Model-based Analysis of Ventilation Inhomogeneity in Respiratory Mechanics

doi:10.4236/eng.2013.510B073

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Engineering, 2013, 5, 363-367

http://dx.doi.org/10.4236/eng.2013.510B073 Published Online October 2013 (http://www.scirp.org/journal/eng)

Model-Based Analysis of Ventilation Inhomogeneity

in Respiratory Mechanics

Christoph Schranz1, Kévin Meffray1, Claudius Stahl2, Knut Möller1

1Institute of Technical Medicine, Furtwangen University, Villingen-Schwenningen, Germany

2Department of Anaesthesiology and Critical Care Medicine, University of Medical Center Freiburg, Germany

Email: [email protected]

Received June 2013

ABSTRACT

Individualized models of respiratory mechanics help to reduce potential harmful effects of mechanical ventilation by

supporting the evaluation of patient-specific lung protective ventilation strategies. Assessing ventilation inhomogenei-

ties might be an important aspect in optimizing ventilator settings. The aim of this study is to capture and analyze ven-

tilation inhomogeneity by a mathematical model using clinical data. The results show that the lung physiology of me-

chanically ventilated patients without lung condition can be described by an inhomogeneity model revealing two alveo-

lar compartments with median time constants of 0.4 an d 3.9 s. Thus, the IHM in combination with specific ventilation

maneuver might be suitable to capture lung physiology for model-based optimization of ventilator settings but requires

additional image-based investigations to further support the validity of the model.

Keywords: Respiratory Mechanics; Inhomogeneity Model; Parameter Identification; Model-B ased Therapy

1. Introduction

Non-adapted ventilator settings risks are severe side ef-

fects in intensive care patients during mechanical venti-

lation [1]. Optimized patient-specific settings can be ob-

tained by individualizing physiological models using

clinical data and p ar ameter identification methods. Indi-

vidualized models provide insight into patient’s physiol-

ogy that is not directly measurable. Thus, they offer sig-

nificant potential to evaluate and guide personalized lung

protective ventilator strategies on intensive care units

[2-4]. The concept of model-based therapy applicable at

the bedside of the patient requires models that are as

simple as possible, while capturing all relevant dynamics

and being identifiable with limited available measure-

ment set.

Relevant dynamics of lung mechanics are significantly

affected by ventilation inhomogeneity [5]. Thus, inho-

mogeneities in lung mechanics might provide useful in-

formation on the lung tissue response to modified venti-

lator settings. Currently, ventilation inhomogeneity can

be captured by computed tomography (CT) [6] or by

electro impedance tomography [7]. An alternative ap-

proach involves the Inhomogeneity Model (IHM) of res-

piratory mechanics [8], wh ich has been a strong force in

the field of pulmonary physiology ev er since [5].

This paper presents the assessment and analysis of the

inhomogeneity model in mechanically ventilated patients

to evaluate its potential for model-based therapy.

2. Material & Methods

2.1. Models and Parameter Identification

First Order Model (FOM): The FOM is the simplest re-

presentation of lung mechanics and considers homoge-

neous ventilation. The equation of motion is given in (1)

and the electrical analog is shown in Figure 1. The res is-

tive element R (cmH2O·s/L) corresponds to the resistance

of the central and peripheral airways and the compliant

compartment C (mL/cmH2O) represents the elasticity of

alveolar tissue and the chest wall [5] defining the respi-

ratory time constant τ = R·C. The patient-specific para-

meters R and C are determined by Multiple Linear Re-

gression using measured data samples of flow rate (



)

as model input and airway pressure (paw) as model output

[9]. pC represents the pressure in the elastic compartment.

VRpp

Caw



(1)

Inhomogeneity Model (I HM): The IHM is a two-

compartment model representing two different alveolar

regions by two compliances (C1, C2 in mL/cmH2O) with

their own local airway (R1, R2 in cmH2O∙s/L) connected

to the airway opening. This model assumes parallel ven-

tilation inhomogeneity in the lungs described by the two

C. SCHRANZ ET AL.

364

Figure 1. Electrical analog of respiratory mechanics models.

Left: First Order Model—FOM, Right: Inho moge neity M o-

del—IHM.

time constants τ1 = R1·C1 and τ2 = R2·C2. Thus, this mod-

el is able to simulate redistribution processes between

these two compartments (Pendelluft) [5]. The electrical

analog is given in Figure 1, and the mathematical de-

scription is presented in state-space representation in (2)

11 211 2

21 221 2

11 2

()()

() ()

()

CR RCR R

CR RV

CR R



−



 



 



 

−









+







1 112

12 1212

aw C

R RRR

RR RRRR



=−+



++ +





(2)

where pC1 and pC2 (cmH2O) are state-signals correspond-

ing to the pressure components gene rated by the volumes

stored in the compliant compartments C1 and C2. Para-

meter identification is performed by minimizing the sum

of squared error (SSE) b etween measured (paw,meas) and

simulated airway pressure using the iterative Integral-

Method (IIM) [10,11]:

2.2. Clinical Data

Measurement sets of ten mechanically ventilated patients

without lung conditions were selected from a previous

study [12], where Super-Syringe Maneuvers were per-

formed. During the Super-Syringe Maneuver small vo-

lume portions (100 mL) are administered with a constant

flow rate (30 L/min), followed by an airway occlusion of

3 s allowing a static pressure-volume relation. Each por-

tion increments the alveolar pressure in the lungs. Meas-

ured airway pressure and flow were sampled at 125 Hz

and are shown exemplarily in Figure 2.

Informed consent was obtained from patients or their

legally authorized representative.

2.3. Analysis

Each inspiration cycle was selected and referenced to its

plateau pressure (pPlat), reached at the end of occlusion.

Patient-specific FOM parameters (R, C) and IHM para-

meters (R1, C1, R2, C2) were identified for each cycle.

The identified parameters of the cohort were plotted in

boxplots illustrating the median and interquartile range

(IQR) to present general trends with respect to plateau

pressure.

3. Results

3.1. Model Individualization

Overall 381 breathing cycles were available to identify

model parameters. FOM identification leads to physio-

logical plausible values in every case tested, whereas

IHM identification revealed partly negative and un-phy-

Figure 2. Airway pressure and fl ow rate during a Super-Syringe Maneuver, initiated after baseline ventilation.

020406080100 120 140

pressure in cmH

020 40 60 80100120140

-40

-20

t in s

flow in L/min

C. SCHRANZ ET AL.

365

siological parameter values in 39 cases. These erroneous

identifications occur r ed mainly in breathing cycles in low

pressure regions. Figure 3 shows comparisons of meas-

ured and simulated model responses of the FOM and

IHM in low and high pressure regions. Obviously, the

pressure relaxation during the occlusion is more pro-

nounced in higher pressure regions. Fitting the IHM to

the data assigns these relaxation effects to redistribution

processes. Pressure responses at low plateau pressure

show no relaxation effects and thus impair IHM identifi-

cation.

The identified parameters resulting from the success-

fully fitted cycles are summarized in a statistical analysis

and presented as overall cohort medians and IQR in Ta-

ble 1 and in terms of plateau pressure in Figure 4. Gen-

erally, the individualized IHM parameters indicate two

heterogeneous compartments with significant different

time constants of τ1 = 3.9 s (IQR: 2.1 - 7.7) and τ2 = 0.4 s

(IQR: 0.2 - 0.5). In addition the global median time con-

stant of the FOM equals 0.9 s (IQR : 0.6 - 1.1).

The pressure dependency of the FOM parameters

show a constant trend in terms of resistance, and a para-

bolic trend for the compliance with a maximum value at

pPlat = 20 cmH2O. The IHM parameter of compartment 1

reveal an increase in R1 and a parabolic trend of C1 simi-

lar to C. R2 and C2 tend to remain constant, with R2 being

in the same orders of magnitude as R.

4. Discussion

The presented an alysis show s the pressur e depend ency of

the identified parameters of the FOM and IHM in pa-

tients without lung condition.

FOM identification shows a parabolic trend in com-

pliance C increasing by more than factor 2 with increas-

ing pressure. The maximal compliance was reached at 20

cmH2O.

IHM identification reveals inhomogeneous ventilation

represented by two compartments with significant dif-

ferent time constants. The compartment with the larger

compliance shows similar behavior as the global com-

pliance trend of the FOM. Simultaneously, the com-

pliance of the second compartment is smaller by factor 3.

Similar findings of inhomogeneity of two different com-

partments with various time constants were obtained with

EIT, where inhomogeneity was related to regional dy-

namics differences in ventral and dorsal areas in patients

under general ane s t he s i a wi thout lun g c onditi on [13].

Figure 1. Measured and simulated pressure of First Order Model (FOM) and Inhomogeneity Model (IHM) at various plateau

pressures of 4 and 36.5 cm H2O.

Table 1. Medi ans and I Q R f rom FOM and IHM i dentified param eters

Model Parameter Valuea

FOM R (cmH2O·s/L) 11.6 (11.2 - 12.1)

C (mL/c mH2O) 78.8 (52.9 - 93.7)

IHM

R1 (cmH2O·s/L) 41.0 (39.0 - 59.6)

C1 (mL/cmH2O) 96.0 (53.3 - 128.7)

R2 (cmH2O·s/L) 15.4 (13.0 - 17.0)

C2 (mL/cmH2O) 29.3 (18.5 - 30.7)

amedian and interquartile range

00.5 11.5 22.5 3

t in s

press ure in c m H2O

measurement IHM sim.FOM sim.

00.5 11.5 22.5 3

t in s

press ure in c m H2O

C. SCHRANZ ET AL.

366

Figure 4. Statistical analysis of identified model parameters in terms of plateau pressure (pPlat). Top line: FOM parameters,

Bottom lines: IHM parameters.

Thus, these model-based results may indicate the IHM

as an alternative approach to obtain measures of dynamic

changes of inhomogeneous lung aeration. Still, the inter-

pretation of model parameters, in particular, the validity

of the identified compartments are only valid if the mod-

el assumption is correct.

However, the same model prediction quality could be

obtained by the viscoelastic model (VEM), which de-

scribes the observed by the same equation but different

coefficients [5,14]. In this case, measured data of flow

rate and airway pressure lead to the problem of undistin-

guishable models. It is unclear whether the observed dy-

namics can be assigned to viscoelastic or inhomogeneity

characteristics. Thus, further investigations combined

with imaging methods are necessary to analyze both dy-

namics separately to further validate the model assump-

tions of the IHM.

Once the IHM is fully validated, it might offer a new

possibility to easily assess ventilation inhomogeneities to

evaluate and guide personalized lung protective ventila-

tor strategies on intensive care units.

5. Acknowledgements

The authors thank the McREM Study Group and Dräger

Medical for providing the clinical data for the evaluation.

This research was supported by the German Federal

Ministry of Education and Research (WiM-Vent, Grants

01IB10002D, PulMODS Grant 01DR12095) and by EU

FP7 PIRSES--GA-2012-318943 eTime.

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