Efficient 3-D Reconstruction in Ultrasound Elastography via a Sparse Iteration Based on Markov Random Fields

Percutaneous needle-based liver ablation procedures are becoming increasingly common for the treatment of small isolated tumors in hepatocellular carcinoma patients who are not candidates for surgery. Rapid 3-D visualization of liver ablations has potential clinical value, because it can enable interventional radiologists to plan and execute needle-based ablation procedures with real time feedback. Ensuring the right volume of tissue is ablated is desirable to avoid recurrence of tumors from residual untreated cancerous cells. Shear wave velocity (SWV) measurements can be used as a surrogate for tissue stiffness to distinguish stiffer ablated regions from softer untreated tissue. This paper extends the previously reported sheaf reconstruction method to generate complete 3-D visualizations of SWVs without resorting to an approximate intermediate step of reconstructing transverse C planes. The noisy data are modeled using a Markov random field, and a computationally tractable reconstruction algorithm that can handle grids with millions of points is developed. Results from simulated ellipsoidal inclusion data show that this algorithm outperforms standard nearest neighbor interpolation by an order of magnitude in mean squared reconstruction error. Results from the phantom experiments show that it also provides a higher contrast-to-noise ratio by almost 2 dB and better signal-to-noise ratio in the stiff inclusion by over 2 dB compared with nearest neighbor interpolation and has lower computational complexity than linear and spline interpolation.