# Machine learning model for fast prediction and uncertainty quantification of needle deflection during prostate biopsy

## TL;DR

This paper presents a fast machine learning model to predict needle deflection during prostate biopsies and quantify uncertainty for better procedure planning.

## Contribution

A fast Fourier feature neural network model for needle deflection prediction and low-cost uncertainty quantification in prostate biopsies.

## Key findings

- The FFNN model showed close agreement with experimental data and introduced only 0.3-mm tip deflection error.
- The model enabled a low-cost Monte Carlo uncertainty quantification with about 20 CPU seconds of computational time.
- The model demonstrated how tissue depth, stiffness, and uncertainty affect needle deflection in a clinical example.

## Abstract

Accurate needle placement is essential for prostate biopsy. Recently, transperineal prostate biopsies are receiving renewed interest due to concern over infection from conventional transrectal biopsies. However, accurate needle placement is more challenging in the transperineal approach than in the transrectal approach due to the long insertion distance leading to a large targeting error and repeated insertion attempts. Improved procedure planning tools that can predict the deviation of the needle can potentially reduce the targeting error and number of insertion attempts. Prediction of deflection magnitude requires a model of biopsy needle deflection, which in turn requires information about tissue material properties. However, material properties of tissue in patients cannot be easily obtained. Accounting for this uncertainty in patient tissue properties requires a model capable of quantifying uncertainty in needle deflection as a function of a distribution of tissue properties. A Monte Carlo uncertainty quantification requires 1000s of samples, but it is not possible to obtain this many samples in a short enough time for intraoperative procedure planning using published needle deflection prediction models.

This work seeks to develop a model of needle deflection fast enough for use in intraoperative procedure planning, validate this model against experimental results, and integrate it into a Monte Carlo uncertainty quantification model.

This work used a mechanics‐based model of biopsy needle deflection to train a Fourier feature neural network (FFNN) model in order to make predictions with a low computational cost. Both models were validated against experimental data. The neural network model was used in a Monte Carlo uncertainty quantification model to quantify uncertainty in needle deflection arising from uncertain tissue mechanical properties.

This work (1) implemented a mechanics‐based model and a FFNN model. Both models were validated against previously published experiments carried out with tissue phantoms. Both models showed close agreement with the experimental data. (2) We showed that our FFNN model was more accurate than a baseline ordinary least squares model, introducing only about 0.3‐mm tip deflection error compared to the mechanics‐based model. We also showed that our FFNN model makes unbiased predictions with respect to the amount of deflection. (3) We demonstrated a Monte Carlo uncertainty quantification model of needle deflection with a low computational cost of about 20 CPU s. We used our uncertainty quantification model to show how the depth, stiffness, and magnitude of uncertainty in a layer of tissue affect needle deflection. In addition, we showed a simple clinical example of the use of our model.

This work demonstrates a Monte Carlo uncertainty quantification model of needle deflection with a low computational cost. This method shows promise for future applications in procedure planning for prostate biopsies as well as other transperineal procedures conducted with flexible needles such as cryoablation and brachytherapy.