IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 63, NO. 4, APRIL 2016 775 Noninvasive Estimation of Respiratory Mechanics in Spontaneously Breathing Ventilated Patients: A Constrained Optimization Approach Francesco Vicario ∗ , Member, IEEE, Antonio Albanese, Member, IEEE, Nikolaos Karamolegkos, Student Member, IEEE, Dong Wang, Member, IEEE, Adam Seiver, Member, IEEE, and Nicolas W. Chbat, Member, IEEE Abstract—This paper presents a method for breath-by-breath noninvasive estimation of respiratory resistance and elastance in mechanically ventilated patients. For passive patients, well- established approaches exist. However, when patients are breathing spontaneously, taking into account the diaphragmatic effort in the estimation process is still an open challenge. Mechanical ventila- tors require maneuvers to obtain reliable estimates for respiratory mechanics parameters. Such maneuvers interfere with the desired ventilation pattern to be delivered to the patient. Alternatively, in- vasive procedures are needed. The method presented in this paper is a noninvasive way requiring only measurements of airway pres- sure and flow that are routinely available for ventilated patients. It is based on a first-order single-compartment model of the respira- tory system, from which a cost function is constructed as the sum of squared errors between model-based airway pressure predictions and actual measurements. Physiological considerations are trans- lated into mathematical constraints that restrict the space of feasi- ble solutions and make the resulting optimization problem strictly convex. Existing quadratic programming techniques are used to efficiently find the minimizing solution, which yields an estimate of the respiratory system resistance and elastance. The method is illustrated via numerical examples and experimental data from animal tests. Results show that taking into account the patient ef- fort consistently improves the estimation of respiratory mechanics. The method is suitable for real-time patient monitoring, providing clinicians with noninvasive measurements that could be used for diagnosis and therapy optimization. Index Terms—Mechanical ventilation, noninvasive parameter estimation, optimization, patient monitoring, respiratory compli- ance, respiratory mechanics, respiratory resistance. I. INTRODUCTION M EASUREMENTS of the mechanical properties of the respiratory system are of paramount importance to clin- icians for the management of mechanically ventilated patients. Quantitative assessment of respiratory mechanics can aid the Manuscript received April 13, 2015; revised July 20, 2015; accepted August 8, 2015. Date of publication August 20, 2015; date of current version March 17, 2016. Asterisk indicates corresponding author. ∗ F. Vicario is with Philips Research North America, Briarcliff Manor, NY 10510 USA (e-mail: francesco.vicario@philips.com). A. Albanese, D. Wang, and N. W. Chbat are with Philips Research North America. N. Karamolegkos is with Philips Research North America and also with Columbia University. A. Seiver is with Philips Healthcare and also with Sutter Health. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2015.2470641 clinician to: 1) diagnose the disease underlying respiratory fail- ure; 2) monitor the status and progression of the disease; 3) measure the effects of treatments; 4) tune the ventilator set- tings to the patient specific needs, and thus minimize the risk of ventilator-induced complications, such as ventilator-induced lung injury [1], [2]. Respiratory system mechanics is typically described via two parameters, the resistance (R) and the elastance (E), which account for the tendency of the system to oppose air flow and to return to its original volume after being stretched, respectively. For ventilated patients, methods for the assessment of R and E from noninvasive measurements of airway pressure and flow exist but they all present limitations. A well-established technique is the inspiratory hold maneu- ver, also called flow interrupter technique [3] or end-inspiratory pause. This technique consists of rapidly occluding the circuit through which the patient is breathing under conditions of con- stant inspiratory flow, while measuring the pressure in the circuit behind the occluding valve. The technique is noninvasive, easy to perform and the majority of the modern commercial ventila- tors have software that automates this procedure and computes resistance and elastance values. However, the maneuver inter- feres with the normal operation of the ventilator. As a result, it is not suitable for continual monitoring of respiratory mechanics and patient status. This is a severe limitation, as in critically ill patients the mechanical properties of the respiratory systems can rapidly change. Moreover and very importantly, the measure- ments provided by this technique are reliable only if the patient is completely passive throughout the duration of the inspiratory hold. An alternative to the inspiratory hold maneuver consists of using the least squares (LS) method to fit a suitable mathemat- ical model of the respiratory system to the pressure and flow measurements obtained noninvasively at the patient’s airway [4], [5]. In this context, the most widely used mathematical representation of the respiratory system is the first-order single- compartment model that describes the system as an elastic com- partment, representing the lung, served by a single resistive pathway, representing the upper airways [6]. Its parameters, R and E, can be either assumed constant (linear model), or varying with flow and/or volume (nonlinear models) [7]. Typ- ically, data from an entire respiratory cycle are used in batch LS algorithms to estimate the values of R and E, thus allow- ing for breath-by-breath monitoring of respiratory mechanics. 0018-9294 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.