Force and temperature modelling of bone milling using artificial neural networks
Introduction
Bone machining is a common practice in modern surgery [1]. Bones are rigid elements, living organs that form the framework of the human body. Bones have different sizes, shapes, and functions. In general, bone tissues can be categorized into cortical tissue and cancellous tissue [2]. The cortical or hard tissue is located at the outside part of a bone; while the cancellous or spongy bone is mainly located in skull bones, vertebrate bones, and at the end of long bones.
The most common bone machining procedures are bone drilling and bone milling [1]. Bone drilling is the process of making a hole in the bone tissue, whereas bone milling is used for bone resection or to create cavities within the bone tissue. Bone drilling is a part of many surgical procedures in orthopaedics, neurosurgery, reconstructive and plastics surgeries [3]. Bone milling, on the other hand, is a common procedure in Total Knee Replacement (TKR) surgery, cranial surgery, ontological surgery, and spinal surgery [4], [5], [6], [7].
The rigidity nature of the bone tissue has motivated the use of surgical robots for bone machining. The bone rigidity and the high contrast of bone imaging using X-ray, Computed Tomography (CT), or Magnetic Resonance Imaging (MRI), help develop preoperative and intraoperative models for patient anatomy. These models stay valid in most circumstances during robotic based bone machining procedures [8]. In an orthopaedic surgery, for example, it has been shown that precision, stability, and dexterity can be enhanced by using robots for bone machining [9]. However, using surgical robots for bone machining, whether the robot works autonomously (active robots) or cooperatively (semi-active robots), requires many considerations to minimize damage to the bone tissue and avoid injury to the surrounding soft tissues [10]. Therefore, robotic bone machining should be performed with minimum complications to ensure better outcomes and reduce recovery time.
Bone cutting force and temperature are of vital importance during bone machining. Excessive cutting forces can lead to mechanical damage to the bone tissue, or break the drill bit itself, in addition to increasing the bone cutting temperature [11], [12]. On the other hand, exposing the bone cells to heat, above a threshold for a certain duration, causes bone necrosis (death of bone cells) [3]. Avoiding bone necrosis during bone machining is essential; e.g. in Total Knee Arthroplasty (TKA), bone necrosis disables the bone cells ingrowth between a cut bone and an implanted artificial bone [13]. Therefore, avoiding excessive milling forces and temperature is critical during bone milling.
Damage to the bone tissue during bone milling can be reduced by optimizing milling parameters based on mathematical models of the milling force and temperature. These models can be used to find the optimal or ‘best’ milling parameters that can minimize the bone tissue damage due to bone machining [3]. These mathematical models give the relationship between the milling parameters (the independent variables) and the produced milling force or temperature (the dependent variables). They can be used as the objective function or constraints in an optimization problem [14].
To regulate the bone cutting force, a model based controller can be used. The controller generates a series of feed rate command signals to keep the cutting force as close as possible to a predefined allowable setting. However, in a force control systems the bone stiffness forms part of the control loop gain, and the lack of an accurate force model often leads to low loop gain settings. For instance, the lack of drilling force models to represent different bone densities in [15] led to choosing a low force loop gain to prevent high force fluctuations when the drill moves from low density (cancellous bone) to higher density (cortical bone) regions. Therefore, to solve this problem, the establishment of different bone force models to accurately estimate the bone machining force at different types of bone density is important; therefore the motivation of this research.
Finally, bone machining force models can be used for bone state recognition. In some surgical operations, identifying different bone machining stages is critical important to ensure the correctness of the bone machining process, and enhance patient safety [16]. Many techniques have been used to identify bone drilling and milling states, and model-based bone state recognition is one of these techniques [17], [18], [19]. Although bone sate recognition is mostly used to stop the cutting process before damaging the surrounding soft tissues, it can be employed to apply an optimized cutting parameter setting that corresponds to each bone layer. Specifically, the cutting process requires the optimal feed rate and spindle speed for the cortical bone when the cutting tool is in the cortical bone region, and, similarly, if the cutting tool is within the cancellous bone region, the corresponding optimal cutting parameter settings for cancellous bone should be applied.
The subsequent sections of this paper is organized as follows: Section 2 reviews the related research in bone milling. Section 3 shows the experimental setup and design. Section 4 presents the modelling of milling force. Section 5 presents the modelling of milling temperature of the milling tool and the fresh-milled bone surface. Section 6 discusses the experimental finding compared to related work in the literature. Finally, Section 7 suggested future work and concludes the paper.
Section snippets
Modelling of bone milling
According to the review in [12], there are only few studies that deal with modelling of bone milling. Furthermore, there is a lack of information concerning cancellous bone machining in the literature. The review [12] also shows an emphasis to use the finite element modelling (FEM) methodology to estimate the cutting force in bone drilling. However, the main drawback of the FEM methodology is its limitations for real-time applications, or during controller tuning and optimization. Bone
Materials
Different materials were used by researchers in bone machining experiments. For instance, procine bones were used in [35], [36], [37], [38], based on the assumption that procine and human bones are similar in their mechanical and composition properties. Bovine bones were also used based on the same reason in [5], [39]. In the literature, it is well established that mechanical and thermal properties of bone tissues are subject to many factors, including health condition, age, sex, diet, and race
Modelling of milling force
A force model is needed to estimate the steady state mean value of the milling force in the specified range of milling parameters. The mean value of the milling force vector is related to the Material Removal Rate (MRR), which is an important factor in milling optimization problems [54]. Furthermore, the milling force variable can be used as a constraint in the optimization problem. Indeed, the milling force describes the net effect of all milling parameters, and is one of the most important
Modelling of milling temperature
In each experiment shown in Table 1, the temperature values of the bur and the fresh-milled bone are measured to form the required data set for developing the ANN-based temperature model. The thermal camera is fixed above the bone block, as shown in Fig. 2, to measure the temperature of the fresh-milled bone surface and that of the bur during bone milling. A real time video shows the temperature profile for each point on the path of the milling bur including the milling bur itself. Fig. 9 shows
Discussion
Bone milling force and temperature depends on many factors, which include milling tool material and geometrical design, milling parameters, and bone material properties. Cortical and cancellous bone tissues differ in their thermal and mechanical properties. In the literature, most studies focus on cortical bone, as compared with cancellous bone, machining [12], [58]. This could be due to the fact that cortical bone tissue form around 80% of the human skeleton, while the remaining 20% of the
Conclusions and future work
In this paper, we have developed ANN models of bone milling force and temperature based on a real experimental study using a cancellous bone with 30 pcf density. The milling force model provides estimation of the mean value for the milling force, while two milling temperature models provide estimation of the mean value of the milling bur temperature and the fresh-milled bone temperature, respectively. These models provide the milling force and temperature estimation as a function of feed rate
Conflicts of interest
None.
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