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 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.

(Left) An overview of the problems of traditional steerable needles and the solutions provided by waterjet steerable needles. (A) Traditional tip-steerable needles and tip-bent needles suffer from poor curvature, especially in soft tissues. (B) Traditional steerable needles are unable to accomplish many bends because the cutting force only results from drastic tissue deformation. (C) The first step for realization of waterjet steerable needles is to understand and model the interaction between waterjet and soft tissues at the tip (predictive model for depth of cut). (D) Then, the equilibrium between shapes cut in the tissue and the straight elastic needle should be understood. (Right) Waterjet steerable needles in which the direction of the tissue fracture is contr olled by waterjet and then the flexible needle follows. The first step for waterjet steerable needle realization is to predict the depth of waterjet cut

现在在医疗应用中普遍使用水刀技术，包括手术，软组织切除，切骨，水刀可控针和伤口清创术。软组织中水刀的切割深度（DOC）是在这些应用中应预测的重要参数。例如，对于水刀辅助手术，必须选择性切割组织层，以避免损坏较深的组织层。对于我们提出的骨折导向的水刀可操纵针，预测水刀在软组织中的切割深度对于开发精确的运动模型以及此类操纵针的控制算法很重要。迄今为止，大多数提出的模型仅在实验条件下有效，如果软组织或系统特性发生变化，则这些模型将无效。本文提出的模型是为了允许与水刀几何形状和组织有关的参数变化而制定的。本文首先通过实验测量了软组织模拟物中水刀的切入深度，然后研究了组织刚度，水刀速度和喷嘴直径对DOC的影响。然后，提出了一种基于组织和水刀特性的模型来预测软组织中水刀的DOC。为了验证模型，使用低应变率压缩测试，Split-Hopkinson-Pressure-Bar（SHPB）测试和断裂韧性测试来测量软组织特性（本构响应和断裂韧性）。结果表明，如果已知组织和水射流特性，则该模型可以以可接受的精度预测软组织中水射流的DOC。

（左）传统可控针的问题以及水刀可控针提供的解决方案的概述。（A）传统的针尖可控式针和针尖可弯曲的针具有较差的曲率，尤其是在软组织中。（B）传统的可转向针无法完成许多弯曲，因为切割力仅是由剧烈的组织变形引起的。（C）实现水刀可控针的第一步是了解和建模水刀与尖端软组织之间的相互作用（切割深度的预测模型）。（D）然后，应该理解在组织中切开的形状与笔直的弹性针之间的平衡。（右）水刀操纵针，其中组织断裂的方向由水刀控制，然后是柔性针。