The heat transfer modelling for bone metastatic lesion minimization using two different cement types

* Centro Hospitalar e Universitário do Porto, Institute of Biomedical Sciences Abel Salazar, University of Porto (CHUP-ICBAS), Portugal, vaniacoliveira@icbas.up.pt; ** LAETA, INEGI, School of Engineering, Polytechnic of Porto (ISEP), Mechanical Engineering Department, Portugal, elz@isep.ipp.pt, job@isep.ipp.pt; ***LAETA, INEGI, Polytechnic of Institute of Bragança (IPB), Department of Applied Mechanics, Portugal, claudiarua_17@hotmail.com, ppiloto@ipb.pt ****LAETA, INEGI, Faculty of Engineering of the University of Porto (FEUP), Mechanical Engineering Department, Portugal, rnatal@fe.up.pt


Introduction
Bone metastases, which are frequently diagnosed late, translate an advanced tumor stage and have a high impact in patients' quality of life and survival. After the diagnosis and tumor staging, it is important to characterize the bone tumor lesions with a specific attention regarding the identification of the size, type (osteolytic, osteoblastic, mix), location, etc. in the involved bone [1]. Tumors can destroy the spongy and cortical bone and extend to soft tissues. The bone cancer treatment is complex, and can include surgery, chemotherapy and radiotherapy, or other local or systemic treatments combinations, with the aim to cure or control the affected anatomical area.
Bone cement is widely used in orthopaedic surgeries due to their structural and physical properties, excellent biocompatibility and easy manipulation. This material has an exothermic reaction where volumetric dimension changes during the polymerization process with heat generation [2]. The amount of heat generated depends on cement mantle volume and type of cement [3]. The use of low viscosity cement poured into the bone leads to a relatively deep cement penetration, and a large volume especially when anchoring holes are used. The use of high viscosity cement is manually applied to the bone leading to a homogeneous and thinner cement mantle [3]. The high heat generated can lead to thermal necrosis of bone cells and also residual stresses formation that can affect the intramedullary systems fixation and loosening. Different authors studied the exothermic reaction of cement polymerization and reported in different publications predictive results regarding the temperature rise and residual stresses using time-dependent polymerization function [2], [4]. Others proposed empirical models for the prediction of heat generated using experimental and numerical tests [3], [5]- [9]. There are studies in the literature that point out thermal necrosis in cortical bone, usually when it reaches a temperature of 47ºC for 1 min [10]- [11]. Other authors showed that temperature values above 55ºC for a period longer than 30 seconds could cause great irreversible lesions in bone tissue [10], [12]- [13]. Eriksoon and Albrektsson [14] concluded that heating up to 47ºC could be considered as the optimal limit that bone can withstand without necrosis. In another investigation, the thick cement showed maximum temperature approximately 45ºC [15].
In this work, we included two different cements types (cement A and cement B) from literature. Cement type A [6] was used previously in a similar research [16] and cement type B [3] represents Palacos R brand (Heraeus Medical GmbH, Wehrheim, Germany) largely used in patients of CHUP-ICBAS. Palacos R is a high-viscosity bone cement type and it is the gold standard due to its widespread use for conventional and minimally invasive surgeries. In the computational models cement was injected into an isolated mould region (20mm in depth and variable width 15 and 25mm), and the cement temperature polymerization introduced as a boundary condition. A two dimensional thermal and transient model based on finite element method was built to predict the temperature field produced by cement polymerization in a metastatic bone tumor lesion in comparison with two different bone cements types, complementing the initial research from the authors [16]. The bone cement was introduced to fill in a metastatic lytic lesion area with or without an intramedullary titanium nail. Different geometries were tested to represent metastatic lytic lesion models. For each model, the temperature field due to the cement polymerizing effect is represented for the critical time (time corresponding to the most severe thermal condition), which affects thermal necrosis and the amount of bone cells penetration. For a more efficient clinical benefit, all results were presented to stimulate a discussion regarding if the introduction of bone cement is an alternative procedure in a metastatic lytic lesion local control to add to the mechanical stabilization with an intramedullary nail. Furthermore, allows to verify the effect of using different bone cements types with thin or thick mantle amount

Methods
To analyse the effect of cementing technique, computational models were created according to average dimensions of the sub-trochanteric femoral area, using digital X-ray from patients of CHUP-ICBAS and proved from a biomechanical data control group [16]- [17]. Figure 1 a) shows a metastatic lytic lesion of the proximal left femur (subtrochanter) identified on a plain pelvic X-ray, where the patient was diagnosed with metastatic disease of a breast cancer. The right image represents other bone metastasis on the right femoral diaphysis of a male patient with clear renal cells carcinoma. Both metastatic lytic lesions have in width between 16 and 25mm, and 20mm in depth. The size characterization of the metastatic lesions is important to introduce the same dimensions for bone cement filling minimization. Figure 1 b) shows the measurement of the proximal femur (sub-trochanteric area) based on conventional pelvic X-ray of 2 patients of CHUP-ICBAS with determination of the internal and external cortical bone, spongy bone and complete femoral diaphysis diameter. On average, the measured bone geometries of 6 non-tumor patients considered for the model have an external diameter equal to 31.2mm and a cortical thickness of 7.35mm.

Fig.1 (a) Metastatic lytic lesion of the proximal left femur and on the diaphysis of the right femur. b) Measurements on
control group patients Figure 2 shows a conventional A-P and lateral X-ray of two patients submitted to internal fixation using a femoral intramedullary nail (Gamma 3 nail, Stryker®). Both patients presented an imminent or pathological fracture due to bone metastases of different primary tumors [16].

Fig. 1 Internal fixation with intramedullary nailing of femur.
Two computational models were reproduced without a femoral intramedullary system and other two extra models with an intramedullary nail with a diameter equal to 11mm. In the middle of the model, bone cement was introduced to fill in a metastatic lytic lesion area minimization with the dimensions equal to 20mm in depth and variable width of 15 and 25mm. The bone lytic lesions were filled with bone cement. When the intramedullary systems are included, the cement material was spread in the same amount of affected area through the spongy bone. The numerical models were produced representing two-dimensional bone geometry with an external diameter equal to 31.2mm and with cortical thickness of 7.35mm. In the middle length of the model a cement bone was introduced with the dimensions equal to 20mm in depth and variable width 15 and 25mm. Numerical models were built accordingly to average dimensions obtained from digital medical images from patients in CHUP-ICBAS and agreed with a biomechanical data control group [17].

Models:
Width cement 15x20 mm (thin mantle) Width cement 25x20 mm (thick mantle) without intramedullary nail with titanium intramedullary nail Fig. 3 Numerical models without intramedullary nail and with intramedullary titanium nail. Figure 3 represents the geometries in the study without and with the internal stabilization, where blue zone represents the cortical tissue, violet is the spongy bone, the red colour is the used cement and the intramedullary nail is in dark blue colour. The numerical simulations were performed using the finite element method with ANSYS Multiphysics software. The geometrical model was meshed with a 2D thermal solid element (PLANE 77) with 8 nodes and a single degree of freedom, temperature, at each node. All material properties (cortical, spongy bone, cement A or B and intramedullary titanium nail) are in accordance with the literature [2], [16] and summarized in Table 1.  figure 4. According to the cement polymerization, a total simulation time equal to 1800 seconds was established for the numerical model: 384 seconds of heating with a peak of temperature equal to 83ºC and 1416 seconds of cooling for cement A and 600 seconds of heating with a peak of temperature equal to 68ºC and 1200 seconds of cooling for cement B. During the cement exothermic stage, there is no significant intramedullary blood flow increase. Thus, the ending time of the numerical analysis was 1800 seconds with an incremental time step equal to 5 seconds.

Fig. 4 Time-temperature curing effect of two bone cements
As seen in patients' imaging, the metastatic lytic lesion frequently affects spongy bone and one cortical bone (imminent or pathological fracture). For these models, a perfect contact was assumed between all interfaces. The cortical bone is a barrier for cement interdigitation independently of achieving cortical bone cells necrosis, due to its structural and physical properties. The bone cement fills in the lytic lesion area of the proximal femur minimization and easily interdigitate through the adjacent spongy bone with an expected higher porosity due to the non-blastic metastatic systemic disease. The pressure during the intramedullary titanium nail introduction, with an 11mm diameter nail, compacts bone cement all around the nail through the spongy bone and until contact to both internal and external cortical bone, confirmed on patients` imaging. We also assumed the heat transfer between different materials is performed exclusively by heat conduction. The boundary conditions considered in these simulations are the prescribed temperature in the bone cement region according the curing effect. The initial temperature in the model was assumed equal of 37ºC, mimicking the human body temperature.

Results and Discussion
The accuracy that can be obtained from finite element method is related to the mesh that is used. The presented results were obtained after a mesh convergence reducing the element size, that is an attractive approach due to its simplicity, validating and gaining confidence with the software and the obtained solution. The temperature field due to the cement type (A or B) curing effect is represented for the critical time equal to the maximum peak at 384s and 600s, respectively, see figure 5 and 6. Figure 5 represents the temperature field in the models without intramedullary nail system. The results show that the temperature in cement zone reaches the maximum value of 83ºC when using cement type A and 68ºC when using cement B, and that the heat is spread through cortical and spongy bone. The thermal necrosis effect in bone tissue is represented in grey colour. Increasing the amount of the metastatic lytic lesion filled with cement type A (from 15 to 25mm in width), the thermal necrosis increases the surrounding spongy region width by 10mm equal in both models, increasing in lateral corners of the cement zone with more pronounced effect in depth. When using cement type B and with a mantle of 15 to 25mm in width, the thermal necrosis region is reduced and the surrounding spongy region width is 5mm equal in both models.  Figure 6 represents the same computational models but including the intramedullary titanium nail, represented by the dark blue colour in figure 3. The intramedullary fixation pressures the bone cement to fill from one cortical bone to another, around the nail. The temperature distribution is represented by the critical time (the peak temperature for each cement type polymerization). In the lytic lesion (and with the consequent increase of cement filling), the heat affects all bone tissue diameter due to the high thermal conductivity properties of the intramedullary titanium systems. All cement type A filling induced in the metastatic lytic lesion area affects the spongy bone and the cortical bone, and even small cement quantities produce high temperature in the surrounding region. When using cement type B the surrounding affected region is smaller, affecting only the adjacent area to the spongy bone. When comparing the temperature field between the two cement types used, cement A spread a higher necrosis effect and cement B has a pronounced effect only in the surrounding area to the cement or neighbour to the intramedullary nail. Bone necrosis was found in both models with either a thin or thick cement mantle.
The results, obtained from the numerical analysis using the finite element method, allow to conclude about the high temperature spread in bone material. The presented results could play a key role in the multidisciplinary management of bone metastases. As refereed by [18] the cementoplasty can be used in difficult cases if there is good control of cement injection and real time quality imaging during the clinical procedure.

Conclusions
The temperature field located on the intramedullary system induces heat transfer in all the models due to higher heat conduction effect from the titanium material of the intramedullary nail, justified by the high material thermal conductivity. From the results, it can be concluded that with an increased lytic lesion and cement width, the thermal necrosis produces the same bone effect by adding the affected dimension by the amount of cement. There was a significant temperature difference between the different cement amounts used in this study due to the inclusion of the intramedullary nail, where the maximum temperatures at the bone increases significantly. The temperature at cementbone interface reaches the peak temperature values with both cement A and B. When using cement type A, the surrounding necrotic cells above 45°C represent on average 10mm of the bone layer. With cement type B only 5mm on average of the bone layer is affected, representing 50% of the previous value. Nevertheless, the peak temperature between the cements used represents only a difference of 15°C, corresponding to a reduction of 18% when using cement type B, a high viscosity cement. As a general conclusion, bone cement filling and the structural stabilization with an intramedullary titanium nail have a synergic effect that can be applied to long bones metastatic lytic lesions treatment on a clinical practical application, either with low or high viscosity cement types.