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Predictive mechanics-based model for depth of cut (DOC) of waterjet in soft tissue for waterjet-assisted medical applications

Our new paper entitled “Predictive mechanics-based model for depth-of-cut (DOC) of waterjet in soft tissue for waterjet-assisted medical applications” is recently accepted to be published in Medical & Biological Engineering & Computing journal and is now online at the following address: Click HERE!

This paper solves the fundamental physics problem of the interaction of the waterjet with the surrounding soft tissue for waterjet-assisted cutting in medical and surgical applications.

Mahdieh Babaiasl, Stefano Bocelli, Yao Chen, and Fan Yang conducted this research under the supervision of Dr. John P. Swensen, and Dr. Jow-Lian Ding

waterjet cut depth definition

Watch a short video of the experiments below:

The abstract of the paper is as follows:


The use of waterjet technology is now prevalent in medical applications including surgery, soft tissue resection, bone cutting, waterjet steerable needles, and wound debridement.

The depth of the cut (DOC) of a waterjet in soft tissue is an important parameter that should be predicted in these applications.

For instance, for waterjet-assisted surgery, selective cutting of tissue layers is a must to avoid damage to deeper tissue layers.

For our proposed fracture-directed waterjet steerable needles, predicting the cut depth of the waterjet in soft tissue is important to develop an accurate motion model, as well as control algorithms for this class of steerable needles.

To date, most of the proposed models are only valid in the conditions of the experiments and if the soft tissue or the system properties change, the models will become invalid.

The model proposed in this paper is formulated to allow for variation in parameters related to both the waterjet geometry and the tissue.

In this paper, first, the cut depths of waterjet in soft tissue simulants are measured experimentally, and the effect of tissue stiffness, waterjet velocity, and nozzle diameter are studied on DOC.

Then, a model based on the properties of the tissue and the waterjet is proposed to predict the DOC of the waterjet in soft tissue.

In order to verify the model, soft tissue properties (constitutive response and fracture toughness) are measured using low strain rate compression tests, Split-Hopkinson-Pressure-Bar (SHPB) tests, and fracture toughness tests. The results show that the proposed model can predict the DOC of waterjet in soft tissue with acceptable accuracy if the tissue and waterjet properties are known.

Full Pre-publication Article:

You can also see the accepted pre-publication article written in LaTex HERE!

Experimental Data, Model, and Necessary Codes:

Below are the experimental data, model, and necessary codes to run them. Feel free to use them in your research with proper citations to our work.

The penetration pressure of the waterjet in soft tissue is found to be:

\[\begin{split} P_w = \frac{4}{D(1-(\frac{d}{D})^2)} \left\{ J_{IC} \left(\frac{d}{D}\right) + \frac{D}{4} \frac{2\mu}{\alpha^2} \left[\int_1^{\infty} f\left(\frac{d}{D},\gamma\right)d\gamma \right.\right. + \\ \left.\left. 2\left(\frac{d}{D}\right)^{2-\alpha} + \left(\frac{d}{D}\right)^{2\alpha + 2} – 3\left(\frac{d}{D}\right)^2 \right]\right\} \label{eq:penetration pressure ultimate} \end{split}\]

\[f\left(\frac{d}{D}, \gamma \right) = \left(\frac{\gamma + \left(\frac{d}{D}\right)^2 – 1}{\gamma}\right)^{\frac{\alpha}{2}} + \left(\frac{\gamma}{\gamma + \left(\frac{d}{D}\right)^2 – 1}\right)^{-\frac{\alpha}{2}} – 2\]

In order to understand what each parameter means please refer to the article.

We found out that the penetration occurs when Pw is minimum. Now the question is we want to find a d/D that minimizes Pw. In order to do so, the following MATLAB code is written: Click HERE!

Depth-Of-Cut (DOC) experimental data

For Depth-Of-Cut (DOC) experimental data along with a MATLAB code to run them click HERE!

Image Processing Code:

Note that CalibrationDistance.m code measures the depth of cut by image processing from the photos. First, you should select the area of interest and then calibrate the distance using the rulers on the photo and then measure the depth of cut. Here are the steps to measure the distance in any photo:

Step 1. Select the area of interest and do the Spatial Calibration by choosing say 10 mm on the ruler:

image processing cut depth
image processing cut depth

Step 2: After calibration, select Measure Distance from the menu and then select the area of interest that you want to measure:

image processing cut depth

The result will be the measured distance in mm:

image processing cut depth

Depth of Cut Mechanics-based Model Code:

You can find the code for the model proposed in the paper HERE!

If you want to use the data and need to cite our work here are the links:

For Static Compression Tests, and Split-Hopkinson Pressure Bar SHPB tests on SEBS Soft Tissue Simulants, you can find the data in the following links:

Loadcell Code

Needle Insertion Controller in Python and C

Visual Studio Code

Below is a short video of Trouser Tear Test to Find Mode I Fracture Toughness:

Short Video below shows the difference between a conventional needle and a waterjet needle:

You can see the other posts on waterjet steerable needles in the links below:

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