## 1 Introduction
The Hertz contact theory provides a framework for quantifying non-adhesive elastic contact mechanics in terms of effective contact surface and material deformation by means of an apparent penetration. The general method has been validated against nonlinear finite element models, where it has been shown that it is a valid approach at small deformations [30]. When studying VF contact with Hertz contact [24; 25], the VF geometry has been assumed to conform to a spherical shape and the Hertz penetration depth was estimated from surface strain extrapolation for known synthetic materials. The resulting contact pressure yielded results comparable to prior experimental studies [8; 16]. It is worth noting that DIC is currently not feasible in vivo, since there is no safe way to apply a speckle pattern to the VF tissue. In addition and up to this point, the Hertzian approach required a calibration stage for the laryngeal HSV to compute the exact contact surface and apparent penetration in physical units. Raw HSV recordings can only provide relative VF dimensions. For the in vivo experiments, this problem is solved by projecting an additional laser grid on the glottis that is used to determine the scale with offline processing. However, the projected grid can introduce problems in the lighting conditions, can affect the temporal resolution as the grid can be difficult to observe at high frame rates, and requires custom made hardware [13; 14; 31; 32]. Note that Hertz contact pressure also requires knowledge (or estimation) of VF tissue properties that are difficult, if not impossible, to directly measure in vivo. Despite the simplicity and apparent validity of the Hertzian approach for estimating VF contact pressure in vivo, there are limitations that need to be addressed: (1) A possible bias of VF collision pressure since the superior surface stress may yield larger deformations than that of the actual contacting tissue; (2) the use of a non-physiological VF contact geometry (i.e., contact between two spheres); (3) the requirement of calibrated laryngeal HSV to obtain physical dimensions; and (4) the need for VF tissue properties (Young's modulus and Poisson's ratio) that are difficult to measure in practice. The aim of this work is to obtain in vivo estimations of the VF contact pressure directly from laryngeal HSV recordings using a modified version of Hertz contact that addresses the current limitations of the approach. We hypothesize that the apparent penetration and contact surface can be approximated solely from raw HSV videos, which will allow an estimation of the collision forces directly from the observed kinematics. We expect that these direct estimations are simple enough to be applied in a clinical setting. Specifically, we propose a Hertz contact geometry based on two contacting cylinders both to improve the physiological representation of VF contact and to remove the need for a calibrated HSV system. In this formulation, contact pressure is normalized by the tissue properties and a correction factor is introduced to remove the potential bias in estimating contact from employing only a superior view; this enables a focus on same-subject variations. At the same time, we construct an underlying elastic model with an appropriate stiffness and damping to relate deformation and apparent Hertz tissue penetration and to account for prestress conditions. Finally, to interface the proposed elastic model with a non-colliding condition, a Kalman filter approach is proposed. The approach is contrasted against a separate numerical VF model, silicone VF model experiments, reported experimental data, and in vivo HSV videos to allow for comprehensive insights.