Ultrasound simulation with deformable and patient-specific scatterer maps

Abstract

Purpose

Ray-tracing-based simulations model ultrasound (US) interactions with a custom geometric anatomical model, where US texture can be emulated via real-time point-spread function convolutions of a tissue scatterer representation. Such scatterer representations for realistic appearance are difficult to parameterize or model manually and do not respond to volumetric deformations such as those caused with tissue compression by the probe. Herein we utilize brightness mode (B-mode) estimated scatterer maps for ray tracing and propose to enhance the realism of ray-tracing-based simulations by incorporating dynamic speckle patterns that change compliant with tissue deformation.

Methods

In this work, we realistically simulate US texture deformations in the scatterer domain via back-projection of ray segments into a nominal state before sampling during simulation runtime. We estimate scatterer maps from background in vivo images using a pretrained generative adversarial network.

Results

We demonstrated our proposed scatterer estimation and runtime background fusion method on simulated transvaginal US scans of detailed surface-based foetal models. We show the viability of modelling deformations in the scatterer domain at interactive frame rates of 28 frames per second. A quantitative and a qualitative evaluations indicated improved realism in comparison to the state of the art.

Conclusions

Transferring a background image in a scatterer representation enables us to capture anatomical content in a physical space, in which deformations can be incorporated physically consistently before convolving with a US point-spread function during simulation runtime. This then uses the same imaging model on both the background and the hand-crafted models leading to a consistent and seamless compounding of contents in the scatterer space.

Appendix A: Shape function

Consider a FEM mesh consisting of tetrahedral elements, which are commonly used in tessellations. The position ${\mathbf {x}}$ inside a tetrahedral element can be represented in terms of the barycentric coordinates $r_{k}$ of ${\mathbf {x}}$ with respect to the four element corner positions ${\mathbf {c}}_{k}$ that correspond to the deformed state of the mesh, i.e. ${\mathbf {x}} = \sum _{k=1}^{4} r_{k} {\mathbf {c}}_{k}$. This can be written as [6]:

$$\begin{aligned} \begin{bmatrix} x \\ y \\ z\\ 1 \end{bmatrix} = \begin{bmatrix} c_{11}&c_{12}&c_{13}&c_{14} \\ c_{21}&c_{22}&c_{23}&c_{24} \\ c_{31}&c_{32}&c_{33}&c_{34} \\ 1&1&1&1 \end{bmatrix} \begin{bmatrix} r_{1} \\ r_{2} \\ r_{3}\\ r_{4} \end{bmatrix} \quad \text{ i.e. } \quad {\mathbf {x}} = {\mathbf {C}}{\mathbf {r}}. \end{aligned}$$

(1)

Similarly, the position ${\mathbf {x}}^{0}$ corresponding to the same barycentric coordinates $r_{k}$ in the nominal mesh can be found as ${\mathbf {x}}^{0}={\mathbf {C}}^{0}{\mathbf {r}}$, where ${\mathbf {C}}^{0}$ contains the nominal corner position. The transformation given by ${\mathbf {x}}^{0}=f^{-1}({\mathbf {x}})$ can be expressed as ${\mathbf {x}}^{0}={\mathbf {C}}^{0}{\mathbf {C}}^{-1}{\mathbf {x}}$, where ${\mathbf {C}}^{0}{\mathbf {C}}^{-1}$ is the inverse transformation $f^{-1}$ at ${\mathbf {x}}$.