# Quantitative Optical Coherence Elastography for Robust Stiffness Assessment
## 1 Introduction  
Breast conserving surgery is one of the most frequently practiced surgical procedures for the treatment of breast cancer. In breast conserving surgery, a negative surgical margin is essential to reduce the risk of local recurrence and reduce the need for repeated surgery. The capability to assess surgical margin intraoperatively can benefit both patients and clinicians [1]. It is known that cancerous breast tissue usually has higher stiffness compared to normal breast tissue [2]. Therefore, manual palpation is frequently used in clinical examination of breast cancer. Elastography techniques based on cross-sectional imaging modalities, such as ultrasound imaging and magnetic resonance imaging (MRI), have also been used for breast imaging [3, 4]. Optical coherence tomography (OCT), a microscopic tomographic imaging modality based on low coherence light interferometry, has found applications in breast cancer management [5, 6, 7, 8]. A functional extension of OCT, optical coherence elastography (OCE) provides mechanical contrast and can be used to differentiate cancerous breast tissue and normal breast tissue [9, 10, 11]. Compared to other elastography technologies, OCE has much higher spatial resolution and allows mechanical characterization on a small volume of breast tissue. An OCE instrument can be fabricated using fiber-optic components and can be integrated into a handheld probe that is compact and lightweight [12]. Therefore, an OCE instrument will allow convenient assessment of tissue malignancy for margin assessment during breast conserving surgery, and has the potential to significantly improve patient outcome by ensuring negative margin. However, conventional OCE that only tracks the deformation of the sample is inherently qualitative because the reaction force considered as the mechanical excitation is unknown. Therefore, the results obtained from different OCE measurement sessions can vary significantly for the same sample, making it challenging to establish reliable criteria for tissue classification. In our laboratory, we recently developed and validated a unique fiber-optic quantitative OCE (qOCE) technology [13, 14]. For mechanical characterization, the qOCE probe is translated to compress the sample. The OCT signal is obtained from the qOCE probe during the indentation and analyzed for simultaneous quantification of reaction force (\(F\)) and depth resolved sample displacement (\(d(z)\)) that is considered as the material's response to the excitation.  
Nevertheless, quantitative extraction of material properties remains challenging because the results of qOCE characterization (reaction force and displacement field established within the sample) not only depend on material properties, but also depend on the geometric boundary condition [15; 16]. In this manuscript, we describe a method that achieves robust stiffness assessment using qOCE data (\(F\) and \(d(z)\)) and validate the method using experimental data. The capability to measure stiffness under different boundary conditions is crucial for intraoperative assessment of tumor margin in situ where the boundary condition is usually not known.