UltraFlex: Iterative Model-Based Ultrasonic Flexible-Array Shape Calibration

Benjamin N. Frey1, Dongwoon Hyun2,3, Walter Simson2, Louise Zhuang5,
Hoda S. Hashemi2, Martin Schneider2, Jeremy J. Dahl2,
Departments of 1Applied Physics, 2Radiology, and 5Electrical Engineering, Stanford University
3Siemens Healthineers
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Overview

Ultrasound imaging is a non-invasive, portable, and inexpensive imaging modality. Despite commonly being known for its applications in fetal imaging during pregnancy, ultrasound imaging can be used to monitor, quantify, and diagnose a wide variety of diseases. Until recently, ultrasound imaging has been confined to conventional rigid-transducer systems within clinics and hospitals. These systems require trained ultrasonographers to continuously navigate an ultrasound probe.

Wearable- and flexible-array ultrasound devices have the potential to overcome this limitation. While flexible arrays have previously been experimentally demonstrated, image reconstruction is compromised without knowledge of the array element positions. We present UltraFlex, an iterative model-based flexible-array shape calibration framework that does not require external sensors. In this work, we evaluate array shape calibration model performance while examining multiple image quality metrics. We achieve median position mean Euclidean error (MEE) values of 3.7 μm for simulation, 29.7 μm for phantom, and 69.0 μm for in vivo liver data. These results show promise for the current and future development of experimental flexible- and wearable-ultrasonic arrays.

UltraFlex Framework

UltraFlex utilizes iterative optimization with automatic differentiation to provide lower element position estimation errors than previous models in the literature.

Technical approach diagram
(a) First, a multistatic ultrasound dataset \( \Psi \) is collected. (b) Element delays are calculated, an ultrasound image is beamformed, and the image quality is evaluated. Errors are backpropagated to update the array element positions \( \vec{\boldsymbol{r}}_\mathcal{A} \). (c) This iterative process provides accurate flexible-array shape estimation using ultrasound autofocusing.

Quality Metric Evaluation

The efficacy of multiple image quality metrics have been previously investigated for flexible array shape estimation. In this work, we present a direct comparison of multiple quality metrics using MEE as an evaluation metric.

Description: Averaged over nine array geometries and four simulation targets, the MEE corresponding to each quality metric-based model is reported over 1000 optimization iterations.

Image focusing is also qualitatively evaluated for a simulated sinusoidal array and flat array shape model initialization. The coherence-factor based model fails to estimate the array shape for the Stanford logo, and the envelope entropy-based model fails to estimate the array shape for all simulation targets. The common-midpoint (CM) phase error and CM correlation coefficient-based models achieved the best point grid focusing and final MEE values.

Description: Simulation results for array shape estimation using different quality metrics.

Additive Noise Study

We explored the robustness of different metric-based models to increasing decreasing levels of signal-to-noise ratio (SNR) through additive white noise. The white noise represents thermal noise in an ultrasound imaging system. Models based on CM signal-based metrics, such as CM phase error and CM correlation coefficient, are the most robust against additive white noise while achieving final-iteration median position MEE values as low as 3.7 µm for simulation data.

Noise study results

Experimental Results

Model performance on experimental phantom and in vivo liver datasets was investigated using transducers with known geometries. In total, 12 data samples were obtained: three Verasonics L12-3v samples each of a phantom and rat liver, and three Verasonics C5-2v samples each of a phantom and human liver. In all cases, B-mode focusing is improved compared with the intial array shape assumption.

Next, a quantitative comparison of model-calibrated array shapes was performed. Models based on the CM phase error and CM correlation coefficient quality metrics enabled median position MEE values of 29.7 µm for phantom data and 69.0 µm for in vivo liver data across the two metrics.

Metric results
Description: For each boxplot grouping, three L12-3v datasets and three C5-2v datasets are utilized. The model is initialized with all nine array geometries using the indicated sound speed of each grouping.

Related Projects

Check out some related projects on adaptive ultrasound imaging with automatic differentiation!

Differentiable Beamforming for Distributed Attenuation Estimation and Spatial Gain Compensation (SGC)

Benjamin N. Frey, Dongwoon Hyun, Walter Simson, Thurston Brevett, Louise Zhuang, Jihye Baek, Sergio Senabria, Jeremy J. Dahl

IEEE Ultrasonics, Ferroelectrics, and Frequency Control Joint Symposium, 2024 (project page)

Distributed attenuation estimation can enable local application of gain compensation in space, compensating for energy loss due to attenuation through Spatial Gain Compensation (SGC).

Differentiable Beamforming for Ultrasound Autofocusing

Walter Simson, Louise Zhuang, Sergio Senabria, Neha Antil, Jeremy J. Dahl, Dongwoon Hyun

MICCAI, 2023 (project page)

Applying differentiable beamforming to auto-focus ultrasound and high-resolution estimate sound speed in tissue.

Paper

BibTeX


      @article{frey2025ultraflex,
        title={UltraFlex: Iterative Model-Based Ultrasonic Flexible-Array Shape Calibration},
        author={Frey, Benjamin N. and Hyun, Dongwoon and Simson, Walter and Zhuang, Louise and Hashemi, Hoda S. and Schneider, Martin and Dahl, Jeremy J.},
        journal={IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control},
        year={2025},
        note={Under revision}
      }