Question

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Yazar: N. G. McCrum, C. P. Buckley, C. B.. Bucknall, Clive B. Bucknall, C. B. Bucknall

Part Viscoelasticity Page 179

Now suppose a tube of poly(methyl methacrylate) (PMMA) with lenght 200 mm, diameter 20 mm, and wall thickness 1 mm, is subjected to sinosoidal torsional oscillations at 1 Hz, in which the relative rotation of its ends will be +/- 10o . Before the oscillations commence the tube is in equilibrium with air at 20 oC. Predict the initial rate of temperature rise and the final equilibrium temperature. The density and specific heat of PMMA are 1.2 kg/cm3 and 1450 J/kg-K, respectively. The heat transfer coefficent for convective heat transfer from the external surface of the tube to air at about 20 oC may be assumed to be 10 W/K-m2 . The heat loss from the inside surface can be neglected. The loss modulus of PMMA at the given deformation conditions is 137 MPa (Hint: use the first law of thermodynamics. Check how strain is defined for a tube in torsional shear deformation). Note that this is a torsional deformation

Answer 1

Abstract

The spinal column is the most common site for bone metastasis. Vertebral metastases with instability have historically been treated with corpectomy of the affected vertebral body and adjacent intervertebral discs, and have more recently been treated with separation surgery. With demographics shifting towards an elderly population, a less-invasive surgical approach is necessary for the repair of vertebral defects. We modified a previously reported expandable hollow cage composed of an oligo[poly(ethylene glycol) fumarate] (OPF) containment system that could be delivered via a posterior-only approach. Then, the polymer of interest, poly (methyl methacrylate) (PMMA) bone cement, was injected into the lumen of the cage after expansion to form an OPF/PMMA cage. We compared six different cage formulations to account for vertebral body and defect size, and performed a cage characterization via expansion kinetics and mechanical testing evaluations. Additionally, we investigated the feasibility of the OPF/PMMA cage in providing spine stability via kinematic analyses. The in-vitro placement of the implant using our OPF/PMMA cage system showed improvement and mechanical stability in a flexion motion. The results demonstrated that the formulation and technique presented in the current study have the potential to improve surgical outcomes in minimally invasive procedures on the spine.

Keywords: spine; expandable cage; kinematic testing; minimally invasive surgery; OPF formulation

1. Introduction

The spinal column is the most common site for bone metastasis, with the latter occurring in one third of cancers [1,2,3,4]. Other pathologies including fractures and infection can also affect the vertebrae, increasing the risk for vertebral collapse or nervous tissue injury, and reducing spinal stability [5]. Vertebral collapse with instability, from tumors, trauma, or infections, has historically been treated with corpectomy of the affected vertebral body and adjacent intervertebral discs. This defect can then be replaced with structural autografts, allografts, or a variety of titanium or polymeric cages [6,7] with the purpose of reducing pain, decompression of neural elements, spinal stabilization, and resection of the malignancy [8]. Even though these materials have specific advantages, they have their own limitations that may result in postsurgical complications and negatively affect the intended outcomes [9,10,11]. In addition, these open surgical procedures require a significant surgical exposure, typically through a thoracotomy or costotransversectomy, which is highly invasive [12] particularly in elderly and frail patients, posing greater surgical risks and a challenging recovery [13]. With demographics shifting towards an elderly population, a less-invasive surgical approach is necessary for the repair of vertebral defects so commonly present in this population [14].

To achieve this goal, a polymeric expandable cage composed of oligo[poly(ethylene glycol) fumarate] (OPF) was previously developed that could be delivered via a posterior-only surgical approach [15]. The OPF hollow cage can expand to a predetermined size within a surgical time frame making it possible to perform a less-invasive surgery compared with current surgical approaches, and minimizing associated complications with the procedure.

An important limitation of our previous study was the size of the hollow cage, which did not conform to in-vivo measurements of a defect. Thus, in the current study, we modified our polymeric formulations to allow for a more accurate cage size. We then performed expansion kinetics, augmented the cages with poly(methyl methacrylate) (PMMA) to form an OPF/PMMA cage for spine stability, and conducted kinematic analysis on a cadaveric spine as a proof-of-concept to evaluate the range of motion (ROM) and the effect of corpectomy and treatment. Therefore, the purpose of the current study was twofold: first, to optimize the cage formulations to account for vertebral body and intervertebral discs’ defect size, and perform a characterization via expansion kinetics and mechanical testing evaluations; second, to investigate the feasibility of the OPF/PMMA cage in providing spine stability via kinematic analyses.

2. Materials and Methods

2.1. OPF Expandable Cage

2.1.1. OPF Synthesis

OPF was synthesized using fumaryl chloride (Sigma Aldrich Co., Milwaukee, WI, USA) and poly(ethylene glycol) (PEG; Sigma Aldrich Co., Milwaukee, WI, USA) with an average molecular weight of 2000 Da, as previously described [15]. Briefly, PEG (100 g) was placed in a two-neck flask in an ice bath and purged with nitrogen for 10 min; this process was repeated three times. Then, 1000 mL of anhydrous methylene chloride (CH2Cl2, Fisher, Pittsburgh, PA, USA) and molecular sieves (3Å, beads 4-8 mesh; Sigma Aldrich Co., Milwaukee, WI, USA) were added to the flask to dissolve the PEG and remove any water. Potassium carbonate powder (K2CO3; Sigma Aldrich Co., Milwaukee, WI, USA) (40 g) was then added, with a subsequent dropwise addition of fumaryl chloride (1:1 in molar ratio to PEG) under stirring conditions. The reaction was kept at room temperature for 48 h and then filtered to remove the solid K2CO3 powder. The filtrate was concentrated by rotary evaporation to remove any CH2Cl2 remnant and precipitated in 1 L diethyl-ether at −20 °C overnight. The precipitate was then filtered and fully dried in vacuum. Before storing the synthesized OPF at −20 °C for future use, gel permeation chromatography (GPC) was performed to evaluate its molecular weight. Briefly, 34 mg of OPF was dissolved in 3.5 g of tetrahydrofuran (THF) and the solution was run four times to obtain an average molecular weight.

2.1.2. Fabrication and Expansion of Cages

The synthesized OPF of molecular weight (Mn) of ~4000 Da was used to fabricate cylindrical hollow cages of 12 mm in diameter. Six different formulations were used to improve the rigidity and failure of the hollow cages upon expansion (Table 1). 1-Vinyl-2-pyrrolidinone (NVP), as a crosslinker, was provided from Sigma Aldrich Co., Milwaukee, WI, USA.

Table 1. Six different formulations implemented to make oligo[poly(ethylene glycol) fumarate] (OPF) hollow cages. NVP: 1-Vinyl-2-pyrrolidinone.

For each formulation, OPF, phenyl bis (2,4,6-trimethylbenzoyl)-phosphine oxide (BAPO) as a photo initiator, and CH2Cl2 were combined into a flask according to Table 1. The mixture was vortexed until all solutes were dissolved. As a cylindrical mold, a metal rod of 12 mm in diameter was fabricated to construct the inner diameter of the OPF hollow cage. After greasing the metal rod, the resin was added to the mold. The mold containing the resin was placed in a UV oven to initiate crosslinking. After 1 h, the center metal rod of the mold was removed and the hollow cage placed back in the UV oven for an additional 2 h. The cage was placed in the fume hood at room temperature overnight to fully dry.

Sodium methacrylate (SMA) was then physically infiltrated into the network for faster expansions of the OPF hollow cages. The crosslinked OPF cages were soaked for 8 h in ddH2O containing 0.5% SMA. Cages were subsequently dried overnight in a 70 °C oven by placing the expanded hollow cages around the metal mold. Because drying of the 12-mm-diameter cages in the oven induced shrinking, the cages were dried on an 8-mm, metal-rod mold, leading to a thicker, cylindrical, and uniform cage (Figure 1). Expansion kinetics of the cages was then evaluated by immersion in 50 mL of phosphate buffered saline (PBS) at 37 °C. Mass, length, and diameter were measured at serial time points from 0–100 min. The averaged sample dimensions were as follows: for pre-expansion, internal diameter was 8.07 mm, wall thickness was 0.78 mm, and length was 10 mm. After expansion (after 100 min), the internal diameter increased to 17.63 mm, the wall thickness changed to 1.74 mm, and the length increased to 21.39 mm.