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Biomechanics

Biomechanics - Poster Session E

Poster P19 - Nonlinear Resonant Acoustic Spectroscopy Characterization of Dry Cranial Sutures

Saturday, October 26, 2024
10:00 AM - 11:00 AM EST
Location: Exhibit Hall E, F & G

Introduction:  Cranial sutures are fibrous joints that connect the bones of the skull, allowing for growth and flexibility. Abnormal growth or premature fusion of these sutures, as seen in conditions like craniosynostosis, can lead to significant health issues affecting skull shape and brain development. While the static linearized properties of sutured bones have been widely studied in the literature, there has not been any characterization of nonlinear elastic behavior of sutures. Understanding the nonlinear acoustic properties of cranial sutures could provide new insights into their behavior and may find potential applications in diagnostics. It is well known in structural mechanics that micro-damage or close interface/contact in the micro-structure is the source of hysteretic nonlinearity and sutures are considered as interface/contact between bone regions, hence they may yield such nonlinear behavior. This study utilizes Nonlinear Resonant Acoustic Spectroscopy (NRAS) to investigate the acoustic properties of cranial sutures, aiming to characterize their nonlinear behavior and correlate it with their micro-structural features. The results present opportunities spanning from leveraging such suture nonlinearities for diagnostic purposes to understanding the nonlinearities coming from the skull in transcranial ultrasound.

Materials and

Methods:  NRAS is a vibration-based technique used to measure the hysteretic nonlinearity parameter $\alpha_f$. Hysteretic nonlinearity is manifested as a nonlinear dependence of stress on strain in a rate-dependent fashion, or mathematically the second term in the equation (1)

Using NRAS, $\alpha_f$ is estimated based on the shift in resonance frequency as the excitation amplitude increases (Fig. 2(a) $\frac{f-f_0}{f_0}=\alpha_f \Delta \varepsilon$, where $\Delta \varepsilon$ is peak strain amplitude in the suture region). To this aim, piezoceramic disks were employed to excite the bone segments and a Laser Doppler Vibrometer (LDV) was used to measure the vibration response (Fig. 1(a) ). Bones were excited at the frequency range around their second flexural vibration mode. Samples were obtained from two human skulls: sutured bones (S1-S6) from a 54-year-old male and non-sutured bones (P1, P2 and O1) from an 87-year-old male. See Fig. 1(b) for the location of bone segments and sutures. Micro-CT scans were performed on the bone segments to infer micro-structure and suture contact geometry

Results, Conclusions, and Discussions: Sutured bones (S3-S6) exhibit significant hysteretic nonlinearity, as evidenced by a linear decrease in resonance frequency with increasing strain amplitude (Fig. 2(a) and 2(b) ). In contrast, the non-sutured bones (P1, P2, O1) do not show nonlinearity. From Fig. 2(b) we observe that the non-sutured bone (P1) shows no decrease in the resonance frequency compared to the sutured bone (S5). This observation aligns with existing literature on the relationship between micro-structure and hysteretic nonlinearity, where it is well established that closed cracks or contacts contribute to hysteretic nonlinearity which can open/close during high voltage amplitude excitations, while porosity does not. Among the different suture regions evaluated, the sagittal (S4, S5), squamous (S3), and lambdoidal (S6) sutures demonstrate nonlinearity, whereas the coronal sutures (S1, S2) do not. Micro-CT images reveal that coronal sutures do not show close contact between bone regions and appear porous, whereas the sagittal, squamous, and lambdoidal sutures display close contact geometry (Fig. 4). These observations also confirm that the hysteretic nonlinearity in cranial bones is solely attributed to the presence of sutures, as non-sutured bones, which are predominantly porous, do not exhibit close contact or interfaces in their structure. Although the sutured bones and non-sutured bones were not extracted from the same skull, they remain comparable. This is because the non-sutured bones were taken from an older skull, and literature reports that nonlinearity tends to increase with age. The nonlinearity parameter $\alpha_f$ correlates well with micro-damages and suture contact conditions inferred from micro-CT images, indicating that the observed nonlinearity is related to the micro-structural characteristics of the sutures. Our results indicate that sutures are a source of nonlinearity in skull dynamics, which can have various implications spanning from the leveraging of that nonlinearity in diagnosis to understanding the sources of nonlinearity in medical ultrasound.

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