4D MAP image reconstruction incorporating organ motion

Hodge Decomposition of Single-Cell RNA Velocity

RNA velocity has the ability to capture the cell dynamic information in the biological processes; yet, a comprehensive analysis of the cell state transitions and their associated chemical and biological processes remains a gap. In this work, we provide the Hodge decomposition, coupled with discrete exterior calculus (DEC), to unveil cell dynamics by examining the decomposed curl-free, divergence-free, and harmonic components of the RNA velocity field in a low dimensional representation, such as a UMAP or a t-SNE representation. Decomposition results show that the decomposed components distinctly reveal key cell dynamic features such as cell cycle, bifurcation, and cell lineage differentiation, regardless of the choice of the low-dimensional representations. The consistency across different representations demonstrates that the Hodge decomposition is a reliable and robust way to extract these cell dynamic features, offering unique analysis and insightful visualization of single-cell RNA velocity fields.

Respiratory motion estimation of the liver with abdominal motion as a surrogate

Background: Respiratory‐induced motion (RIM) causes uncertainties in localizing hepatic lesions, which could lead to inaccurate targeting during interventions. One approach to mitigate the problem is respiratory motion estimation (RME), in which the liver motion is estimated by measuring external signals called surrogates.

Methods: A learning‐based approach has been developed and validated to estimate the RIM of hepatic lesions. External markers placed on the human's abdomen were chosen as surrogates. Accordingly, appropriate motion models (multivariate, Ridge and Lasso regression models) were designed to correlate the liver motion with the abdominal motion, and trained to estimate the superior–inferior (SI) motion of the liver. Three subjects volunteered for 6 sessions of such that liver images acquired by magnetic resonance imaging (MRI) were recorded alongside camera‐tracked external markers.

Results and conclusions: The proposed machine learning approach was validated in MRI on human subjects and the results show that the approach could estimate the respiratory‐induced SI motion of the liver with a mean absolute error (MAE) accuracy below 2 mm.

Local incompressible registration for liver ablation surgery assessment

PURPOSE

In liver microwave ablation (MWA) surgery, the ablation area covers the tumor to generate tissue necrosis and treat the cancer. As the liver deforms during the operation, deviation between the target area determined during preoperative planning and the resultant ablation area is inevitable. Therefore, an accurate assessment of tumor coverage is crucial for treatment. Through registration between the pre- and postoperative livers, the ablation area is warped on the preoperative liver for the computation of tumor coverage. However, large deformations between the pre- and postoperative livers are caused by multiple factors, and these diverse deformations make registration a challenging task. The purpose of this paper was to develop an automatic method that can accurately register post- to preoperative livers.

METHODS

In the proposed method, nonrigid deformations caused by respiratory movement and edema are separately considered and estimated by the local incompressible model in the registration of livers. The pre- and postoperative livers are first aligned by a rigid registration based on a convex hull. In the nonrigid registrations, local incompressible constraints are then set on the liver and the ablation area to estimate the deformations caused by respiratory movement and edema, respectively. The concatenation of the rigid and nonrigid deformations is used to warp the ablation area on the preoperative liver.

RESULTS

The proposed method was evaluated using clinical CT datasets from 20 patients. The Dice similarity coefficient (DSC) between the preoperative and warped postoperative livers is 94.35%, the mean surface distance (MSD) between the livers is 1.65 mm, the mean Hausdorff distance (HDD) between the livers is 3.36 mm, and the mean corresponding distance (MCD) between the corresponding landmarks is 1.70 mm. Compared with five other state-of-the-art methods, the proposed method achieves automatic ablation assessment with highly accurate registration.

CONCLUSIONS

The proposed method achieves a high accuracy for registering the livers. The sizes and positions of the ablation area and tumor are accurately compared for the assessment of ablation surgery.

Patient-specific biomechanical model for the prediction of lung motion from 4-D CT images

This paper presents an approach to predict the deformation of the lungs and surrounding organs during respiration. The framework incorporates a computational model of the respiratory system, which comprises an anatomical model extracted from computed tomography (CT) images at end-expiration (EE), and a biomechanical model of the respiratory physiology, including the material behavior and interactions between organs. A personalization step is performed to automatically estimate patient-specific thoracic pressure, which drives the biomechanical model. The zone-wise pressure values are obtained by using a trust-region optimizer, where the estimated motion is compared to CT images at end-inspiration (EI). A detailed convergence analysis in terms of mesh resolution, time stepping and number of pressure zones on the surface of the thoracic cavity is carried out. The method is then tested on five public datasets. Results show that the model is able to predict the respiratory motion with an average landmark error of 3.40 ±1.0 mm over the entire respiratory cycle. The estimated 3-D lung motion may constitute as an advanced 3-D surrogate for more accurate medical image reconstruction and patient respiratory analysis.

The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis

The Helmholtz-Hodge decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.

The Helmholtz-Hodge decomposition--a survey

The Helmholtz-Hodge Decomposition (HHD) describes the decomposition of a flow field into its divergence-free and curl-free components. Many researchers in various communities like weather modeling, oceanology, geophysics, and computer graphics are interested in understanding the properties of flow representing physical phenomena such as incompressibility and vorticity. The HHD has proven to be an important tool in the analysis of fluids, making it one of the fundamental theorems in fluid dynamics. The recent advances in the area of flow analysis have led to the application of the HHD in a number of research communities such as flow visualization, topological analysis, imaging, and robotics. However, because the initial body of work, primarily in the physics communities, research on the topic has become fragmented with different communities working largely in isolation often repeating and sometimes contradicting each others results. Additionally, different nomenclature has evolved which further obscures the fundamental connections between fields making the transfer of knowledge difficult. This survey attempts to address these problems by collecting a comprehensive list of relevant references and examining them using a common terminology. A particular focus is the discussion of boundary conditions when computing the HHD. The goal is to promote further research in the field by creating a common repository of techniques to compute the HHD as well as a large collection of example applications in a broad range of areas.

Building motion models of lung tumours from cone-beam CT for radiotherapy applications

A method is presented to build a surrogate-driven motion model of a lung tumour from a cone-beam CT scan, which does not require markers. By monitoring an external surrogate in real time, it is envisaged that the motion model be used to drive gated or tracked treatments. The motion model would be built immediately before each fraction of treatment and can account for inter-fraction variation. The method could also provide a better assessment of tumour shape and motion prior to delivery of each fraction of stereotactic ablative radiotherapy. The two-step method involves enhancing the tumour region in the projections, and then fitting the surrogate-driven motion model. On simulated data, the mean absolute error was reduced to 1 mm. For patient data, errors were determined by comparing estimated and clinically identified tumour positions in the projections, scaled to mm at the isocentre. Averaged over all used scans, the mean absolute error was under 2.5 mm in superior-inferior and transverse directions.

Four-dimensional tissue deformation reconstruction (4D TDR) validation using a real tissue phantom

Calculation of four‐dimensional (4D) dose distributions requires the remapping of dose calculated on each available binned phase of the 4D CT onto a reference phase for summation. Deformable image registration (DIR) is usually used for this task, but unfortunately almost always considers only endpoints rather than the whole motion path. A new algorithm, 4D tissue deformation reconstruction (4D TDR), that uses either CT projection data or all available 4D CT images to reconstruct 4D motion data, was developed. The purpose of this work is to verify the accuracy of the fit of this new algorithm using a realistic tissue phantom. A previously described fresh tissue phantom with implanted electromagnetic tracking (EMT) fiducials was used for this experiment. The phantom was animated using a sinusoidal and a real patient‐breathing signal. Four‐dimensional computer tomography (4D CT) and EMT tracking were performed. Deformation reconstruction was conducted using the 4D TDR and a modified 4D TDR which takes real tissue hysteresis (4D TDRHysteresis) into account. Deformation estimation results were compared to the EMT and 4D CT coordinate measurements. To eliminate the possibility of the high contrast markers driving the 4D TDR, a comparison was made using the original 4D CT data and data in which the fiducials were electronically masked. For the sinusoidal animation, the average deviation of the 4D TDR compared to the manually determined coordinates from 4D CT data was 1.9 mm, albeit with as large as 4.5 mm deviation. The 4D TDR calculation traces matched 95% of the EMT trace within 2.8 mm. The motion hysteresis generated by real tissue is not properly projected other than at endpoints of motion. Sinusoidal animation resulted in 95% of EMT measured locations to be within less than 1.2 mm of the measured 4D CT motion path, enabling accurate motion characterization of the tissue hysteresis. The 4D TDRHysteresis calculation traces accounted well for the hysteresis and matched 95% of the EMT trace within 1.6 mm. An irregular (in amplitude and frequency) recorded patient trace applied to the same tissue resulted in 95% of the EMT trace points within less than 4.5 mm when compared to both the 4D CT and 4D TDRHysteresis motion paths. The average deviation of 4D TDRHysteresis compared to 4D CT datasets was 0.9 mm under regular sinusoidal and 1.0 mm under irregular patient trace animation. The EMT trace data fit to the 4D TDRHysteresis was within 1.6 mm for sinusoidal and 4.5 mm for patient trace animation. While various algorithms have been validated for end‐to‐end accuracy, one can only be fully confident in the performance of a predictive algorithm if one looks at data along the full motion path. The 4D TDR, calculating the whole motion path rather than only phase‐ or endpoints, allows us to fully characterize the accuracy of a predictive algorithm, minimizing assumptions. This algorithm went one step further by allowing for the inclusion of tissue hysteresis effects, a real‐world effect that is neglected when endpoint‐only validation is performed. Our results show that the 4D TDRHysteresis correctly models the deformation at the endpoints and any intermediate points along the motion path.

PACS numbers: 87.55.km, 87.55.Qr, 87.57.nf, 87.85.Tu

Incompressible deformation estimation algorithm (IDEA) from tagged MR images

Measuring the 3D motion of muscular tissues, e.g., the heart or the tongue, using magnetic resonance (MR) tagging is typically carried out by interpolating the 2D motion information measured on orthogonal stacks of images. The incompressibility of muscle tissue is an important constraint on the reconstructed motion field and can significantly help to counter the sparsity and incompleteness of the available motion information. Previous methods utilizing this fact produced incompressible motions with limited accuracy. In this paper, we present an incompressible deformation estimation algorithm (IDEA) that reconstructs a dense representation of the 3D displacement field from tagged MR images and the estimated motion field is incompressible to high precision. At each imaged time frame, the tagged images are first processed to determine components of the displacement vector at each pixel relative to the reference time. IDEA then applies a smoothing, divergence-free, vector spline to interpolate velocity fields at intermediate discrete times such that the collection of velocity fields integrate over time to match the observed displacement components. Through this process, IDEA yields a dense estimate of a 3D displacement field that matches our observations and also corresponds to an incompressible motion. The method was validated with both numerical simulation and in vivo human experiments on the heart and the tongue.