Theoretical and experimental model to describe the injection of a polymethylmethacrylate cement into a porous structure
Introduction
Due to population ageing, osteoporosis is becoming one of the largest medical problems [1]. Osteoporosis leads to an enormous increase of the incidence of bone fracture. Additionally, the fixation of fractures in osteoporotic bone can be extremely difficult due to the limited anchoring force of bone screws. Considering this problem, surgeons have proposed to reinforce or stabilize osteoporotic bone with polymethylmethacrylate (PMMA) bone cement. With the use of PMMA, it is possible to achieve an adequate anchorage of the implant or to prevent further collapse, for example, in vertebral bodies. PMMA cements hardens via a very exothermic reaction, which may lead to bone necrosis. Additionally, the monomer of PMMA is toxic. Despite these drawbacks, PMMA cements have been increasingly used because the outcome expressed in terms of fracture stability and pain relief is very good. So far, a large number of studies have been published on the topic, ranging from the clinical use of PMMA cement [2], [3], [4], [5], to the effects of the exothermic setting reaction [6], via the selection of an adequate material [4], [7], [8], or the mechanical effects of bone augmentation [8], [9], [10]. Surprisingly, very few studies have been devoted to the rheological properties of the cement [11], [12], [13], even though the cement viscosity plays a key role in determining the force required to inject the cement, the distribution of the cement in bone, and the occurrence of cement extravasation [3], [14], [15]. More importantly, there is to our knowledge no study linking the degree of bone filling with the viscosity of the cement. In most studies, the conditions for cement injection are hardly described. These conditions include the time elapsed between the start of mixing and the injection, the injection rate, the needle size, or the syringe size. Moreover, surgeons tend to use a different powder-to-monomer ratio than the value adviced by the cement producer to prolong the injection period [5], [16]. This can lead to large changes of the physical properties of the cement, in particular the rheological and mechanical properties [16]. Furthermore, a contrasting agent is typically added to improve the visualization of the cement during injection and hence decrease the extravasation risk [2], [5], [9], [10]. Examples of contrasting agents used in vertebroplasty are barium sulfate powder [9], tungsten powder [5], tantalum powder [2], [3], [4], and an iodine solution [8]. Finally, all results depend on the structure of the patient bone which of course vary a lot from one patient to the other. Therefore, it is difficult to determine adequate conditions for bone augmentation based on clinical or cadaveric studies.
The goal of the present study is to understand what flow characteristics a cement must have to be a good bone augmentation material. For that purpose, a theoretical approach is used. Two important rheological laws are considered: the law of Hagen–Poiseuille and the law of Darcy. A particular attention is devoted to the changes of pressure during cement injection and possible risks of cement extravasation. In the second part of the study, experiments are performed and compared with theoretical predictions.
Section snippets
Theoretical
The goal of this section is to predict theoretically the behavior of the cement paste during its injection into a porous matrix. A particular attention is paid to the effects of injection parameters (flow rate, cement viscosity, matrix geometry) on the injection force and the occurrence of extravasation. The calculations are based on the law of Hagen–Poiseuille and the law of Darcy. The law of Hagen–Poiseuille describes the flow of a fluid in a cylindrical tube. The law of Darcy describes the
Experimental
The PMMA cement. “Palacos LV-40+gentamicinum” (Essex Chemie AG, Luzern, Switzerland) was used here. “Palacos LV-40” is a so-called low-viscosity bone cement [13], i.e. it has an extended low-viscosity phase. At the experimental temperature used in this study (22±1°C), the cement viscosity is low for about 3.5 min after the start of mixing [14]. In the following 2.5 min, the viscosity quickly increases and the dough becomes warm. The cement hardens after approximately 7–8 min.
Each cement package
Results
Two types of injection curves were observed (Fig. 5). First, the force was large enough to inject the cement into the filter (Fig. 5a). The curve was characterized by three parts: (i) a steep increase of force (up to 5 mm in Fig. 5a); (ii) an intermediate domain where the force increases moderately (from 5 to 23 mm in Fig. 5a); (iii) a final steep increase (after 23 mm in Fig. 5a). In the second type of injection, the force was not large enough to inject the cement into the filter (Fig. 5b). As a
Discussion
The large deformation of the syringes under loading prevented the systematic determination of the forces required for cement injection. An attempt was made to substract the deformation curve of the syringe to the measured injection curves. Unfortunately, the local maximum that was observed along the injection curves (e.g. at 500 N in Fig. 5b) was not always at the same position, which rendered the substraction useless. This local maximum was in fact due to the sudden flattening of the conical
Conclusion
In conclusion, a good agreement was seen between our analytical model, experimental results, and surgical observations. Therefore, our theoretical approach resulted in a very good model, able to predict qualitatively which factors are important for cement extravasation. Among these factors, the cement viscosity is certainly the most important, because it is the easiest to modify. The model predicts that cement extravasation can be drastically reduced by increasing the cement viscosity.
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