Engineering, 2013, 5, 363-367 Published Online October 2013 (
Copyright © 2013 SciRes. 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
Received June 2013
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.
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
Copyright © 2013 SciRes. ENG
Figure 1. Electrical analog of respiratory mechanics models.
Left: First Order ModelFOM, Right: Inho moge neity M o-
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
11 2
() ()
 
 
 
1 112
12 1212
aw C
++ +
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
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
t in s
flow in L/min
Copyright © 2013 SciRes. ENG
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-
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
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)
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
Copyright © 2013 SciRes. ENG
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.
[1] A. S. Slutsky, “Lung Injury Caused by Mechanical Ven-
tilation,” Chest, Vol. 116, 1999, pp. 9-15.
[2] A. Sundaresan, J. G. Chase, G. M. Shaw, Y. S. Chiew and
T. Desaive, “Model-Based Optimal PEEP in Mechani-
cally Ventilated ARDS Patients in the Intensive Care
Unit,” Biomed Eng Online, Vol. 10, 2011, p. 64.
[3] S. Lozano, K. Möller, A. Brendle, D. Gottlieb, S. Schu-
mann, C. A. Stahl, et al., “AUTOPILOT-BT: A system
for Knowledge and Model Based Mechanical Ventilation,”
Technol Health Care, Vol. 16, 2008, pp. 1-11.
[4] S. E. Rees, C. Allerød, D. Murley, Y. Zhao, B. W. Smith,
S. Kjaergaard, et al., “Using Physiological Models and
Decision Theory for Selecting Appropriate Ventilator
Settings,” Journal of Clinical Monitoring and Computing,
Vol. 20, 2006, pp. 421-429.
[5] J. H. Bates, “Lung Mechanics: An Inverse Modeling Ap-
proach,” 1st Edition, Cambridge University Press, New
York, 2009.
[6] K. Markstaller, B. Eberle, H. U. Kauczor, A. Scholz, A.
Bink, M. H. Thelen, W., et al., “Temporal Dynamics of
Lung Aeration Determined by Dynamic CT in a Porcine
Copyright © 2013 SciRes. ENG
Model of ARDS,” British Journal of Anaesthesia, Vol. 87,
2001, pp. 459-468.
[7] Z. Zhao, K. Möller, D. Steinmann, I. Frerichs and J.
Guttmann, “Evaluation of an Electrical Impedance To-
mography-Based Global Inhomogeneity Index for Pul-
monary Ventilation Distribution,” Intensive Care Medi-
cine, Vol. 35, 2009, pp. 1900-1906.
[8] A. B. Otis, C. B. McKerrow, R. A. Bartlett, J. Mead, M.
B. McIlroy, N. J. Selver-Stone, et al., “Mechanical Fac-
tors in Distribution of Pulmonary Ventilation,” Journal of
Applied Physiology, Vol. 8, 1956, pp. 427-443.
[9] C. Schranz, C. Knöbel, J. Kretschmer, Z. Zhao and K.
Möller, “Hierarchical Parameter Identification in Models
of Respiratory Mechanics,” IEEE Transactions on Bio-
medical Engineering, Vol. 58, 2011, pp. 3234-3241.
[10] C. Schranz, P. D. Docherty, K. Möller and J. G. Chase,
“Integral-Based Identification of an Inhomogeneity Mod-
el in Respiratory Mechanics,” 6th International Confe-
rence on Bioinformatics and Biomedical Engineering,
Shanghai, 2012, pp. 575-578.
[11] C. Schranz, P. D. Docherty, Y. S. Chiew, K. Möller and J.
G. Chase, “Iterative Integral Parameter Identification of a
Respiratory Mechanics Model,” BioMedical Engineering
OnLine, Vol. 11, 2012.
[12] C. A. Stahl, K. Möller, S. Schumann, R. Kuhlen, M. Sy-
dow, C. Putensen, et al., “Dynamic versus Static Respi-
ratory Mechanics in Acute Lung Injury and Acute Respi-
ratory Distress Syndrome,” Critical Care Medicine, Vol.
34, 2006, pp. 2090-2098.
[13] S. Pulletz, M. Kott, G. Elke, D. Schädler, B. Vogt, N.
Weiler, et al., “Dynamics of Regional Lung Aeration De-
termined by Electrical Impedance Tomography in Pa-
tients with Acute Respiratory Distress Syndrome,” Multi-
disciplinary Respiratory Medicine, Vol. 7, 2012, p. 44.
[14] G. Avanzolini and P. Barbini, “Comments on “Estimating
Respiratory Mechanical Parameters in Parallel Compart-
ment Models”, IEEE Transactions on Biomedical Engi-
neering, Vol. 29, 1982, pp. 772-774.