We focus on the problem of evaluating the velocity field outside a solid object moving in an incompressible Stokes flow using the boundary integral formulation. For points near the boundary, the integral is nearly singular, and accurate computation of the velocity is not routine. One way to overcome this problem is to regularize the integral kernel. The method of regularized Stokeslet (MRS) is a systematic way to regularize the kernel in this situation. For a specific blob function which is widely used, the error of the MRS is only of first order with respect to the blob parameter. We prove that this is the case for radial blob functions with decay property ϕ(r)=O(r−3−α) when r→∞ for some constant α>1. We then find a class of blob functions for which the leading local error term can be removed to get second and third order errors with respect to blob parameter. Since the addition of these terms might give a flow field that is not divergence free, we introduce a modification of these terms to make the divergence of the corrected flow field close to zero while keeping the desired accuracy. Furthermore, these dominant terms are explicitly expressed in terms of blob function and so the computation time is negligible.

The intraoperative assessment of tumor margins of head and neck cancer is crucial for complete tumor resection and patient outcome. The current standard is to take tumor biopsies during surgery for frozen section analysis by a pathologist after H&E staining. This evaluation is time-consuming, subjective, methodologically limited and underlies a selection bias. Optical methods such as hyperspectral imaging (HSI) are therefore of high interest to overcome these limitations. We aimed to analyze the feasibility and accuracy of an intraoperative HSI assessment on unstained tissue sections taken from seven patients with oral squamous cell carcinoma. Afterwards, the tissue sections were subjected to standard histopathological processing and evaluation. We trained different machine learning models on the HSI data, including a supervised 3D convolutional neural network to perform tumor detection. The results were congruent with the histopathological annotations. Therefore, this approach enables the delineation of tumor margins with artificial HSI-based histopathological information during surgery with high speed and accuracy on par with traditional intraoperative tumor margin assessment (Accuracy: 0.76, Specificity: 0.89, Sensitivity: 0.48). With this, we introduce HSI in combination with ML hyperspectral imaging as a potential new tool for intraoperative tumor margin assessment.

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