Impact Testing of a Surrogate Human Head Model for Correlation of Bulk Acceleration to Intracranial Pressure

Abstract

This research focused on correlating the macroscopic blunt impact conditions to the internal pressure developed in the coup and contrecoup regions for water and gelatin-filled surrogate human head models. Obtaining a relationship between bulk acceleration and localized internal pressure of a human head surrogate will allow for correlation to the damage done on tissue level length scales. Internal pressure information also allows for investigation into the possibility of cavitation inside the head phantom, a potential damage mechanism for TBI. Two separate 3D printed head models were studied: the coronal model simulates a frontal impact and the sagittal simulates a side impact. A dynamic impacting test platform was designed and manufactured in-house to deliver varying controlled impact conditions. The coup and contrecoup are the measured regions of interest due to the potential for the highest magnitude pressure spikes. A range of experiments were performed measuring the resulting bulk acceleration and internal fluid pressure response over varying impact velocities for both water and gelatin filled surrogates. The experimental results were compared with an ANSYS Explicit Dynamics simulation. The resulting pressure in the coup and contrecoup region are recorded for varying impact velocities. The experiment shows that at the maximum impact velocity of 5.5 m/s in the frontal impact of the water filled model, the coup pressure is approximately + 96 kPa while the contrecoup is – 47.3 kPa. The finite element model shows reasonably good agreement with the coronal experimental results for the 5.5 m/s impact condition with a coup pressure of + 102 kPa and a contrecoup pressure of  – 68 kPa.

Appendices

Appendix

Experimental Setup

(See Fig. 16).

Fig. 16

Experimental Setup a Pendulum Impactor and b Coronal Head model equipped with coup/contrecoup sensors and two accelerometers

Mesh Convergence Study

A mesh convergence study was performed for both the coronal and sagittal plane models. Several simulations were run using the 80-degree impact conditions while varying element size from 14 to 3 mm. Figure 17a and b shows the maximum pressure developed in the coup and contrecoup region for the coronal and sagittal models, respectively. As the element count was increased the recorded pressure in the regions of interest was tracked until convergence was assumed within an acceptable tolerance of 5%. For the coronal model, the mesh was assumed to converge at an element size of 3 mm. For the sagittal model, the mesh size was assumed to have converged for an element size of 4 mm. The simulation time for the coronal model took 63 min. The time for one sagittal simulation to complete was 28 min. The approximate times that each simulation took for the respective element size are included in Fig. 17a and b.

Fig. 17

Finite Element Model mesh convergence study (all simulations run with 14 cores at an impact velocity of 5.5 m/s) for a the Coronal model and b the Sagittal model

Characterization of Dynamic Test Platform

The characterization of the impacting test platform is necessary for correlation of the impact conditions to the developed internal pressure. It is also important for the proper representation of the initial conditions for the FEM model. Using rigid body dynamics, the mass and inertia properties for both the pendulum arm and the impact ball can be considered and included in the formulation of the equation of motion. Solving the equation of motion for the acceleration and velocity at the position of the impact ball will give all necessary input parameters for the study. Figure 18 gives a schematic of the test platform containing the two rigid bodies.

Fig. 18

Schematic of the dynamic impact system used to derive the equation of motion

Half the length of the pendulum arm is$L=0.4572 m$. Body A has a mass of 2.4 kg and an inertia${I}_{z{z}_{A}}=0.49 kg{m}^{2}$. Body B has a mass of 0.22 kg and an inertia of${I}_{z{z}_{B}}=1.2*{10}^{-4} kg{m}^{2}$. The generalized active forces and inertia forces are given by Eqs. (8) and (9), respectively. Kane’s method is given by Eq. (10) and is developed from Euler’s First and Second Laws with consideration of the total work done on the system [35].

$$F_{i} = \sum\limits_{K}^{{bodies}} {\left( {\Sigma F} \right)_{K} } \cdot \frac{{\partial V_{K} }}{{\partial \mathop {q_{i} }\limits^{.} }} + \left( {\Sigma M} \right)_{K} \cdot \frac{{\partial \omega _{{NK}} }}{{\partial \dot{q}_{i} }}$$

(8)

$$F_{i}^{*} = \sum\limits_{K}^{{bodies}} {m_{K} } \dot{V}_{K} \cdot \frac{{\partial V_{K} }}{{\partial \dot{q}_{i} }} + \frac{{dH_{{KK}} }}{{dt}} \cdot \frac{{\partial \omega _{{NK}} }}{{\partial \dot{q}_{i} }}$$

(9)

$${F}_{i}-{F}_{i}^{*}=0$$

(10)

Using the above equations, the equation of motion for the system is derived as shown in Eq. (11).

$$-2gL{m}_{B}\mathrm{sin}\left({q}_{1}\right)-gL{m}_{A}\mathrm{sin}\left({q}_{1}\right)-\left({{I}_{ZZ}}_{A}+{{I}_{zz}}_{B}+{m}_{A}{L}^{2}+4{m}_{B}{L}^{2}\right){\ddot{q}}_{1}=0$$

(11)

A rigid body dynamics simulation software called Autolev was used to solve the equation of motion for the position, velocity, and acceleration of body B for initial conditions ${q}_{1}={20}^{^\circ }$ to ${q}_{1}={80}^{^\circ }$ in increments of ${10}^{^\circ }$. The acceleration and velocity of the impact ball were calculated at the moment of impact when ${q}_{1}={0}^{^\circ }$. To verify the dynamic simulation, digital image correlation (DIC) was utilized with a Photron FASTCAM high-speed camera. For each system initial condition, a high-speed video was taken of the impact ball at the moment of impact (${q}_{1}={0}^{^\circ }$). The results of the rigid body dynamics simulation and the high-speed camera DIC analysis are shown in Fig. 19 [25].

Fig. 19

a Comparison of the rigid body dynamic simulation and digital image correlation for impact velocity at specified drop angle and b Six images taken 1 ms apart during an impact event

The rigid body dynamic simulation and the DIC agree well with one another. At drop angels of 20°, 40°, 70°, and 80°, the calculated velocity is within 4% of the observed value. The largest difference is at a drop angle of 60° where the calculated value is within 9% of the observed value. Discrepancies in the impact velocity can be attributed to errors associated with the digital angle measure device.