# Clinical proof of concept of dynamic reconstruction of digital breast tomosynthesis

Matteo Barbieri, Clément Jailin, Laurence Vancamberg, Stéphane Roux

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## To cite this version:

Matteo Barbieri, Clément Jailin, Laurence Vancamberg, Stéphane Roux. Clinical proof of concept of dynamic reconstruction of digital breast tomosynthesis. Physics in Medicine and Biology, 2025, 70 (21), pp.5022. 10.1088/1361-6560/ae134f hal-05327992v2

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PAPER

Clinical proof of concept of dynamic reconstruction of digital breast tomosynthesis

Matteo Barbieri¹,² ID, Clément Jailin²,\* ID, Laurence Vancamberg¹ ID and Stéphane Roux² ID

¹ GE HealthCare, Buc, France

² Université Paris-Saclay, Centrale Supélec, ENS Paris-Saclay, CNRS, LMPS—Laboratoire de Mécanique Paris-Saclay, Gif-sur-Yvette, France

\* Author to whom any correspondence should be addressed.

E-mail: clement.jailin@ens-paris-saclay.fr

**Keywords:** digital breast tomosynthesis, dynamic tomosynthesis, dynamic reconstruction, local reconstruction, 3D motion estimation

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Abstract

**Objective.** Motion artifacts in digital breast tomosynthesis (DBT) are concerning in clinical practice. Although their impact varies, correcting them is crucial to maintain diagnostic performance. This paper presents advances in dynamic reconstruction for DBT, based on a previously proposed phantom-validated dynamic reconstruction methodology. The main contributions include qualitatively and quantitatively validating the methodology on a 212-case clinical database, proving that real texture and more complex kinematics are not a limitation. The introduction of local dynamic reconstruction described here is a fundamental aspect of this success. **Approach.** Building on a validated dynamic reconstruction strategy—combining motion-corrected reconstruction and projection-based digital volume correlation — the focus is on designing clinically tailored kinematic bases and evaluating their performance in local or global reconstructions. Local bases are derived from an incompressibility constraint and initiate the exploration on clinically exploitable bases, while a finite-element mesh supports the full-field correction. **Main results.** Validation of local dynamic reconstruction showed 90.1%–97.5% of cases had reduced loss, with improvements ranging from 11.8% to 15.4%. Kinematic comparisons with manually tracked references showed improvements in 54.6%–75.8% of cases. A preliminary human reader study found a 77.2% preference for dynamic reconstruction in cases where readers agreed. Initial evaluation of global reconstruction showed a 4.2% loss decrease and significant improvement in clinical features. **Significance.** This paper adapts a dynamic reconstruction strategy for DBT to clinical settings, leveraging specific kinematic bases and validating the method on a 212-patient dataset. The approach improves analytical reconstruction metrics, including loss reduction and alignment with manual kinematic references. A human reader study further supports the method, indicating better image quality in dynamically reconstructed volumes, with sharper edges and fewer replication artifacts. Importantly, the global finite-element model provides the first known full-field 3D dynamic reconstruction in breast tomosynthesis.

1. Introduction

Digital tomosynthesis (DTS) is an x-ray imaging technique which was extensively developed in the last three decades (Dobbins III and Godfrey 2003) for applications in breast, Haas et al (2013), Skaane et al (2013), Sharpe et al (2016) thoracic (Langer et al 2016, Ferrari et al 2018, Baratella et al 2023) and orthopedic (Blum et al 2018) care. It is a type of limited-angle computed tomography (CT) imaging technique which usually provides 9–60 projections and has gantry angles of ±25 – 40°. As such, the result of the reconstruction process yields a pseudo-3D visualization of the imaged volume which is exploited for screening and diagnostic purposes.
As in CT, a crucial condition for classical tomosynthesis to deliver exploitable images is that the patient remains still during the projection acquisition process, which is hardly possible when imaging living tissues. The consequence—depending on the amplitude of the motion during the examination—is the appearance of blurred texture and replication artifacts in the reconstructed volumes, which may jeopardize the outcome of the diagnostic process. Unfortunately, patient motion is the most common patient-related artifact in digital breast tomosynthesis (DBT). Possible sources include insufficient breast compression, imperfect breath-hold, heartbeat-induced displacements or soft tissue relaxation during acquisition. If the problem is detected by the technician while the patient is still under examination, a straightforward remediation lies in the retake of the image with proper patient instructions and breast compression. In fact, a paper from Geiser et al at the MD Anderson Cancer Center of the University of Texas states 'Patient motion is the most common reason for repeat views at our facility.' Geiser et al (2011) This claim is further supported by the analysis of technical repeat studies from Martaindale et al which states that on all 452 technical repeat cases collected between April 2017 and December 2018, 253 of them (56.0%) were induced by patient motion. Martaindale et al (2023) The fact that this data is collected on 2D mammographies, ie the equivalent of a 10th of a DBT examination, further highlights the importance of providing an appropriate correction for when the patient is no longer onsite and diagnostic is time-sensitive. These observations demonstrate that breast motion is not anecdotal but represents a frequent and clinically significant limitation of DBT. Retakes are to be reduced not only because they expose the patient to additional radiation, but also because they interrupt the workflow and delay analysis and reporting. Hence, there is a strong need for dedicated correction strategies that can operate retrospectively on the acquired data, even when motion is not visible at once.

Since this problem is already well known in CT imaging, several solutions have been implemented to prevent or correct motion artifacts in patient examinations. They are mostly focused on thoracic imaging and range from acquisition gating (McKinnon and Bates 1981, Lauritsch et al 2006) to 2D projection correction, Eldib et al (2018), 2D/3D strategies, Marchant et al (2011), 3D strategies like projection-based digital volume correlation (P-DVC), Taillandier-Thomas et al (2016), Bouterf (2017), Jailin et al (2021)4D-CBCT (Nassi et al 1982, Li et al 2007) and AI powered (Huang et al 2020, Li et al 2021, 2022). For a more detailed explanation of these techniques and use cases, the reader is referred to previous work from the authors. Barbieri et al (2024a), Barbieri (2025)However, applying these methodologies to DBT is often impossible or not straightforward. For instance, gating does not apply since heartbeat and breathing have low impact on the acquired images. 2D or 2D/3D image corrections are unreliable for resolving small details, which is problematic given that clinical findings in breast are potentially small and the breast does not have a general structure (bones) that can be restored with rigid or elastic registration. An example of the failure of such algorithms was shown in Barbieri et al (2024a). Additionally, transposing 4D-CBCT is inappropriate for breast screening since it would notoriously increase the patient's radiation dose. Finally, while AI motion correction methods have shown their potential in CT images, the lack of data available for both reconstruction and comparative motion/no motion in DBT is too large an obstacle to tackle before achieving full AI dynamic reconstruction on DBT. As previous work showed promising potential for P-DVC-based reconstruction on phantoms, the current paper aims to assess the validity of the method on a more realistic texture and kinematics provided by actual clinical cases. While motion correction is a well-established topic in CT, the DBT setting poses unique challenges: limited number of projections, strongly ill-posed reconstruction, and the absence of large annotated datasets. This motivates the exploration of mechanically-based approaches specifically tailored to breast imaging.

In fact, the limited information embedded in tomosynthesis is a hindrance for the volume reconstruction problem which is notoriously ill-posed and introducing additional degrees of freedom for kinematic correction is difficult. As such, an initial proof-of-concept for P-DVC-based dynamic reconstruction was realized on the CIRS breast imaging phantom BR3D model 020 (Sun Nuclear 2023) in our previous work. Barbieri et al (2024a) Since clinical data has a higher kinematic complexity than phantoms, the idea of limiting the dynamic reconstruction to local areas was exploited to study regions requiring a simpler kinematic description and partial results were presented in Barbieri et al (2024b). This enabled obtaining improved residual norms and better image quality on specific clinical features. As a counterpart, local reconstruction requires particular attention with regards to border artifacts, as they take a larger proportion in the reconstruction area and cannot be ignored. A suggested solution will also be explored in section 2.2.

Building on the previous phantom-based proof-of-concept (Barbieri et al 2024a) and the preliminary application to small clinical regions of interest (Barbieri et al 2024b), this study documents the application of the P-DVC-based dynamic reconstruction in DBT to a large number of DBT. The novelty of this study lies in: (i) the first large-scale clinical validation of dynamic reconstruction in DBT (212 patients,
282 ROIs), (ii) introduction and evaluation of incompressibility kinematic bases, and (iii) the first global finite-element correction on clinical DBT data. By establishing the feasibility of dynamic reconstruction directly on clinical DBT images, this study is intended as a foundation for the integration of dynamic approaches into routine clinical practice. While not yet optimized for workflow or speed, the results demonstrate that dynamic reconstruction can improve image quality in real cases, thereby paving the way for clinical solutions that reduce retakes, radiation dose, and diagnostic uncertainty.

## 2. Methods

### 2.1. Dynamic reconstruction general framework

The classical approach to volume reconstruction from projection images assumes that the source is monochromatic, that the irradiated object is motionless and neglects scattering within the sample. In the following, two orthonormal frames are defined $X = \{x, y, z\}$ and $\Xi = \{\xi, \eta\}$ which respectively pave the volume (of size $n_x \times n_y \times n_z$) and detector plane (of size $n_\xi \times n_\eta$). The negative-log transformed projections are denoted $p$ or $p(\Xi) = \{p_{\theta_i}(\Xi)\}_{i \in [1, n_\theta]}$ of size $(n_\theta \times n_\xi \times n_\eta)$ with $n_\theta$ the number of acquired projections and are assumed to be flatfield-corrected. $\Pi = \{\Pi_{\theta_i}\}_{i \in [1, n_\theta]}$ of size $(n_x \times n_y \times n_z, n_\theta \times n_\xi \times n_\eta)$ is the associated projection operator. Finally, let $\psi$ be a gray value 3D image representing any volume then, the reconstructed volume $f$ is the solution of the problem described by

$$f(\mathbf{X}) = \underset{\psi}{\operatorname{Argmin}} \sum_{i=1}^{i=n_\theta} \|\Pi_{\theta_i}[\psi(\mathbf{X})] - p_{\theta_i}\|^2 = \underset{\psi}{\operatorname{Argmin}} \sum_{i=1}^{i=n_\theta} \|r_i(\psi)\|^2. \quad (1)$$

When the patient moves during the examination, the kinematic fields $U = \{U_i\}_{i \in [1, n_\theta]}$ are added as extra unknowns to the above problem. $f(\mathbf{X} + U_i)$ describes the deformed volume at the time of projection $i$ and $V(\mathbf{X})$ representing the displacement field at position $\mathbf{X}$, the initial reconstruction problem (1) becomes

$$(f(\mathbf{X}), \mathbf{U}) = \underset{\psi, \mathbf{V}}{\operatorname{Argmin}} \sum_{i=1}^{i=n_\theta} \|\Pi_{\theta_i}[\psi(\mathbf{X} + \mathbf{V}_i)] - p_{\theta_i}\|^2 = \underset{\psi, \mathbf{V}}{\operatorname{Argmin}} \sum_{i=1}^{i=n_\theta} \|r_i(\psi, \mathbf{V}_i)\|^2. \quad (2)$$

The detailed algorithm for addressing the dynamic reconstruction process is described in Barbieri et al (2024a) and briefly summarized hereafter. Since dynamic reconstruction is a combined problem of motion estimation and motion-corrected reconstruction, both processes are run iteratively to provide a solution. Given a measured kinematic field, it is possible to reconstruct the corrected volume from the motion-polluted projections using algorithms like McSIRT (Barbieri et al 2024a) or McSART (Rit et al 2009, Chee et al 2019). The motion estimation is performed by the P-DVC framework which is based on the minimization of the norm of projection residual fields under the degrees of freedom provided by a kinematic basis $\Phi$.

In this case, P-DVC aims at producing a displacement field which aligns the projection of the current evaluation of the reconstructed volume $f(\mathbf{X})$ with the original projections, thus minimizing the quantity

$$\mathbf{U} = \underset{\mathbf{V}}{\operatorname{Argmin}} \sum_{i=1}^{i=n_\theta} \|\Pi_{\theta_i}[f(\mathbf{X} + \mathbf{V}_i)] - p_{\theta_i}\|^2. \quad (3)$$

This is performed by a Gauss-Newton scheme after each corrected reconstruction (based on the previously estimated kinematic field) and provides an updated estimation of the kinematic field $U$ and position of the patient at each projection time step.

In addition, this process is performed at several scales to ensure that the linearization performed to solve the motion-estimation problem is valid. The whole process is then summarized in figure 1.

For reproducibility, the motion-corrected reconstruction was stopped after a maximum of 200 iterations or when the relative improvement in residual norm fell below 10%. Multiscale steps were defined with down-sampling factors of 16, 8, 4, 2, and 1. At each scale, the Gauss-Newton solver was run for a maximum of 20 iterations, and regularization weights were empirically set to 0.1, 0.05, and 0.01. These values were found to provide a good trade-off between convergence and computational efficiency in the clinical setting. The process is considered to have reached convergence if the relative improvement (prior and after the last motion-corrected reconstruction) is lower than 30%.
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## 2.2. Local reconstruction

Performing local reconstruction is an efficient way to obtain data on an area of interest but it requires additional precautions. In fact, the size of the reconstruction box should be defined to prevent propagation of truncation artifacts and ensure that the margins are sufficiently large to allow correcting patient motion in the process. Figure 2 shows the respective size of the volume of interest (VOI) (red) and the actual reconstructed volume (green). The size of the ‘optimal recon area’ box should then be increased by a value of $2\alpha$ in each direction to ensure that a motion of at maximum $\alpha$ will be properly processed.

## 2.3. Kinematic bases

The choice of the kinematic basis $\mathbf{\Phi}$ on which the displacement fields $U_j = \sum_{i=1}^{N} u_{ij} \mathbf{\Phi}_j(\mathbf{X})$ are defined is an important part of the dynamic reconstruction process as it describes the types of corrections authorized.

### 2.3.1. Local kinematic bases

Since the analysis is performed on small VOIs, the motion in the axial plane is limited and describing it with translations in the x and y directions has led to the improvement of quantitative and qualitative results, as was previously shown in Barbieri *et al* (2024b). The introduction of additional assumptions, such as considering that the density of breast tissue does not significantly change under compression (i.e. breast tissue is incompressible), enables the inclusion of additional complexity to the description. By modeling the breast as an incompressible Newtonian flow between two plates (the breast support and the compression paddle) enables to define an additional complexity along the breast thickness. In this direction, hierarchically complex kinematic bases are considered from the combination of the three first polynomials (up to second order polynomials in z, conveniently described through the Legendre basis). The first, constant, is the description of a ‘plug’ flow. The second represents a Couette flow (the velocity is zero at one interface and increases linearly with the distance from it) and the third one accounts for a Poiseuille flow (the velocity is zero at both interfaces and varies quadratically between the two).
<figure><img src="image_7.png" /><figcaption>**Figure 3.** Illustration of the 3 types of degrees of freedom defined in the breast thickness.</figcaption></figure>

A representation of the presented basis is provided by figure 3. The three levels of complexity are then
defined as:

* Plug (P): A combination of the *x* and *y* translations, uniform in the height, resulting in 2 degrees of freedom.

* Plug + Couette (PC): A combination of the *x* and *y* translations with a uniform and linear freedom along the height, resulting in 4 degrees of freedom.

* Plug + Couette + Poiseuille (PCP): A combination of the *x* and *y* translations with a uniform, linear and quadratic freedom along the height, resulting in 6 degrees of freedom.

2.3.2. Global kinematic basis

Finite element (FE) meshing is a powerful tool used in computational physics to finely describe vector
fields. General areas of application include fluid dynamics, mechanics and many others. In the present
case, a simplified FE formalism is provided to describe the motion of a tissue element. As a first step,
a set of *N* nodes is created to mesh the inside of an axial slice of the patient, and a set of *B* nodes
describes the border (see figure 11(a) for an example). Then, 2D shape functions are created by quad-
ric interpolation, so that for every interior node, the nodal value is 1 at the node and 0 at all other
nodes. Finally, the 3D shape functions are obtained by extruding the 2D shape functions along the thick-
ness of the breast. As a result, if *x*, *y* motion is allowed, the kinematic basis $\mathbf{\Phi}$ contains 2*N* degrees of
freedom that describe the acceptable motions of the reconstructed volume. The *B* nodes describing the
border were added to ensure boundary conditions in the dynamic reconstruction. An example of the
construction of such basis will be shown in section 3.3.

**2.4. Evaluation metrics**

For comparison purposes, the state-of-the-art SIRT reconstruction method (uncorrected motion) will be called ‘static reconstruction’, as opposed to the ‘dynamic reconstruction’ method developed in this paper.

2.4.1. Analytic metrics

As defined in equation (1), the natural metric to assess the quality of the reconstruction is the norm of the residual fields $||r(f)||$. For a fair comparison, all cases are computed on the same number of reconstruction iterations between the static and dynamic reconstructions.

As the dynamic reconstruction process also provides the estimated displacement fields, it is pos-
sible to evaluate their quality when a reference is available. For this purpose, a manual tracking of the
objects was obtained by GE HealthCare Image quality experts, who manually tracked consistent clin-
ical features throughout projections images, enabling the estimation of a rough 3D position. Let **p**<sub>m</sub> be
the projected coordinates of the moving point and *P* the projection operator that gives the projected
coordinates of a point *X* in the volume. Then the position *X*<sub>e</sub> estimated from the polluted data of the
moving point is given by *X*<sub>e</sub> = Argmin<sub>X</sub> ||**P**[*X*] − **p**<sub>m</sub>||<sup>2</sup>. By reprojecting the position of this estimate, it is
possible to compute the distance between the manually tracked feature in the projection and the pos-
ition of its reprojection, thus providing an initial evaluation of the patient motion. By integrating the
kinematic estimates before the reprojection process, it is then possible to obtain a new position of the
reprojected feature. Hence, for an estimated kinematic field *U*, the comparison between ||**p**<sub>m</sub> − **P**[*X*<sub>e</sub>]||
and ||**p**<sub>m</sub> − **P**[*X*<sub>e</sub> + *U*(*X*<sub>e</sub>)]|| (or the angle-wise version) is an indicator of the quality of the kinematic
estimation process. Figure 4 shows how the projected positions of a moving point relate to the ones of
its estimated 3D position.
<figure><img src="image_8.png" /><figcaption>**Figure 4.** Relation between projections of a moving point (red dots) with respect to the ones of its average position (green dots).</figcaption></figure>

### 2.4.2. *Quantitative metric: Pilot preference study*

The final and most clinically relevant evaluation metric is the visual assessment of improved volume reconstruction quality. The aim is to assess whether the conspicuity of the clinical findings is improved, without compromising the sharpness of the surrounding tissue. To estimate the impact of the local dynamic reconstruction process, a preliminary blind study was performed, and the protocol details are presented hereafter.

From the 282 available VOIs and for the sake of reader time availability, 131 of the most motion-polluted were selected and reconstructed using the *xy*-plug flow basis. They were then ordered randomly and displayed to two readers, with 5+ years of experience in tomography and experimental image-guided measurement techniques. For each identified VOI, two volumes (static and dynamic) are shown to the reader in ImageJ. They are placed side by side, synchronized over the slice number, window width and window level and with a randomized left/right placement. The reader may scroll freely through the volumes in the *z* direction and adapt the brightness/contrast level of the images to determine the focal plane(s) of the object of interest in each of the volumes (it may differ). Given this knowledge, the reader is then prompted to determine which of the volumes displays the better image quality for the clinical finding in the respective focal planes, and does so by selecting the window before confirming. In case of doubt, the opportunity to pass on the case without expressing a preference is also provided by selecting a third window with an 'indecisive smiley'. A visual of the reader prospective for an example case is given in figure 5. The data collected under these conditions was then processed to exclude all the cases where at least one of the readers doubted—as they are believed to be the most unreliable cases to sort in any category (success/fail). Under the same reasoning, cases where no clear strict majority preference is visible are equally excluded as they are deemed unclear. Then, on those remaining cases, the preference ratio between the *dynamic* and *static* is computed.

## 3. Results

### 3.1. Clinical data collection

For the purpose of this study, a total number of 212 patient screening examinations acquired with a GE HealthCare Senographe Pristina™ were considered out of a mixed database of cases with proven motion and standard cases. These anonymized data were collected from a single institution in France following the EU General Data Protection Regulation. Then, 282 specific VOIs were selected in all the reconstructed volumes such that 1) they contained at least one point-like object of interest that could be clearly identified and manually tracked throughout all 9 projections of the examination, 2) the object of interest is further than 10 mm apart from breast border and chest wall and 3) is not part of a cluster larger than 20 × 20 mm. From this information, the approximate 3D position of the object was determined (as expressed in section 2.4.1) and was used to produce a preliminary estimation of the amplitude of the patient's motion during the examination. The histogram of the measured values for all 282 volumes of interest is presented in figure 6. All 282 volumes are then reconstructed to provide a statistical analysis based on the quantitative metrics of section 2.4.1 while a subset of 131 most polluted cases were considered for the purpose of the clinical preference pilot study.
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

## 3.2. Evaluation of local dynamic reconstruction

Figure 7 shows the dynamic residual norm $||r(f, U)||$ with respect to its static counterpart ($||r(f)||$) given the three local kinematic bases described in section 2.3.1. As can be seen, the dynamic reconstruction has a lower residual norm in the majority of cases for all kinematic descriptions (90.1%, 90.1%, 97.5%), with an average improvement ratio computed on the successful cases (computed as $(||r(f)|| - ||r(f, U)||) / ||r(f)||$) of respectively 11.8%, 12.4% and 15.4%.

Given the manual tracking of all the objects of interest, which allowed to obtain an initial estimate of patient motion for the available volumes, it is possible to assess whether the estimated kinematic fields are consistent with the manual measurements. In this respect, figures 8 and 9 show the reference position (deprived of a constant (resp. linear) component in the x (resp. y) direction) of the object of interest in the original projections compared to the reprojection of the 3D estimated position, 1) uncorrected ('static'), 2) corrected by the Plug flow, 3) corrected by the Plug + Couette flow and 4) corrected by the Plug + Couette + Poiseuille kinematic fields. Each subplot shows the position along the x- and y-axis of a reprojected clinical feature. In this visualization, the uncorrected projection of a motionless object (represented by the 'static' curves in figures 8 and 9) is expected to follow a smooth sinusoidal curve (see Palma et al (2021)) as can be seen for the x coordinate of the dotted orange curve. This is however true if the source moves in a perfectly circular path centered around the rotation center. While no additional information is available with respect to the x position of the source at each
<figure><img src="image_11.png" /><figcaption>**Figure 7.** Comparison of the static vs. dynamic residual loss for an xy Plug, Plug + Couette (PC), Plug + Couette + Poiseuille (PCP) flow corrections on the local reconstruction database.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 8.** Dynamically corrected projection of a clinical feature of interest compared to the uncorrected data and the manually acquired reference.</figcaption></figure>

shooting step (nominal value assumed), a corrected position may be computed in the *y* direction thanks to the available DICOM tags, which displays some fluctuations along the *y*-axis in the sampled angles. It is to be noted that this corrected position is likewise used in the whole dynamic reconstruction process. Nevertheless, the manually acquired reference (plain blue) displays significant fluctuations which range from 0.1 to 0.5 mm in the *x* direction and up to 3 mm in the *y* direction. This perturbation relates to motion and needs to be corrected for a reliable reconstruction. In this respect, the reprojected positions of the volumes reconstructed with the Plug (green), PC (red dash dotted) and PCP (loosely dashed purple) corrected kinematic fields are closer to the manually clicked reference. While it is not clear from this graph which kinematic description better matches the manual reference, the general analysis over all the available cases reveals that the Plug description reduces the gap ($\|p_m - P[X_e + \Phi(X_e)]\| < \|p_m - P[X_e]\|$) on 75.8% of the 282 cases while the PC and PCP bases respectively improve 70.6% and 54.6% of them.

Considering the insights from the last paragraph, figure 10 compares the ‘static’ and ‘dynamic’ reconstructions obtained with a Plug kinematic basis for three cases at hand. In case 112, the two objects visible in the ‘static’ reconstruction merge into one in the ‘dynamic’ counterpart, while in case 209, the
<figure><img src="image_13.png" /><figcaption>(a) Case 44</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(b) Case 60</figcaption></figure>

**Figure 9.** Dynamically corrected projection of a clinical feature of interest compared to the uncorrected data and the manually acquired reference. (part II).

<figure><img src="image_15.png" /></figure>

**Figure 10.** Comparison of the ‘static’ and ‘dynamic’ reconstructed slices of interest of three cases with a ‘Plug’ kinematic basis.

blurred/duplicated borders of the metallic marker become sharper. In case 234, one notices the general refocusing of each small object of the cluster, which leads to brighter centers and tighter boundaries. While there is no clear way to determine what the image should look like, it is sometimes possible to
<table><caption>**Table 1.** Pilot study results.</caption><thead><tr><th></th><th colspan="3">Reader 2</th></tr><tr><th>Reader 1</th><th>Static</th><th>Dynamic</th><th>Unclear</th></tr></thead><tbody><tr><th>Static</th><td>13</td><td>15</td><td>4</td></tr><tr><th>Dynamic</th><td>17</td><td>44</td><td>3</td></tr><tr><th>Unclear</th><td>13</td><td>17</td><td>5</td></tr></tbody></table>

<figure><img src="image_16.png" /><figcaption>**Figure 11.** (a) Visualization of the finite element kinematic basis. The finite element mesh is overlaid with an axial slice of the 'static' reconstruction result. Blue points represent the nodes free to move while red ones define boundary conditions; (b) Measured kinematic field (in millimeters) for the global dynamic reconstruction case.</figcaption></figure>

assess that the proposed reconstruction is reasonable. For instance, the projections of case 112 confirm the presence of a single calcification and thus the reliability of the proposed reconstruction.

Finally, qualitative performance of the dynamic reconstruction was evaluated through a preliminary preference study on the reconstructed volumes, the results of which are reported in table 1.

According to table 1, the readers expressed a preference over 89 cases (13+15+17+44), with a respective score of 68.5% and 66.3% in favor of the *dynamically* reconstructed images. The readers agreed on 57 cases, which makes up 65% of the dataset. Restraining the analysis to this subset, the preference for the *dynamically* reconstructed images rises to 77.2% (44/57).

### 3.3. Evaluation of global dynamic reconstruction

Global reconstruction is an important step towards the adoption of dynamic reconstruction in the clinical setup as it provides an overall estimation and correction of patient motion in one single step. For this purpose, the kinematic basis was extended in an attempt to match the complexity of patient motion of the whole breast. A construction strategy of such a basis is given in section 2.3.2 and an example is shown in figure 11(a). As a first attempt, the test volume was meshed by hand to facilitate the positioning of the nodes in areas with high contrast. The basis contains 43 free/internal nodes (blue) and 20 fixed/boundary nodes (red) materializing the kinematic degrees of freedom considered for this experiment. This enabled to compute the kinematic fields visible in figure 11(b), detailing for each of the 9 acquisition angles the value (in millimeters) of the x-displacement of a given voxel of the volume. Namely, the kinematic field gives for every anatomical point the sign and value of the required displacement to restore the reconstructed volume to the anatomical position at the time of a given acquisition. It should be noted that the displacement fields are relative to the central projection (in angle and acquisition time). This means that if the first (resp. last) projections are red (resp. blue) and need to move to the right (resp. left) to align with the central projection, the total motion is a consistent displacement from left to right. This motion from left to right is then consistent with the retraction of the patient from the imaging device. Finally, it is also reminded that since the kinematic basis is an extrusion of a 2D mesh, a slice in the kinematic field is sufficient to describe the obtained result.

In addition, figure 12 shows the successive evaluation of the residual norm (normalized by the scale) during the dynamic reconstruction process. The final result shows a reduction of 4.2% of the residual norm compared to the 'static' reference and consistent better behavior of the dynamic residual norm
<figure><img src="image_17.png" /><figcaption>**Figure 12.** Comparison of the evolution of the residual norm $||r(f, U)||$ (equation (2)) during the static and dynamic reconstruction process as a function of the reconstruction iterations.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 13.** Visual comparison of a microcalcification before (left) and after (right) dynamic reconstruction with an additional 250% zooming on the microcalcification of interest.</figcaption></figure>

during the whole process. The peaks visible in the figure during the optimization correspond to the change of scale, where the reconstruction is compared with the upscaled projections and needs several iterations to incorporate the additional data. From the computational point of view, it should be noted that the global dynamic reconstruction takes significantly longer than the static reconstruction (by a factor 10, without specific optimization). However, many acceleration opportunities could be investigated such as the adaptation of the convergence criterion or the introduction of initialization strategies. For instance, implementing available computer aided detection algorithms could enable tracking clinical features in the projections and generating an initial estimate of their motion in 2D as explained in figure 4. This procedure should provide a fairly reasonable first guess from which the convergence rate of the dynamic reconstruction will benefit. For the purpose of checking whether an acquisition is motion-polluted or not onsite by the technician, a low-resolution reconstruction may be generated at first and the full image may then be computed later on for display to the radiologist.

Finally, figure 13 compares the same area after the static (left) and dynamic (right) reconstruction. In this figure, the large macrocalcification is observed to be less elongated in the horizontal direction in the dynamic reconstruction and the microcalcification highlighted in the red box becomes visible after the correction.

## 4. Discussion

The dynamic reconstruction process presented in this paper is, to the best of our knowledge, the only attempt to perform a kinematic correction in DBT based on a fully 3D kinematic field. Following the phantom proof-of-concept (Barbieri et al 2024a) and initial investigation of local dynamic reconstruction (Barbieri et al 2024b), the study presented here aimed to assess the efficiency of the pipeline on a larger clinical database and provide an example of the performance of global dynamic reconstruction in the clinical setup.
Overall, the local dynamic validation has shown that at least 90% of the cases achieve a significant reduction of the residual norm when compared to the static reconstruction. In spite of this value, the reason why some cases do not respond as expected is still not clear and needs to be further investigated, as no clear pattern of failure is yet visible. While some of the cases produce a higher residual norm, (worse result), it should be noted that since the static reconstruction runs alongside the dynamic one, a straightforward guard-rail consists in showing to the radiologist the image with the lowest residual norm, ensuring that they only get the best result between the static and dynamically reconstructed volume. From the kinematic validation point of view, the results are also very encouraging with improvements of $||p_m - P[X_e + \Phi(X_e)]||$ over $||p_m - P[X_e]||$ of 54.6% (PCP), 70.6% (PC) and 75.8% (Plug). The apparently superior performance of the Plug basis compared to PC or PCP can originate from multiple factors. First, the algorithm minimizes the global residual norm of the reconstructed volume, rather than focusing on individual focal features. As such, the kinematic field estimated for each local reconstruction is computed to improve the reconstructed volume as a whole and not focused on a single detail. While smaller areas and limited number of degrees of freedom encourage attention on the details purposely included in the areas, introducing additional degrees of freedom, like in the PC and PCP kinematic bases, reduces the already limited weight of punctual features in the reprojection residual and deteriorates the quality of a feature-based kinematic assessment. Secondly, it should be considered that the acquired reference is also a biased object. Since the position $X_e$ obtained from the manual measurements is uncertain, and (apart from the Plug flow basis, invariant along z), the error is propagated through the reprojection of the estimated point modified by the kinematic field, thus polluting the final reading. This may lead to the degradation of the error indicator for the PC and PCP bases. This behavior suggests that more complex kinematic bases may indeed better capture the global motion of the breast, but that simplified descriptions such as the Plug basis remain more reliable when the evaluation metric is based on small calcifications or markers. Designing hybrid strategies that combine global accuracy with local fidelity will be an important direction for future work.

From the visual assessment point of view, the preliminary results of the preference study show that, when a preference is expressed, readers prefer the dynamically reconstructed volumes over the original ones in 77.2% of the cases. However, additional analysis is required to sustain this affirmation, especially with regard to the number of cases (which is too low to provide statistical power) and the number of readers. The correlation between residual norm, estimated motion amplitude and preference is also left for further investigations. For instance, stratifying the cases over the estimated patient motion amplitude presented in figure 6 should help determining in which motion amplitude range the dynamic reconstruction is best suited. Given the current status, it is hereby highlighted that if only 77.2% of the cases are deemed better by the readers, it should be noted that for the sake of initial evaluation the current reading experiment does not differentiate the cases that achieved a better residual norm score from the ones that did not. This means that a progression margin is to be expected following the enforcement of residual norm filtering as a fallback solution and will be evaluated in future work. Unfortunately, gathering cases with visible patient motion is not an easy task as most of them are usually discarded on the spot and reacquired (Geiser et al 2011, Martaindale et al 2023), thus submitting the patient to additional radiation dose. Hence, many of the available cases in the database do not display large motion, which gives little opportunity to evaluate the impact of the dynamic reconstruction algorithm, and future work will focus on acquiring additional motion-polluted cases (with the associated retake), to be read by a larger pool of clinical experts on a standardized review station. This should help providing a more definitive statistical evidence of the behavior of the process presented here. In addition, combining the reader preference ratings with a numeric evaluation of the conspicuity of a detail would be very beneficial. An option could be to double the study with a model observer trained to assess whether the image displays patient motion artifacts. While this strategy was not yet employed because of the insufficient clinical data at hand available to train the model, it could be of great value in determining an objective scoring of the artifacts intensity that could be integrated in the current residual loss. In addition, this new metric could also provide a way to automatically determine which areas should be picked for local dynamic reconstruction by estimating where the largest artifacts are located.

On a more practical level, the first validation of global dynamic reconstruction is very promising as it produced a volume with lower residual norm globally and improved image quality on a small detail without resorting to local shortcuts. However several directions remain to be explored. For instance, the current generation of the global kinematic basis was performed by hand, by visually modifying the position of internal points to match clinical features and prevent distortion from boundary effects. Incorporating automatic meshing tools should be considered, in combination with selecting areas with the highest residual norm. Standardizing the generation of the FE basis also brings us one step closer to performing an adequate preference study for image quality assessment in global dynamic reconstruction.
Furthermore, the FE description may be combined with the above ‘PCP’ basis for additional degrees of freedom including variability of the fields in the z direction, but the number of degrees of freedom rises fast as the size of the basis elements decreases and the computational cost is rapidly huge. Finally, additional constraints may be included in the finite element formalism. For instance, the incompressibility constraint (in the axial plane as well) developed above is a good candidate. However, applying this condition globally to 2D triangular meshes is usually a non-starter as it results in locking the whole kinematic description. However, relaxing the constraint locally may lead to its consideration globally. Le Tallec (2004) Finally, progressive enrichment of the basis could be considered as an alternative to regularization in order to minimize the computational cost of the dynamic reconstruction process.

## 5. Conclusions

This paper aims to show the recent advances of motion artifact correction through dynamic reconstruction in digital tomosynthesis. Following the initial proofs-of-concept published on phantoms and small clinical datasets, it presents quantitative and qualitative assessment of the performance of dynamic reconstruction on a 212-case large clinical dataset (282 regions of interest) for local reconstruction. For local feature evaluation, the dynamic reconstruction process allowed to improve the residual norm for more than 90% of the cases and improve object kinematics for 54%–75% of them. A preliminary visual preference study also determined that the image quality of the dynamic reconstruction was better for 77.2% of the cases on which readers agreed. Finally, the introduction of finite element kinematic basis tailored to a clinical case enabled to perform a global reconstruction which successfully decreased the projection residual norm over the whole case while significantly improving the image quality around a given radiological feature. Overall, this study shows a baseline for dynamic reconstruction in DBT and provides the first evidence that clinically feasible solutions are within reach, paving the way toward reducing retakes, lowering radiation dose, and ultimately improving diagnostic confidence in breast imaging.

Considering these results, further work will be focused on generalizing the usage of global dynamic reconstruction by focusing on the automatic determination of finite element basis. The amount of cases which will be treated thanks to this progress will enable to perform a statistical analysis on the relevance of degrees of freedom, which can then be sorted to generate an ‘optimal’ kinematic basis for global DBT reconstruction. Integrating model observers (He and Park 2013, Yao et al 2022) or AI-based motion detection could allow automatic selection and quantitative artifact scoring, complementing residual norm metrics. Such developments would enable larger-scale evaluations without relying only on manual tracking or limited reader studies.

## Data availability statement

The data cannot be made publicly available upon publication because they contain commercially sensitive information. The data that support the findings of this study are available upon reasonable request from the authors.

## Acknowledgment

M B acknowledges the support of a CIFRE PhD Grant from ANRT # 2021-1460, and GE HealthCare.

## Compliance with ethical standards

This research study was conducted retrospectively using anonymized human subject data made available by research partners. All clinical data were acquired with the approval of the ethical committee. Applicable law and standards of ethic have been respected.

## ORCID iDs

Matteo Barbieri ID 0009-0005-3495-9994

Clément Jailin ID 0000-0002-6414-6039

Laurence Vancamberg ID 0009-0003-0104-0645

Stéphane Roux ID 0000-0003-4885-6732
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