In this paper we present a method for the estimation of leaks in non-invasive ventilation. Accurate estimation of leaks is a key component of a ventilator, since it determines the ventilator performance in terms of patient-ventilator synchrony and air volume delivery. In particular, in non-invasive ventilation, the patient flow is significantly different from the flow measured at the ventilator outlet. This is mostly due to the vent orifice along the tube that is used for exhalation, but also to the non-intentional leaks that occur elsewhere in the circuit (e.g., at the mask). Such leaks are traditionally quantified via a model with two parameters, but only one of them is continually updated - the other is fixed. The new algorithm allows for breath-by-breath update of both parameters. This was made possible by leveraging a model describing the patient respiratory mechanics.

Our goal is to develop methods to improve the efficiency of computational models of the cochlea for applications that require the solution accurately only within a basal region of interest, specifically by decreasing the number of spatial sections needed for simulation of the problem with good accuracy. We design algebraic spatial and parametric transformations to computational models of the cochlea. These transformations are applied after the basal region of interest and allow for spatial preservation, driven by the natural characteristics of approximate spatial causality of cochlear models. The project is of foundational nature and hence the goal is to design, characterize and develop an understanding and framework rather than optimization and globalization. Our scope is as follows: designing the transformations; understanding the mechanisms by which computational load is decreased for each transformation; development of performance criteria; characterization of the results of applying each transformation to a specific physical model and discretization and solution schemes. In this manuscript, we introduce one of the proposed methods (complex spatial transformation) for a case study physical model that is a linear, passive, transmission line model in which the various abstraction layers (electric parameters, filter parameters, wave parameters) are clearer than other models. This is conducted in the frequency domain for multiple frequencies using a second order finite difference scheme for discretization and direct elimination for solving the discrete system of equations. The performance is evaluated using two developed simulative criteria for each of the transformations. In conclusion, the developed methods serve to increase efficiency of a computational traveling wave cochlear model when spatial preservation can hold, while maintaining good correspondence with the solution of interest and good accuracy, for applications in which the interest is in the solution to a model in the basal region.

We develop an analytic model of the mammalian cochlea. We use a mixed physicalphenomenological approach by utilizing existing work on the physics of classical boxrepresentations of the cochlea, and behavior of recent data-derived wavenumber estimates. Spatial variation is incorporated through a single independent variable that combines space and frequency. We arrive at closed-form expressions for the organ of Corti velocity, its impedance, the pressure difference across the organ of Corti, and its wavenumber. We perform model tests using real and imaginary parts of chinchilla data from multiple locations and for multiple variables. The model also predicts impedances that are qualitatively consistent with current literature. For implementation, the model can leverage existing efforts for both filter bank and filter cascade models that target improved algorithmic or analog circuit efficiencies. The simplicity of the cochlear model, its small number of model constants, its ability to capture the variation of tuning, its closed-form expressions for physically-interrelated variables, and the form of these expressions that allows for easily determining one variable from another make the model appropriate for analytic and digital auditory filter implementations as discussed here, as well as for extracting macromechanical insights regarding how the cochlea works.