Proceedings of Meetings on Acoustics - ICA 2013 Montreal

Catelani et al.

Proceedings of Meetings on Acoustics Volume 19, 2013

http://acousticalsociety.org/

ICA 2013 Montreal Montreal, Canada 2 - 7 June 2013 Biomedical Acoustics Session 5aBAa: Acoustic Characterization of Biological Media 5aBAa7. Ultrasound propagation through bone fractures with reamed intramedullary nailing: results from numerical simulations Fernanda Catelani, Ana Paula M. Ribeiro, Carlos Alberto V. Melo, Wagner C. Pereira and Christiano B. Machado* *Corresponding author's address: Biomedical Ultrasound Laboratory, Estácio de Sá University, Sans Souci s/n, Nova Friburgo, 28600000, Rio de Janeiro, Brazil, [email protected] Low-intensity pulsed ultrasound stimulation (LIPUS) accelerates fracture healing, enhancing the release of inflammatory mediators and subsequent bone formation. The reamed intramedullary nailing (with the same diameter of the medullary cavity) is a surgical procedure widely used in Medicine. The aim of this work was to study ultrasound propagation inside fractures with and without reamed intramedullary nailing using 2D simulations. It was used a custom-made simulation code applied to numerical models (a 4-mm thick cortical plate, a medullary cavity with radius 4 mm with and without reamed nailing, and fracture gaps varying from 1 to 3 mm). A 1-MHz emitter was positioned above fracture center and fourteen receptor transducers were uniformly placed inside fracture gap. The acquired signals were used to estimate the time-of-flight of the first arriving signal (TOF) and the energy amplitude by means of the root mean square (RMS). TOF was slightly influenced by fracture gap variations. It was observed an increase in RMS values with the presence of metal nailing, due to the reflection in the interface water-metal. The receptors placed near cortical plates received more energy (constructive interference between the direct and lateral waves). For the case of reamed nailing, ultrasound stimulation may be intensified. Published by the Acoustical Society of America through the American Institute of Physics

© 2013 Acoustical Society of America [DOI: 10.1121/1.4800016] Received 20 Jan 2013; published 2 Jun 2013 Proceedings of Meetings on Acoustics, Vol. 19, 075093 (2013)

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INTRODUCTION Low-intensity pulsed ultrasound (LIPUS) is a non-ionizing, non-invasive and low-cost therapeutic approach to accelerate the fracture healing process [1,2]. Since the first in vivo study by Duarte in 1983 [3], several works have proved significant effects of LIPUS on fracture regeneration (for example, it can reduce the consolidation period of recent fractures in about 38% [1] and of nonunions in 85% [4]). Fracture healing is a response for a disruption in bone integrity, which promotes a sequence of biological events involving molecular signaling, reprising some embryological development phases, like intramembranous and endochondral ossification [5,6]. The mechanical stimulation (non-thermal effect) of ultrasound may play a role in this process. The underlying mechanisms are not yet well established, but some hypothesis are [7]: (1) the secretion of inflammatory cytokines and angiogenesis-inducing factors, consequently leading to a cell proliferation, collagen production, bone formation and angiogenesis; (2) formation and strengthening of callus tissue; and (3) stimulation of tissue differentiation, for example, cartilage-specific chondrocytes from mesenchymal stem cells. The intramedullary nailing (IMN) (also known as inter-locking nail) is an orthopedic treatment choice for comminuted and displaced fractures. It consists in the insertion of a metal rod into the medullary cavity of a fractured long bone. In reamed intramedullary nailing (rIMN), the metal is tightly fitted, increasing the area of contact between the nail and bone [8]. Literature shows significant results in fracture management with IMN, although rIMN may cause bone necrosis and higher infection rate [9,10]. At the present moment, there are no studies about the association of LIPUS with IMN for fracture healing acceleration. It is expected that the presence of a metal inside the medullar canal may produce reflection on the metal-soft tissue interface due to a high impedance mismatch, leading to an overall change in wave propagation inside fracture gap. Computational simulations have been widely used in acoustical science. Nowadays, according to Kaufman et al. [11], the use of ultrasound propagation softwares enables a broad range of questions to be addressed and to be further demonstrated experimentally. Ultrasound simulation methods in bone were initially applied for osteoporosis assessment. Concerning ultrasound propagation in fractures, the number of scientific works has increased [12-15]. In this context, the aim of this work was to study the basics aspects of ultrasound propagation inside fractures with and without reamed intramedullary nailing using 2D numerical simulations.

MATERIALS AND METHODS Two-dimensional (2-D) numerical simulations of ultrasound wave propagation were run using a custom-made finite-difference time-domain (FDTD) code named SimSonic2D (Laboratoire d’Imagerie Paramétrique, CNRS University Paris 6, France [16,17]), based on the Virieux scheme for discretization of linear elastic wave equations. Figure 1 shows the numerical model developed in Matlab® v. 2008A (MathWorks Inc., Natick, MA, USA), consisting of a 4-mm thick cortical plate, a medullar cavity with radius 4-mm length, and a fracture gap (0.5-mm step variations from 1 to 3 mm), with grid step of 0.05 mm. A 1-MHz (pulse length = 4.28 μs) point emitter was positioned at 4.05 mm above the fracture center and twelve point receptors were uniformly placed inside the fracture gap, with an inter-receptor horizontal distance of 1 mm, along with two other receptors at 1 and 2 mm from the cortical layer. The receptors at the cortical boundaries (3-6-9-12 and 5-8-11-14) were placed at 0.05 mm from bone.

Proceedings of Meetings on Acoustics, Vol. 19, 075093 (2013)

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FIGURE 1. Numerical model used for simulations, consisting of a 4-mm thick cortical plate, a medullar cavity (filled with a metal nailing), and a fracture gap (grid step of 0.05 mm). A point emitter is positioned at 4.05 mm above the fracture center and twelve point receptors are uniformly placed inside fracture gap, with an inter-receptor horizontal distance of 1 mm, along with two other receptors at 1 and 2 mm from the cortical layer.

The elastic constants (Cij) and density values used for modeling the mechanical response of cortical bone and the ASTM F-138 stainless steel (an austenitic metal commonly used for intramedullary nailing [18]) were obtained from the literature [16,19]. The elastic constants of water were used to model the soft tissue layer. Two situations were modeled for each fracture size: with and without reamed intramedullary nailing. Perfectly matched layers (PML’s) were implemented to avoid reflections at the boundaries. A simulation time of 18 μs was applied. The fourteen acquired signals were used to estimate the time-of-flight of the first arriving signal (TOFFAS, defined as the time location of the first signal peak - more details in [14]), and the wave amplitude by means of the root mean square (RMS), with a temporal signal window of 9.2 μs from the first arriving signal (FAS).

RESULTS Figure 2 shows a snapshot of the ultrasound propagation simulation in a 3-mm fracture with rIMN. The direct wave from the emitter touches the cortical bone, and it can be observed a lateral wave propagating in the water-bone interface with a higher longitudinal velocity (the bone acoustic longitudinal velocity) than the direct wave.


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FIGURE 2. A snapshot of the ultrasound propagation simulation in a 3-mm fracture with reamed intramedullary nailing (rIMN). When the direct wave touches the cortical bone, it is possible to observe lateral waves which propagate in the water-bone interface with a higher longitudinal velocity than the direct wave.

The received signals from receptors 5 (with and without metal) and 14 (with metal) are shown in Figure 3. The FAS is marked with an asterisk. In Figures 3(a) and 3(b), it is possible to observe a difference in signals between the situations "with metal" and "without metal". When the metal is present in the intramedullary canal (receptor 5), a second echo appears (Figure 3(b)), being no longer identified by receptor 14 (Figure 3(c)).

FIGURE 3. Received signals from (a) receptor 5 (with metal nailing); (b) receptor 5 (without metal nailing); and (c) receptor 14 (with metal nailing). The first arriving signal (FAS) is identified with an asterisk.


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The results of TOFFAS for each fracture length with the presence of metal nailing are depicted in Figure 4. As it was expected, TOFFAS increases as the receptor distances from the emitter increases. The variation in fracture length does not seem to vary significantly the wave time-of-flight. An interesting aspect is that TOFFAS is sensitive to fracture length at receptors 12 and 14. Snapshots from simulations with a fracture of 1-mm and 3-mm length (at the same moment), are depicted in Figure 5(a) and 4(b), respectively.

FIGURE 4. TOFFAS results for each receptor and for different fracture lengths (with metal nailing).

FIGURE 5. Snapshots from simulations with a fracture of (a) 1-mm and (b) 3-mm length, at the same time period.

Figure 6 shows the RMS amplitude results (14 receptors) for fractures lengths of 1, 2 and 3 mm, with and without metal nailing. It is possible to observe an increase in RMS values with increasing fracture length. The presence of metal nailing also increases the signal energy. Another point to be highlighted is that the RMS values for the central receptors (numbers 4, 7, 10 and 13) and receptors near the cortical bone (3, 6, 9, 12 - left, and 5, 8, 11 and 14 - right) correspond to the minimums and maximums in the curves, respectively.


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FIGURE 6. RMS values (14 receptors) for fractures lengths of 1, 2 and 3 mm, with and without metal nailing.

DISCUSSION AND CONCLUSIONS This work used simulations to analyze the basic propagation aspects of ultrasound in fractures with the presence of a reamed intramedullary nailing. A first observation that could be made is the propagation of lateral waves on the cortical boundaries inside the fracture gap, which arrives faster to the metal than the direct wave (Figure 2). The lateral wave (or head wave) is a linear wavefront connecting the refracted to the reflected wavefront. It is generated when an acoustic wave propagating in a fluid reaches the interface fluid-solid, and it presents the same longitudinal velocity from the solid, making an angle șc with the interface [20,21]. Others have shown that for plate thicknesses larger than the compressional wavelength in bone, the first arriving signal corresponds to the radiation of this lateral wave, with the same bone longitudinal velocity [20,22]. With the presence of a metal nailing, the received signals showed two pulses, one from the emitted wave, and the other from the reflection in the water-metal interface (Figure 3(b)). Receptors close to the metal (numbers 12, 13 and 14) detected a larger first pulse, from which it can be hypothesized that the emitted and reflected waves were summed by a constructive interference (Figure 3(c)). As it was expected, the TOFFAS increases as the receptor distances from the emitter (Figure 4). In the receptors close to the metal, a slight difference was observed for receptors 12 and 14, maybe because of the wave interferences between the lateral wave and its reflection at the metal. The receptors from the center of the fracture receive the FAS some microseconds latter than the receptors close to cortical bone (Figure 5). These results could suggest that, during an ultrasound stimulation by LIPUS, the cells localized at the cortical fragments of the fracture may receive more energy (interferences between the lateral and the direct wave). Figure 6 depicted RMS values for increasing values of fracture lengths, with and without metal nailing. Some points are worthy of attention: (1) the presence of a metal nailing may increase the acoustic energy inside the fracture, mainly for the sites close to the cortical bone (maximums of the curve); (2) the greater the fracture, the greater the RMS value (energy amplitude) and it is clearer with the presence of the metal. It could be a valuable information for therapy. Would the presence of metal nailing (leading to an increase of ultrasound energy) delay fracture healing? Would this increase in ultrasound energy be sufficiently high to damage the forming callus tissue? Could the stimulation by LIPUS be more efficient near cortical boundaries of the fracture? To answer these questions, further experimental studies are needed to address in vitro and in vivo situations. These simulations do not take into account absorption, therefore the results obtained for acoustic energy are due mainly by scattering. However, one may conclude that most of the energy emitted by the transducer would be absorbed during tissue propagation, depending highly on the wave frequency. Another limitation is the simple


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approach of the numerical model. It would be interesting for future works the use of more realistic geometric models from images originated, for example, from scanning acoustic microscopy (SAM) [23] and microtomography [24]. In conclusion, this simulation enabled the analysis of the ultrasound propagation in a simple fracture numerical model, with the inclusion of a reamed metal nailing. These results suggest that the presence of a metal inside the intramedullary canal may increase the acoustic energy inside the fracture gap, and the cortical boundaries may receive more acoustic energy due to the propagation of lateral waves, and these aspects have to be taken into account when planning ultrasound therapy. A next step would be the acquisition of experimental results with phantoms and in animal models in vitro.

ACKNOWLEDGMENTS The authors would like to thank FAPERJ (Rio de Janeiro - Brazil) and Estácio de Sá University for financial support, and Dr. Pascal Laugier (Laboratoire d'Imagerie Paramétrique, CNRS - University Paris 6, France) for scientific collaboration.

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