# Deep Learning Based Uncertainty Quantification for Improving Clinical Diagnostic Tools

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2023

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## Abstract

Deep learning methods have impacted a wide number of fields, and interest in its applications to clinical medicine continues to grow. Interpretable and uncertainty-aware models are critical for the adoption of artificial intelligence and machine learning in medicine, and explicit uncertainty quantification methods are used in this work to train deep neural networks that output an uncertainty value. This dissertation investigates the application of explicit uncertainty quantification with deep learning to tackle data processing problems in tympanometry, ultrasound shear wave elasticity (SWE) imaging, and ultrasound B-mode imaging.To facilitate layperson-guided tympanometry, Chapter 2 describes an uncertainty-aware hybrid deep learning model that classifies tympanograms into types A (normal), B (effusion/perforation), and C (retraction), trained using the audiologist’s interpretation as gold standard. The dataset consisted of 4810 pairs of narrow-band tympanometry tracings acquired by an audiologist and layperson in school-aged children from a trial in rural Alaska with a high prevalence of infection-related hearing loss. The model used a deep neural network (DNN) to estimate the tympanometric peak pressure, ear canal volume, and associated uncertainties, and then used a three-level decision tree based on these features to determine tympanogram classification For layperson-acquired data, the model achieved a sensitivity of 95.2% (93.3,97.1) and AUC of 0.968 (0.955,0.978). The model’s sensitivity was greater than that of the tympanometer’s built-in software [79.2% (75.5,82.8)] or a set of clinically recommended normative values [56.9% (52.4,61.3)]. For audiologist-acquired data, the model achieved a higher AUC of 0.987 (0.980,0.993) but an equivalent sensitivity of 95.2 (93.3,97.1). This chapter demonstrates that automated tympanogram classification using a hybrid deep learning classifier could facilitate layperson-guided tympanometry in hearing screening programs for children in resource-constrained communities. In ultrasound SWE imaging, a number of algorithms exist for estimating the shear wave speed (SWS) from spatiotemporal displacement data. However, no method provides a well-calibrated and practical uncertainty metric, hindering SWE’s clinical adoption and utility in downstream decision-making. In Chapter 3, a deep learning based SWS estimator is designed to simultaneously produce a quantitative and well-calibrated uncertainty value for each estimate by outputting the two parameters m and σ of a log-normal probability distribution. The working dataset consisted of in vivo 2D-SWE data of the cervix collected from 30 pregnant subjects, with 551 total acquisitions and >2 million sample points. Points were grouped by uncertainty into bins to assess uncertainty calibration: the predicted uncertainty closely matched the root-mean-square error, with an average absolute percent deviation of 3.84%. An ensemble model was created using leave-one-out training that estimated uncertainty with better calibration (1.45%) than any individual ensemble member when tested on a held-out patient’s data. The DNN was applied to an external dataset to evaluate its generalizability, and a real-time implementation was demonstrated on a clinical ultrasound scanner. The trained model, named SweiNet, is shared openly to provide the research community with a fast SWS estimator that also outputs a well-calibrated estimate of the predictive uncertainty. Chapter 4 introduces 3D rotational SWE imaging for characterizing skeletal muscle as an incompressible, transversely isotropic (ITI) material in an effort to assess muscle health and function. To facilitate ongoing research, three tools were developed. First, a Fourier-domain approach is described for calculating 3D muscle fiber orientation (MFO) from 3D B-mode volumes acquired using two imaging setups: 1) a cylindrical volume acquired by rotating a linear transducer, and 2) a rectangular volume acquired by a rectilinear matrix array transducer. Most existing approaches apply only to 2D B-mode images and detect individual fibers to extract the tilt, the angle fibers make with a horizontal plane. In a 3D B-mode volume, spherical coordinates and two angles are needed to describe orientation: the tilt and the rotation angles, where rotation is defined relative a reference vertical plane in the volume. The proposed algorithm was validated on in silico and in vivo data: errors in rotation and tilt were within 1° for both imaging setups and less than the observed in vivo MFO heterogeneity. Second, a versatile Radon-transform based SWS estimator was developed that can accept arbitrary masks to select particular regions in space-time data to isolate the two different shear wave propagation modes that are seen in ITI materials and in in vivo muscle data. Hand-drawn masks were initially used to identify these wave modes. These masks were used to train a DNN to automate mask drawing and alleviate the need for manual processing. The DNN identified 91% of the shear waves, and estimated speeds had an average difference of 7.6%. Third, the wave equation for an ITI material was derived and then solved using physics-informed neural networks (PINNs), a relatively new technique for numerically solving differential equations with advantages of being faster, compressed, analytic, and free of space/time discretization. Presently, simulations of ITI materials require time-consuming finite element modeling (FEM) or Green’s function calculations. This approach took roughly six times less time than an equivalent FEM simulation, and the PINN solution had multiple shear wave modes that matched the FEM to first-order. The PINN solution did not have reflection artifacts seen in the FEM solution. Estimated SWSs had a mean absolute difference of 4.7%. The differences in wave width and amplitude between the two suggest the need to further validate the PINN approach in comparison to FEM and Green’s function methods. In skeletal muscle, the primary SWS as a function of propagation angle forms an ellipse with the major axis oriented in the muscle fiber direction. Estimating the fiber rotation angle from a 3D B-mode volume is useful for SWE data processing, SWS estimation, and ellipse fitting. However, existing algorithms are sensitive to artifacts and can produce gross estimation errors differing ¥45° from the true fiber rotation. In Chapter 5, a DNN is designed and trained to predict fiber rotation angle via parameterizing a von Mises distribution, which provides both the estimated rotation and associated uncertainty. On simulated data with known fiber rotation, the model had an RMSE of 3.5°, and uncertainty closed matched the expected theoretical values when known amounts of fiber heterogeneity were introduced. For in vivo data of the vastus lateralis muscle, the SWS ellipse fit was used as ground truth, and DNN model RMSE was 6.9° compared to 16.9° for the existing Fourier-domain algorithm. The DNN had no estimates with an error <30°. Predicted uncertainty correlated with RMSE, but was smaller by a factor of four. This deep learning approach will provide more accurate and robust fiber rotation estimates for use in shear wave data processing and muscle characterization. In summary, this work demonstrates the effectiveness of deep learning methods for addressing specific data-processing needs of research aimed at developing new clinical applications of tympanometry, ultrasound SWE and B-mode imaging for the diagnosis and monitoring of disease. This work also demonstrates effective uncertainty quantification using the explicit estimation method, and suggests how uncertainty values may be useful for downstream decision making and data processing and potentially as a stand-alone characteristic value.

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Jin, Felix Qiaochu (2023). *Deep Learning Based Uncertainty Quantification for Improving Clinical Diagnostic Tools*. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/27571.

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