# Lutchen

"A nonlinear model combining Pulmonary Mechanics and Gas Concentration Dynamics." IEEE Trans.,BME-29, 1982, p. 629-641. Lutchen, F.P. Primiano Jr., G.M. Saidel

Model number: 0005

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## Description

Model Structure with conducting airway {1} and alveolar compartments {2} and {3}. Qao, Q1, Q2, and Q3 are the flows. {m} is the mixing node. The conducting airway in Lutchen is non-dispersive. Here it is modeled as BTEX10 with no axial diffusion. DESCRIPTION: This model simulates "A Nonlinear model combining pulmonary mechanics and gas concentration dynamics" (Lutchen, et al., 1982, hereafter referred to as Lutchen). A non-dispersive airway is connected to a bifurcating alveolar compartment. The naming of variables and parameters follows the nomenclature of the paper. The primary difference between the model in Lutchen and the model presented here is that the non- dispersive airway has been simulated by a non-dispersive BTEX10 model (axial diffusion set to zero). The experiment being simulated is as follows: the human subject is breathing air. The first breath (inspiration and expiration) is also air. At the beginning of the second breath, the air is replaced by pure oxygen for breaths two through seven. It is noted that Figures 2 and 4 in Lutchen have an incorrect abcissa axis annotation. The axis is for 7 breaths (7 breaths*4 seconds/breath equals 28 seconds. Six breaths (shown) would end at 24 seconds. (There is also a minor error in Equation 19.) The normalized nitrogen concentration is tracked in both alveolar compartments and the dead space as washout curves. The model is run for Lutchen's cases 1 and 6 (Parameter sets Case1 and Case6). Figures 1, 2, and 3 correspond to Lutchen's Figure 2. Figures 4, 5, and 6 correspond to Lutchen's Figure 4. Text Table 10 (Stat_ plot displayed as text) gives the results of numerical calculations which may be compared with Lutchen's TABLE II. Case 1 is for normal alveolar compartments which have synchronized flows, concentration changes, and volume changes. The exponential pressure forcing ranges from 5 mmHg to 9 mmHg. Case 6 is for obstructive lung disease affecting just the alveolar compartment labled 3. Using the periodic exponential pressuring forcing, The obstructed lung has a larger volume with reduced tidal range. Clearance in the obstructed lung is slower than in the unobstructed lung. Case 6 Sine for sinusoidal pressure forcing. The pressure fluctuation at the mouth has a range of 5 mmHg to 9 mmHg. The pendelluft fraction is the sum of the two alveolar tidal volumes minus the tidal volume of the pulmonary system (integrated flow at the airway opening over an inspiration), all divided by the tidal volume of the pulmonary system indicates the percentage of inspired air that is being recirculated in the lungs. In Case 6 Sine, it accounts for 46% of the ventilation of the obstructed lung.Pulmonary Tidal Volume * Pendelluft Fraction .434 * 0.200 -------------------------------------------- = -------------- =~0.46. V3T (Tidal Volume) .188

## Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). Of particular interest is the formulation of the boundary conditions for the partial differential equation modeling the oscillating flow in he trachea. See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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## References

K.R. Lutchen, F.P. Primiano Jr., G.M. Saidel, "A nonlinear model combining Pulmonary Mechanics and Gas Concentration Dynamics." IEEE Trans.,BME-29, 1982, p. 629-641.

## Related Models

Lung models

- Lutchen Model,
- BronchTwoAlv: Simplified Lutchen Model,
- BTEX10_OscillatingFlow : BTEX10 used as a pipe for oscillating flow,

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[This page was last modified 14Mar18, 3:17 pm.]

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