近年来，瞬态弹性成像技术已经成为了一种在体表征软组织弹性性质的临床新方法。该方法在脑部疾病和外伤、女性乳房疾病、甲状腺癌、肝脏纤维化等疾病的诊断中发挥着重要作用。超声辐射力弹性成像技术（SSI）作为近几年才被商品化的瞬态弹性成像方法，目前受到了广泛关注。本文着眼于瞬态弹性成像方法背后的非线性力学问题，并且着重研究利用超声辐射力弹性成像技术表征软组织的非线性弹性参数的方法。具体研究了由声辐射力诱发的剪切波在有变形的超弹性软组织中的传播情况。并基于Demiray-Fung本构模型首次推导出了剪切波速与软组织超弹性参数之间的解析表达式。在此基础上，本文建立了一种通过测量生物软组织不同变形程度下的波速从而得到超弹性参数的反方法，并利用反问题中条件数的概念和有限元模拟分析了反问题解的性质，包括解的存在性、唯一性和稳定性。为了验证该新方法的有效性，本文进行了基于猪肝脏的体外实验，所测得的超弹性特性参数和文献中报道的数值相符。进一步设计了在体实验，用上述方法成功测量了女性胸部组织和人体脚跟脂肪垫组织的非线性弹性性质，验证了该方法应用于在体检测的可行性，并且探讨了该方法在临床诊断上的应用价值。作为新方法的重要应用，本文首次利用SSI技术测量得到了脑组织的弹性和超弹性参数，并分析了方法的可靠性，结果有望为脑部疾病的检测以及虚拟手术技术的发展提供有效的方法和数据。本文的最后，我们将上述发展反方法的过程推广到了其他超弹性本构模型。
Transient elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which is important for the disease diagnosis, e.g. the detection of breast and thyroid cancer and liver fibrosis. This thesis investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described using the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach has been established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g. the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and ex vivo experiments conducted on three pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method to measuring the in vivo nonlinear elastic properties of soft tissues. As a significant application of our new method, we acquire elastic and hyperelastic parameters of brain tissue using SSI for the first time, which may provide essential data for the Virtual Surgery Simulation and clinical diagnosis. Generalization of the inverse analysis to other material models and the implication of the results reported here to clinical diagnosis have been discussed.
