Comparison of numerical approaches for inverse Laplace transform by the example of intraocular pressure determination
Comparison of numerical approaches for inverse Laplace transform by the example of intraocular pressure determination
复制标题
以眼压测定为例比较拉普拉斯逆变换的数值方法
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
kspfrolova
中科院分区：
文献类型：
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作者：
Kseniia P. Frolova;E. Vilchevskaya;W. uller;Wolf;Weiss;kspfrolova
现有人眼模型的修改和新模型的创建，考虑到越来越多的巩膜参数，使眼科医生能够更合理和定性地矫正由创伤，疾病或老化引起的眼部疾病。在大多数现有的模型中，巩膜的粘度被忽略。原因是直接测量巩膜粘度会引起技术问题。然而，巩膜具有粘弹性[1]。本文研究了一种确定巩膜剪切粘度的方法，该方法基于数学建模结果与玻璃体内注射（注射到眼球房水中）后几分钟内眼内压（IOP）离散测量的实验数据的比较[2]。我们建议通过应用拉普拉斯变换来获得与时间相关的IOP。在当前情况下，需要数值逆拉普拉斯变换。基于数值方法[3]、[4]、[5]，可以应用几个近似标准。本文的主要思想是以确定IOP为例，比较基于三种不同节点和权值集的拉普拉斯反变换求积公式的数值方法。
The modi cation of existing human eye models and the creation of new ones, which take into account an increasing number of sclera parameters, allow ophthalmologists to correct disorders of the eye created by trauma, disease, or aging more rationally and qualitatively. The viscosity of the sclera is ignored in most existing models. The reason is that direct measurements of the sclera viscosity cause technical problems. However, the sclera has viscoelastic properties [1]. This paper investigates a method for determining the shear viscosity of the sclera based on a comparison of results from mathematical modeling with experimental data from discrete measurements of the IntraOcular Pressure (IOP) during several minutes after intravitreal injection (injection into the eyeball aqueous humor) [2]. We propose to nd the time-dependent IOP by applying Laplace transforms. In the present case a numerical inverse Laplace transform is required. Several approximation criteria can be applied based on the numerical approach [3], [4], [5]. The main idea of this paper is to present a comparison of numerical approaches based on three di erent sets of nodes and weights for a quadrature formula for the inverse Laplace transform by the example of IOP determination.