Constitutive parameter identifiability and the design of experiments for applications in breast biomechanics
Breast cancer is the leading cause of cancer-related death in females, affecting 1 in every 10 women worldwide. Breast conserving therapy (BCT) is the most common procedure used for treating early-stage invasive breast cancers, and involves localised excision of tumorous lesions followed by radiotherapy. Clinical imaging modalities used for diagnosing the disease and performing pre-operative planning (e.g. MRI) acquire information with the patient positioned differently to that assumed during the actual treatment procedures (where images of the internal configuration of the breast are unavailable). These represent some of the biggest challenges that surgeons face when treating the disease, which currently results in incomplete excision in 20 % to 40 % of BCT patients. Patient-specific biomechanical models of the breast have the potential to address these challenges as they allow the different loading conditions imposed on the breast during diagnostic and pre-operative imaging to be simulated. This information can be used to help register regions of interest between the medical images, while also allowing the specific location of tumours to be predicted during treatment procedures. To obtain reliable predictions of tissue movement, the models need to be personalised for the specific geometry, composition, and arrangement of an individual’s breast tissues. Robust calibration of the constitutive parameters describing the mechanical behaviour of these tissues is also required. Determining these parameters is non-trivial due to the difficulty in knowing which calibration experiments are required to obtain reliable parameter estimates. This thesis begins by describing a set of studies aimed at validating the mechanical modelling of heterogeneous layered soft bodies. Two layered arrangements were considered: two adjacent layers with similar thickness (seen, for example, in the arrangement of adipose and muscle tissue in the breast); and a thin membrane attached to a thicker underlying layer (seen, for example, in the arrangement of skin and its underlying tissues). The modelling of the first arrangement was validated by creating and performing experiments on a soft cantilever phantom composed of two layers, each with a different stiffness. The modelling of the second arrangement was validated by creating a composite phantom, composed of a thin rubber membrane bonded to a block of silicone gel. Biaxial stretch and indentation experiments were performed on the individual layers of the phantom, as well as on the composite. Practical issues surrounding the calibration of model parameters were also investigated including the quantification and visualisation of parameter identifiability, and the use of multiple experiments for improving parameter identifiability. Heterogeneous biomechanical models of the breast were developed to aid the registration of diagnostic and pre-operative MRI, and to predict the location of tissue landmarks during treatment procedures. The models were calibrated by identifying the constitutive parameters of the adipose, muscle, and skin tissues of the breast that optimised the registration of these medical images. The results showed that the models could register the diagnostic and pre-operative MRI with errors <5mm. However, the results indicated that the models required further improvement to meet the accuracy requirements for predicting the location of tissue landmarks without image guidance. The development of a model-based design of experiments procedure for determining optimal experimental designs for calibrating biomechanical model parameters was also described. This procedure was applied to determine the optimal orientation in which to image the breast surface under gravity loading to maximise the identifiability of breast tissue constitutive parameters. The ability of the optimal design to provide precise predictions of tissue movement was also investigated. While this approach was demonstrated for identifying model parameters of breast biomechanical models, this technique may be useful for a wide range of biomechanics applications.
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