weak label consistency loss, and BCE represents the binary cross-entropy loss function. Let these be the homogeneous local ultrasound plane coordinates of the pixel. It is a weak label. For the loss of response uniformity along the ultrasonic thickness direction, This indicates the pose smoothing constraint between adjacent frames. This is the volume regularization term. , and These are the weighting coefficients for each loss term.

[0010] Further in step S3: the geometrically prior three-dimensional volume V (r) Composed of in-phase images and sector-shaped effective regions Overall weight and the normalized position Accumulated.

[0011] use Let X represent the prior response of the geometric prior 3D volume at position X in the 3D space during the r-th round. in Represents the spatial kernel function, Let be the homogeneous coordinates of the pixel center in the local ultrasound plane.

[0012] The further step in step S4, training the planar constrained 3D Gaussian explicit model, includes: based on the geometric prior V (r) (X) Initialize the explicit 3D Gaussian model And it uses ultrasonic plane constraint rendering. , This is the explicit 3D Gaussian model obtained from the r-th training round. These are in-phase two-dimensional ultrasound images. The training process is described by the response of the 3D Gaussian model on the 2D ultrasonic plane as follows: ; For a 2D pixel (u,v), multiple 3D points are sampled along the thickness direction ζ. Each sampling point is first passed through... Mapping to a unified 3D space, then querying the explicit 3D Gaussian model. ,;Aggζ represents the polymerization operation along the thickness direction.

[0013] The further second pose optimization in step S5 includes: resampling the r-th round explicit model back to the in-phase two-dimensional ultrasound plane, and calculating the foreground / background response difference between the explicit model reslicing response and the weak label. : Indicates the foreground area. Representing the background region, the optimal pose perturbation is searched. Update the current weak pose. Used to measure the degree of inconsistency between the explicit model reslicing response and the current weak label M(t). This indicates a poor foreground / background response under this perturbation. To penalize excessive pose perturbations, β and γ are weighting coefficients. The current weak pose T(t) is updated with the optimal perturbation ΔT*(t) to obtain the updated pose. .

[0014] Further in step S6: the cardiac function parameters include end-diastolic volume (EDV), end-systolic volume (ESV), stroke volume (SV), ejection fraction (EF), heart rate (HR), and cardiac output (CO); wherein the three-dimensional weight of ED and ES is sampled onto a unified physical grid, and EDV and ESV are statistically analyzed based on the support region caliber.

[0015] The beneficial effects of this invention are: First, this invention creates a frame-level quality control method that integrates rule constraints, motion stability analysis, and visual semantic filtering, thereby improving the input stability of bedside 2D echocardiogram video before segmentation, phase separation, and 3D reconstruction. Since low-quality frames can cause false peaks and valleys in the area curve and pose jumps, pre-processing quality control can reduce error propagation in subsequent modules.

[0016] Second, this invention achieves automatic ED / ES phase separation through left ventricular segmentation, area curves, cycle intensity, and neighborhood expansion, reducing subjective differences and random errors caused by manually selecting a single frame of ED / ES. Since weak pose optimization is performed only within the same phase, this phase separation step can also reduce the interference of cardiac deformation on pose estimation.

[0017] Third, this invention creates a system that, without external positioning equipment, uses weak labels, fan-shaped structures, shared implicit 3D shapes, and smooth constraints between adjacent frames to estimate relatively weak poses, enabling ordinary bedside 2D echocardiogram videos to have the spatial organization capability for 3D reconstruction. This allows ordinary bedside 2D echocardiogram videos to form an iteratively correctable 3D modeling and functional parameter calculation link without external positioning equipment.

[0018] Fourth, this invention creates a free weak pose regularization into a continuous anglefan plane sweep pose, enabling the two-dimensional ultrasonic section to enter the geometric prior and three-dimensional Gaussian reconstruction process in a more stable and interpretable manner, thereby reducing spatial misalignment caused by local pose abrupt changes.

[0019] Fifth, this invention reduces the risk of floating Gaussians, local voids, and non-cardiac artifacts caused by random initialization under sparse ultrasonic section conditions by constraining the three-dimensional Gaussian initialization and training with geometric prior three-dimensional volume.

[0020] Sixth, this invention creates a closed-loop alternating optimization of implicit shape and explicit 3D Gaussian model, so that weak pose no longer depends solely on 2D image similarity, but can accept reverse correction from explicit 3D model; the corrected weak pose further updates the implicit shape and geometric prior, thereby improving the stability of the cross-sectional spatial organization under conditions without external positioning equipment.

[0021] Seventh, this invention creates a method that uses ultrasonic plane-constrained rendering to adapt a 3D Gaussian representation to a 2D cardiac hypersonic sector input, rather than simply applying a standard RGB camera perspective projection model. This design can limit the Gaussian response to the local ultrasonic plane, the effective sector region, and the beam / thickness sampling range.

[0022] Eighth, this invention creates a method to sample the three-dimensional weight of the two phases ED and ES onto a unified physical mesh, reducing the impact of differences in voxel spacing, spatial range, and threshold aperture on the calculation of functional parameters.

[0023] Ninth, this invention creates a method to estimate heart rate by combining the frequency domain dominant frequency of the area curve and the ED / ES period interval, enabling functional parameters such as SV, EF, and CO to be automatically obtained from the same video sequence, providing a technical basis for bedside dynamic monitoring of cardiac function, critical circulatory assessment, ventricular remodeling research after myocardial infarction, and time-series analysis of septic cardiomyopathy. Attached Figure Description

[0024] Figure 1 Flowchart for alternating weak pose and implicit shape optimization.

[0025] Figure 2 Weak pose estimation and Anglefan normalization results.

[0026] Figure 3 Geometric prior three-dimensional volume results.

[0027] Figure 4 3D feedback volume - pose supervision results.

[0028] Figure 5 Comparison of unified physical grids and functional parameter chart results.

[0029] Figure 6 Maximum intensity projection; the top row shows the enhancement area of ​​ED relative to ES, and the bottom row shows the enhancement area of ​​ES relative to ED. Detailed Implementation

[0030] Example 1: Explanation of technical terms Bedside 2D echocardiography video: refers to a dynamic image sequence acquired by 2D transthoracic echocardiography in a bedside setting, which can be video, DICOM sequence or PNG frame sequence.

[0031] ED: end-diastole, usually corresponding to a cardiac cycle phase with a larger left ventricular volume or area.

[0032] ES: end-systole, usually corresponding to a cardiac cycle phase where the left ventricular volume or area is smaller.

[0033] Weak pose: refers to the relative sectional spatial pose estimated from images, weak labels, and continuity constraints under conditions of lack of external positioning equipment and actual probe pose.

[0034] Anglefan planar sweep pose: refers to regularizing a free weak pose into a fan-shaped planar sweep pose that changes continuously around the principal axis, used for tissue two-dimensional ultrasound sections to enter three-dimensional reconstruction.

[0035] Geometric prior 3D volume: refers to a coarse 3D spatial response volume obtained by accumulating phase frames, sector effective regions, image intensity, and weak poses, used to constrain 3D Gaussian initialization and training.

[0036] Three-dimensional Gaussian representation: refers to a method of representing a three-dimensional structure or intensity field using multiple three-dimensional Gaussian primitives with parameters of center, scale, transparency, and intensity.

[0037] Planar constrained 3D Gaussian reconstruction: refers to a reconstruction method that uses 2D ultrasound plane slices as supervision and optimizes the reconstruction by rendering 3D Gaussian aggregate onto the corresponding ultrasound plane.

[0038] Ultrasonic plane constrained rendering: This refers to an ultrasonic cross-section rendering method that differs from ordinary RGB perspective camera rendering. It aggregates the three-dimensional Gaussian response into a two-dimensional ultrasonic intensity slice based on local ultrasonic plane, effective fan-shaped region, beam direction and thickness sampling.

[0039] Unified physical mesh: refers to a mesh that samples the 3D weights of ED and ES to the same physical coordinate range, voxel spacing and affine size, for use in volume and difference calculations.

[0040] support_mask: refers to a three-dimensional structural support mask generated through thresholding, connected component filtering, morphological processing, and soft support regions, used to unify the statistical caliber of ED / ES volume.

[0041] Overall technical solution: An implicit-explicit closed-loop modeling framework centered on weak pose. The overall concept of this invention is divided into two layers. The first layer is the overall innovation layer, which forms a closed loop by shared implicit 3D shape estimation, weak pose optimization, geometric prior construction, and planar constrained 3D Gaussian explicit reconstruction, enabling the explicit 3D model to back-correct weak pose and geometric prior. The second layer is the module implementation layer, which implements shared implicit 3D shape estimation, in-phase weak pose optimization, geometric prior construction, and planar constrained 3D Gaussian explicit reconstruction respectively. These modules are not isolated but are linked together as an iteratively correctable whole through the core variable of weak pose.

[0042] The technical process of this invention is described in formal steps as follows: Step 1: Acquire bedside 2D echocardiogram video and perform basic preprocessing; obtain ED / ES in-phase candidate frames based on left ventricular segmentation results and area curves. Step 2: Perform the first pose optimization using the shared implicit 3D shape and weak pose to obtain the free weak pose within the phase. Step 3: Normalize the free weak pose into an anglefan continuous sweep pose, and construct a geometric prior 3D volume based on the normalized weak pose; Step 4: Train a planar constrained 3D Gaussian explicit model based on geometric priors; Step 5: Project the explicit model backward onto the in-phase two-dimensional ultrasound plane, perform a second pose optimization based on weak label consistency feedback, and simultaneously update the geometric prior and the next round of explicit model. Step 6: After the iteration termination condition is met, output the ED / ES 3D volume and calculate the functional parameters.

[0043] This process overcomes the limitations of existing methods by addressing the shortcomings of traditional 2D methods, which lack the ability to organize 3D space, the reliance on accurate camera pose in conventional 3DGS methods, and the assumption that the spatial relationships of the cross-sections are already given in ultrasound Gaussian reconstruction methods. This invention obtains the phase in-plane relationship through a first pose optimization, and then performs a second pose optimization through explicit model feedback. This enables bedside 2D echocardiography to achieve an iteratively correctable 3D modeling process even in the absence of external positioning equipment.

[0044] Example 2: The specific implementation of this invention includes the following steps: S1 Basic Preprocessing: This includes quality control, segmentation, and ED / ES phase separation. Basic preprocessing is not the primary focus of this invention; its role is to provide stable input for subsequent closed-loop modeling. Quality control includes rule constraints, motion stability analysis, and visual semantic filtering. Rule constraints are used to remove empty frames, excessively dark or bright frames, and frames with incomplete fan-shaped regions; motion stability analysis is used to identify frames with sudden probe jitter, abnormal structural changes between frames, or significant drift; visual semantic filtering is used to determine whether the current frame contains target heart structure or target cross-sectional information.

[0045] After quality control, left ventricular segmentation or weak label extraction is performed on the retained frames to obtain a left ventricular region mask, and an area curve is formed from the mask area. ED / ES phase separation generates a set of in-phase candidate frames based on the peaks and valleys of the area curve, ED / ES alternation constraints, period intensity, and neighborhood expansion. The key role of this step is to avoid mixing the actual cardiac deformations of ED and ES into the same pose optimization problem.

[0046] S2 shared implicit 3D shape estimation and first pose optimization: For the t-th frame within the same phase, define the weak pose matrix T(t), where s(t) is the scale factor. Let be the rotation matrix and b(t) be the translation vector. A two-dimensional pixel (u,v) is mapped to a unified three-dimensional space via local ultrasonic plane coordinates p(t,u,v,ζ). ; The purpose of the above coordinate transformation formula is to convert the pixel positions in each frame of a two-dimensional ultrasound image into candidate sampling points in a unified three-dimensional space. In the formula, (u,v) represents the pixel coordinates of the two-dimensional image, ζ represents the sampling offset along the thickness direction of the ultrasound plane or approximately the direction of the sound beam, and p(t,u,v,ζ) represents the three-dimensional coordinates of the pixel in the local ultrasound plane coordinate system. A constant 1 is added after p(t) to form homogeneous coordinates, and then multiplied by the weak pose matrix T(t) to obtain the unified three-dimensional coordinates X(t,u,v,ζ). Therefore, this formula is used to establish the mapping relationship between "two-dimensional pixel - local ultrasound plane - unified three-dimensional space," serving as the common coordinate basis for subsequent implicit shape estimation, geometric prior accumulation, and explicit model reslicing feedback.

[0047] The shared implicit 3D shape function is denoted as Fφ(X), representing the probability that a 3D point X belongs to the target cardiac cavity or a related structure. The first pose optimization alternates between Fφ and T(t): optimizing Fφ while keeping the pose fixed ensures that multiple 2D weak labels maintain consistency on the same 3D shape; optimizing T(t) while keeping Fφ fixed ensures that the 2D cross-sections in each frame are aligned with the shared implicit shape. Its objective function can be written as: The first term in the formula This represents the two-dimensional weak label consistency loss. BCE is an abbreviation for Binary Cross Entropy, which represents the binary cross-entropy loss function. Let these be the homogeneous local ultrasound plane coordinates of the pixel. It is a weak label. For the loss of response uniformity along the ultrasonic thickness direction, This indicates the pose smoothing constraint between adjacent frames. This is the volume regularization term. , and These are the weighting coefficients for each loss term. Figure 1 This demonstrates the first pose optimization relationship between the shared implicit 3D shape Fφ(X) and the weak pose T(t), illustrating how multiple in-phase 2D sections corroborate each other on the same implicit cardiac cavity structure. Figure 2 This demonstrates the continuous planar sweep pose formed after the first pose optimization and anglefan normalization. This pose result serves as the spatial basis for subsequent geometric prior construction.

[0048] The objective function is calculated through alternating optimization: first, T(t) is fixed while Fφ is updated, ensuring that multiple in-phase 2D cross-sections are interpreted consistently within the same 3D shape; then, Fφ is fixed while T(t) is updated, allowing each 2D cross-section to actively align with this shared 3D shape. This process is repeated until the weak pose variation and weak label consistency loss stabilize. The practical technical function of this formula is not simply fitting a 2D mask, but rather constraining multiple 2D cross-sections through a shared implicit 3D shape, yielding the first weak pose estimate usable for 3D modeling. Without external positioning equipment, the shared implicit 3D shape serves as an intermediate constraint, completing the first phase-intra-phase weak pose optimization, enabling the 2D cross-sections to acquire relative spatial relationships usable for subsequent 3D modeling.

[0049] The code for constructing the weak pose matrix and mapping the coordinates from 2D pixels to 3D space; import numpy as np def rotation_x(angle_deg): angle = np.deg2rad(float(angle_deg)) c, s = np.cos(angle), np.sin(angle) return np.array([[1, 0, 0], [0, c, -s], [0, s, c]], dtype=float) def compose_pose(angle_deg, scale=1.0, translation=(0, 0, 0)): T = np.eye(4, dtype=float) T[:3, :3] = float(scale) * rotation_x(angle_deg) T[:3, 3] = np.asarray(translation, dtype=float) return T def map_pixel_to_world(u, v, depth_offset, T, apex): p = np.array([u - apex[0], v - apex[1], depth_offset, 1.0], dtype=float) X = T @ p return X[:3] Code corresponding to alternating optimization of shared implicit 3D shape and weak pose: def optimize_implicit_shape_and_pose(frames, masks, init_poses,model): poses = init_poses.copy() for outer in range(NUM_OUTER): # step 1: fix poses, update the shared implicit shape F_phi for _ in range(SHAPE_STEPS): pts, labels = sample_plane_points(frames, masks, poses) pred = model(pts) loss_shape = weak_label_loss(pred, labels) loss_shape += LAMBDA_RAY * ray_consistency(model, pts) loss_shape += LAMBDA_VOL * volume_regularization(model) update_model_parameters(model, loss_shape) # step 2: fix F_phi, update weak poses T(t) for _ in range(POSE_STEPS): pts, labels = sample_plane_points(frames, masks, poses) pred = model(pts) loss_pose = weak_label_loss(pred, labels) loss_pose += LAMBDA_S * adjacent_pose_smoothness(poses) update_pose_parameters(poses, loss_pose) return model, poses S3 Geometric Prior 3D Volume Construction: Free weak poses may exhibit local angle jumps, translational anomalies, and scale drifts, therefore they need to be normalized into continuous Anglefan plane sweep poses. The normalized weak poses preserve the relative spatial relationships of the phase in-plane and allow the 2D fan-shaped planes to be continuously and interpretably incorporated into the 3D mesh. In the r-th round, the geometric prior 3D volume V... (r) Composed of in-phase images and sector-shaped effective regions Overall weight and the normalized position Accumulated results: The purpose of this formula is to accumulate the effective structural information scattered across multiple frames of two-dimensional ultrasonic sections into a regular three-dimensional prior volume. In the formula, Σ represents the prior response at position X in the three-dimensional dimension for the r-th round; t This indicates the accumulation of all candidate frames within the same phase; This represents the effective sector Ω for each frame. f The pixel summation within the range; w(t,u,v) represents the overall weight of the pixel, which can be determined by image intensity, sector mask, frame quality weight and weak label weight; This represents a spatial kernel function used to smoothly diffuse the contribution of a pixel on a two-dimensional cross-section to its neighboring three-dimensional voxels. This represents the position of the pixel center in a unified 3D space under the anglefan pose in the r-th round. The calculation result is: if multiple facets repeatedly support the same structure near the same 3D position, then the position of... The response increases; if a response comes from only a few anomalous frames, it is difficult to form a stable prior.

[0050] The geometric prior is not the final reconstruction result, but rather a bridge connecting the initial pose optimization and explicit 3D Gaussian reconstruction. It is used to define the central sampling region of the Gaussian, initialize the Gaussian transparency and intensity, and reduce floating Gaussians, local voids, and non-target region responses caused by random initialization under sparse ultrasonic section conditions. Figure 3 Only the ED / ES geometric prior 3D volume results are retained, showing the prior space distribution obtained after weak pose and fan-shaped cross-section accumulation. This figure does not include other non-prior volume results, highlighting the bridging role of the geometric prior volume in this invention.

[0051] The code for constructing a 3D volume based on geometric priors using fan-shaped slicing sweeps is as follows: def build_prior_volume(frames, masks, angles, grid_size=320, sigma_vox=0.8): all_points = [] all_values ​​= [] for frame, mask, angle in zip(frames, masks, angles): local_points = pixels_to_local_plane(mask) weights = normalize_intensity(frame, mask) Tfan = compose_pose(angle) world_points = transform_points(local_points, Tfan) all_points.append(world_points) all_values.append(weights) points = np.concatenate(all_points, axis=0) values ​​= np.concatenate(all_values, axis=0) volume = gaussian_voxelize(points, values, grid_size, sigma_vox) return volume This excerpt describes how multiple frames of in-phase two-dimensional ultrasound sections are swept onto a unified three-dimensional mesh according to the anglefan pose, and a geometrically prior three-dimensional volume is formed using a Gaussian kernel or trilinear accumulation.

[0052] S4 Plane-Constrained 3D Gaussian Explicit Reconstruction: Based on geometric prior V (r) (X) Initialize the explicit 3D Gaussian model And it uses ultrasonic plane constraint rendering: , This is the explicit 3D Gaussian model obtained from the r-th training round. These are in-phase two-dimensional ultrasound images. Indicates training, Ω f The effective region of the ultrasound sector. The response of the three-dimensional Gaussian model on the two-dimensional ultrasound plane is expressed as follows: ; This formula is used to explain the calculation method of ultrasonic plane constraint rendering. For a two-dimensional pixel (u,v), multiple three-dimensional points are sampled along the thickness direction ζ. Each sampled point is first processed by... Mapping to a unified 3D space, then querying the explicit 3D Gaussian model. Aggζ represents the aggregation operation along the thickness direction, and the predicted response R(r,t,u,v) of this pixel can be obtained by summation, weighted averaging, or maximum response. This response is only valid within the sector Ω. f The model is compared with the original two-dimensional ultrasound image or weakly labeled image to reflect the fan-shaped boundary and thickness response characteristics of the ultrasound image. The explicit three-dimensional Gaussian model no longer relies on the ordinary RGB perspective camera model, but is adapted to the fan-shaped section input, weak pose sweep and ultrasound plane response of bedside two-dimensional cardiac ultrasound.

[0053] Code for explicit 3D Gaussian reconstruction under geometric prior constraints in a plane: def train_explicit_gaussian_model(prior_volume, frames, poses,sector_mask): gaussians = initialize_gaussians_from_prior( prior_volume, prior_ratio=0.7, threshold=0.03) for step in range(TRAIN_STEPS): image, Tfan = sample_training_frame(frames, poses) pred = render_ultrasound_plane( gaussians = gaussians, pose=Tfan, sector_mask=sector_mask, aggregation_mode="plane_sum", chi2_threshold=7.815) loss = 0.2 * l1_loss(pred, image, sector_mask) loss += 0.8 * ssim_loss(pred, image, sector_mask) loss += 0.005 * shape_prior_penalty(gaussians, prior_volume) update_gaussian_parameters(gaussians, loss) return gaussians This excerpt illustrates that the 3D Gaussian is not randomly initialized, but rather initialized within a geometrically prior region and rendered under supervision on a sector-shaped ultrasonic plane.

[0054] S5 Explicit Model Feedback and Second Pose Optimization: After the r-th round of explicit model training is completed, this invention does not directly use it as the final output, but instead back-projects or reslices it onto the in-phase two-dimensional ultrasound plane, calculates the consistency between the explicit model and the weak label, and feeds back to update the weak pose and geometric prior. This step constitutes the second pose optimization.

[0055] Define the foreground region based on weak labeling. and background area The foreground / background response difference of the explicit model reslicing response is: Indicates the foreground area. Representing the background region, the optimal pose perturbation is searched. Update the current weak pose. The previous term indicates the weakly labeled foreground region. The average response within the range, the latter term representing the response in the background region. The average response within. The larger the value, the better the explicit model can concentrate left ventricular-related structures in the foreground region, rather than diffuse them into the background region.

[0056] Feedback pose perturbation can be obtained through the following objective function: The above two equations are used to complete the second pose optimization. The first equation searches for the optimal perturbation ΔT*(t) among the candidate pose perturbations ΔT: Used to measure the response of the explicit model reslicing to the current weak label. The degree of inconsistency; the smaller this item is, the better. This indicates the difference in foreground / background response under the perturbation. The larger this term is, the better. Therefore, it is added with a negative sign in the objective function. This is used to penalize excessive pose perturbations and avoid unreasonable jumps caused by explicit feedback; β and γ are weighting coefficients. The second equation represents updating the current weak pose T(t) with the optimal perturbation ΔT*(t) to obtain the updated pose. This feedback allows weak poses to no longer rely solely on 2D inter-frame relationships, but to accept back-correction from the explicit 3D model. The updated weak poses are then used to re-optimize the shared implicit 3D shape, construct the next round's geometric prior, and train the explicit model for the (r+1)th round. The process stops when the average pose update magnitude, response difference improvement, or consistency loss decreases below a threshold, or when the maximum number of iterations is reached. Figure 4 This figure illustrates the pose supervision relationship between the ED and ES 3D feedback volumes on the 2D ultrasound plane. It demonstrates that the 3D feedback volume can be re-sliced ​​back into the 2D ultrasound plane and used as feedback for a second pose optimization.

[0057] Table 1 Results of Explicit Model Feedback for Weak Pose Optimization Examples

[0058] Note: Table 1 is only used to illustrate that explicit model feedback can improve weak pose consistency and should not be construed as limiting the scope of protection of the claims, the clinical diagnostic threshold, or the quality of the final model.

[0059] Code for optimal pose perturbation search and pose update under explicit model feedback: def refine_pose_with_explicit_feedback(volume, mask, angle,candidate_deltas): best_delta = 0.0 best_objective = float("inf") for delta in candidate_deltas: response = render_response_from_volume( volume=volume, angle=angle + delta, mask=mask) foreground = mask>0.5 background = build_background_region(mask) D = response[foreground].mean() - response[background].mean() The implementation of this segment according to the current formula is as follows: search for the minimum objective function through candidate pose perturbations, and update the weak pose with the optimal perturbation.

[0060] S6ED / ES Unified Physical Mesh and Functional Parameter Calculation After satisfying the closed-loop iteration termination condition, two three-dimensional volumes, ED and ES, are output. To avoid volumetric statistical deviations between the two three-dimensional volumes due to differences in spatial boundaries, voxel spacing, or threshold aperture, this invention samples the ED / ES three-dimensional volumes onto a unified physical mesh and calculates functional parameters under a unified support region aperture.

[0061] Where EDV is the left ventricular end-diastolic volume, ESV is the left ventricular end-systolic volume, SV is stroke volume, EF is ejection fraction, HR is heart rate, and CO is cardiac output.

[0062] The calculation method for the above functional parameter formula is as follows: First, EDV and ESV are statistically analyzed under a unified physical grid and a unified support region diameter. Then, the stroke volume (SV) is obtained by subtracting ESV from EDV. The ejection fraction (EF) is obtained by dividing SV by EDV. Finally, SV is multiplied by the heart rate (HR) and divided by 1000, and mL / min is converted to L / min to obtain the cardiac output (CO). This calculation must be based on a unified physical grid; otherwise, differences in voxel volume, spatial range, or threshold diameter between ED and ES will lead to volume differences that cannot be directly interpreted as actual contraction changes. Figure 5 It displays graphical results of metrics such as EDV, ESV, SV, EF, HR, and CO under a unified physical grid. Figure 6 The enhancement regions of ED relative to ES and ES relative to ED are shown to illustrate that the differences in the three-dimensional structure of ED / ES can be visually compared in the same physical space.

[0063] This invention uses weak pose as its core, connecting various modules in series. Basic preprocessing provides in-phase and high-quality stable 2D frames; shared implicit 3D shapes complete the first pose optimization; Anglefan regularization makes the weak pose continuous; geometric priors transform the weak pose into 3D supports usable by the explicit Gaussian model; a planar-constrained 3D Gaussian model generates an explicit 3D structure; the explicit model then undergoes a second pose optimization through 2D reslicing supervision. These two pose optimizations together compensate for the lack of external positioning equipment, uncertain sectional relationships, and instability in explicit reconstruction under sparse sectional conditions in bedside 2D echocardiography.

Claims

1. A method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters, characterized in that... Includes the following steps: S1: Acquire bedside 2D echocardiogram video and perform basic preprocessing, remove low-quality image frames to obtain retained frames, perform left ventricular segmentation and ED / ES phase separation on the retained frames to obtain a set of in-phase candidate frames; S2: The first alternating optimization is performed using the shared implicit 3D shape function and weak pose to obtain the free weak pose within the phase; S3: Normalize the free weak pose into a continuous planar sweep pose, and construct a geometric prior 3D volume based on the pose; S4: Initialize and train a planar constrained 3D Gaussian explicit model based on the aforementioned geometric prior 3D volume; S5: Back-project the trained explicit model onto the in-phase two-dimensional ultrasound plane, perform a second pose optimization based on weak label consistency, and update the weak pose and geometric prior three-dimensional volume. S6: Repeat steps S2 to S5 until the iteration termination condition is met, output the three-dimensional volumes of end-diastolic (ED) and end-systolic (ES), and calculate cardiac function parameters.

2. The method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters according to claim 1, characterized in that... Step S2: The first alternating optimization includes: optimizing the shared implicit 3D shape function Fφ(X) while fixing the pose, so that multiple 2D weak labels maintain consistency on the same 3D shape; optimizing the weak pose matrix T(t) of each frame while fixing the shared implicit 3D shape function, so that the 2D cross-section of each frame is aligned with the shared implicit shape; its objective function is... in the formula The loss function represents the two-dimensional weak label consistency loss, and BCE represents the binary cross-entropy loss function. Let these be the homogeneous local ultrasound plane coordinates of the pixel. It is a weak label. For the loss of response uniformity along the ultrasonic thickness direction, This indicates the pose smoothing constraint between adjacent frames. This is the volume regularization term. , and These are the weighting coefficients for each loss term.

3. The method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters according to claim 1, characterized in that... Step S3: The geometric prior three-dimensional volume V (r) Composed of in-phase images and sector-shaped effective regions Overall weight and the normalized position Accumulated.

4. The method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters according to claim 3, characterized in that: use Let X represent the prior response of the geometric prior 3D volume at position X in the 3D space during the r-th round. in Represents the spatial kernel function, Let be the homogeneous coordinates of the pixel center in the local ultrasound plane. According to the method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters as described in claim 1, the training plane-constrained three-dimensional Gaussian explicit model in step S4 includes: based on geometric prior volume V (r) (X) Initialize the explicit 3D Gaussian model And it uses ultrasonic plane constraint rendering. , This is the explicit 3D Gaussian model obtained from the r-th training round. These are in-phase two-dimensional ultrasound images. The training process is described by the response of the 3D Gaussian model on the 2D ultrasonic plane as follows: ； For a 2D pixel (u,v), multiple 3D points are sampled along the thickness direction ζ. Each sampling point is first passed through... Mapping to a unified 3D space, then querying the explicit 3D Gaussian model. , Aggζ represents the polymerization operation along the thickness direction.

5. The method for bedside two-dimensional cardiac ultra-three-dimensional reconstruction and calculation of cardiac function parameters according to claim 1, characterized in that... The second pose optimization in step S5 includes: resampling the r-th round explicit model back to the in-phase two-dimensional ultrasound plane, and calculating the foreground / background response difference between the resliced ​​response of the explicit model and the weak label. : Indicates the foreground area. Representing the background region, the optimal pose perturbation is searched. Update the current weak pose. Used to measure the degree of inconsistency between the explicit model reslicing response and the current weak label M(t). This indicates a poor foreground / background response under this perturbation. To penalize excessive pose perturbations, β and γ are weighting coefficients. The current weak pose T(t) is updated with the optimal perturbation ΔT*(t) to obtain the updated pose. .

6. The bedside two-dimensional cardiac ultra-three-dimensional reconstruction and cardiac function parameter calculation method according to claim 1, characterized in that S6: The cardiac function parameters include end-diastolic volume (EDV), end-systolic volume (ESV), stroke volume (SV), ejection fraction (EF), heart rate (HR), and cardiac output (CO); wherein the three-dimensional weight of ED and ES is sampled onto a unified physical grid, and EDV and ESV are statistically analyzed based on the support region caliber.

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