A position- and time-dependent pressure profile to model viscoelastic mechanical behavior of the brain tissue due to tumor growth

This study proposed a computational framework to calculate the resultant position- and time-dependent pressure profile on the brain tissue due to tumor growth. A finite element (FE) patch of the brain tissue was constructed and an inverse dynamic FE-optimization algorithm was used to calculate its viscoelastic mechanical properties under compressive uniaxial loading. Two patient-specific post-tumor resection FE models were input to the FE-optimization algorithm to calculate the optimized 3rd-order position-dependent and normal distribution time-dependent pressure profile parameters. The optimized viscoelastic material properties, the most suitable simulation time, and the optimized 3rd-order position- and -time-dependent pressure profiles were calculated.

Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. STATEMENT OF SIGNIFICANCE: Although the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation).

Inverse dynamic finite element-optimization modeling of the brain tumor mass-effect using a variable pressure boundary

BACKGROUND AND OBJECTIVE

Statistical atlases of brain structure can potentially contribute in the surgical and radiotherapeutic treatment planning for the brain tumor patients. However, the current brain image-registration methods lack of accuracy when it comes to the mass-effect caused by tumor growth. Numerical simulations, such as finite element method (FEM), allow us to calculate the resultant pressure and deformation in the brain tissue due to tumor growth, and to predict the mass-effect. To date, however, the pressure boundary in the brain tissue due to tumor growth has been simply presented as a constant profile throughout the entire tumor outer surface that resulted in discrepancy between the patient imaging data and brain atlases.

METHODS

In this study, we employed a fully-coupled inverse dynamic FE-optimization method to estimate the resultant variable pressure boundary due to tumor resection surgery. To do that, magnetic resonance imaging data of two patients' pre- and post-tumor resection surgery were registered, segmented, volume-meshed, and prepared for fully-coupled inverse dynamic FE-optimization simulations. Two different pressure boundaries were defined on the brain cavity after tumor resection including: a) a constant pressure boundary and b) a variable pressure boundary. The inverse FE-optimization algorithm was used to find the optimum constant and variable pressure boundaries that result in the least distance between the surface-nodes of the post-surgery brain cavity and pre-surgery tumor.

RESULTS

The results revealed that a variable pressure boundary causes a considerably lower mean percentage error compared to a constant pressure one; hence, it can more effectively address the realistic boundary in tumor resection surgery and predict the mass-effect.

CONCLUSIONS

The proposed variable pressure boundary can be a robust tool that allows batch processing to register the brains with tumors to statistical atlases of normal brains and construction of brain tumor atlases. This approach is also computationally inexpensive and can be coupled to any FE software to run. The findings of this study have implications for not only predicting the accurate pressure boundary and mass-effect before tumor resection surgery, but also for predicting some clinical symptoms of brain cancers and presenting useful tools for APPLICATIONs in image-guided neurosurgery.