Parameter Identification

Early recruitment models developed by Yuta were validated and fitted to clinical data [Yuta, 2007, Yuta et al., 2004]. However, the models included four different types of lung units, based directly on work by Schiller et al [Schiller et al., 2003]. Each different type of unit thus required unique unit compliance and threshold pressure distributions. The model therefore required as many as 42 patient specific parameters to be identified [Yuta et al., 2004].

Most of those model parameters were impractical, if not impossible, to obtain clinically, especially with the limited time, data, and resources in a typical ICU. Hence, it was effectively not identifiable from available data. However, the model in [Yuta et al., 2004] was much more physiologically representative. Thus, its relationship to the model presented here is used to define this minimal model’s physiological relevance, and ability to equally capture physiological data.

The model of [Yuta et al., 2004] was thus modified to create the model presented here, requiring only 2 parameters per breathing limb to make it clinically applicable. Reducing the number of unit types to just one and using the hypothesis that most of the volume change is caused by recruitment and de-recruitment (e.g. [Carney et al., 1999, Hickling, 2002]), the unit compliance has a relatively smaller contribution to the overall PV curve shape. As a result, the unit compliance curve defined in Equation (3.1) can be fixed at generic population values.

The minimum and maximum threshold pressures are fixed at 0 and 60 cmH2O respectively, to cover the range of typically used ventilation pressures. The total number of parameters is thus reduced to just four:

 TOP distribution mean − Inspiratory limb of breathing curve

 TCP distribution mean−_{Expiratory limb of breathing curve}  TOP standard deviation − Inspiratory limb of breathing curve

Therefore, there are effectively two parameters for describing each of the inflation and deflation limbs. Other clinical MV related variables, such as PEEP, PIP, and tidal volume are assumed known, as they are set by the clinician or can be obtained directly from ventilator.

Hence, the changes made in reducing 42 parameters to four do not remove any significant physiological representation. What is lost is the level of physiological detail in the number and the types of ARDS affected and healthy lung units. However, these values were not uniquely identifiable without as many as 20 unique PV curves, which was not clinically practical.

In their place, there is now a single unit which takes on two states; recruited and de- recruited. However, these two states can, at a given pressure, represent the level of ARDS by the level of recruitment available at a given pressure. More specifically, as ARDS progresses, there is less recruitment at a given pressure and PEEP, which is effectively captured by the four (2 each) parameters describing TOP and TCP. Hence, alveoli-specific TOP and TCP, summarised by the mean and SD distribution parameters, can effectively capture this level of ARDS.

As a result, the parameter identification is greatly simplified and importantly, is unique, given a reasonably discretized measured PV curve. The main requirement is a minimum of 2 complete PV loops to provide enough data to identify the two parameters for the inflation (TOP distribution) and deflation (TCP distribution) limbs. A second requirement is that these loops be obtained at clinically different PEEP values. TOP and TCP parameter identification is readily done by iteratively modifying the threshold pressure distribution variables to minimize the sum squared error between the model and clinical data for each limb of the PV loops.

Since the inflation and deflation limbs are generated by different independent parameters, each limb can be fitted separately. The PEEP value sets the minimum pressure for the PEEP to PIP breathing cycle. The standard deviation of the TOP or TCP distribution primarily controls the slope of the curve and the mean value primarily controls the location along the pressure axis of the respective curves.

The TOP and TCP distribution parameters are effective for capturing both inter-patient and intra-patient variability. Inter-patient variability is accounted for by the difference in

37 distribution mean values between patients. Each patient may have a different TOP and TCP mean for a given PEEP and the mean is also reflective of the overall level of lung damage. In particular, suppose a patient had PV loops at 3 different PEEP values, then each PEEP would have an associated, patient-specific TOP and TCP mean. However, for a given PEEP, there will almost certainly be different distribution mean values across different patients, indicating the condition-specific level of lung damage in a patient. Intra- patient variability is similarly seen in the different mean values obtained for TOP and TCP at different PEEP in a given patient, where these are obtained at different points in time. These differences indicate the effect of PEEP on recruitment in the patient, as well as their patient-specific evolution of disease state.

Finally, the SD is held constant across all PEEP levels during each trial. The SD represents the compliance of the lungs, and is thus representative of the ARSD state. As SD changes, the severity of the ARDS affected lung changes. More specifically, a lower SD represents a more diseased lung state, while a higher SD indicates a more compliant lung. The SD is held constant across all PEEP as it represents the underlying disease state which does not change for a given trial. Rather, SD can vary over time as the patient condition deteriorates or improves.