Apparatus and method for the estimation of flow -independent parameters which characterize the relevant features of nitric oxide production and exchange in the human lungs

• US 6,866,637 B2
• Filed: 04/26/2001
• Issued: 03/15/2005
• Est. Priority Date: 04/29/2000
• Status: Expired due to Fees

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Tsoukias, Nikolaos, George, Steven C.
• Primary Examiner(s): WU, JACK SHANGTA
• Application Number:
  US10/257,789
• Publication Number:
  US 20030208131A1
• Time in Patent Office: 1,419 Days
• Field of Search: 600/532, 753/8, 73/233, 422/84
• US Class Current: 600/532
• CPC Class Codes: A61B 5/0813 Measurement of pulmonary parameters by tracers, e.g. radioactive tracers
• CPC Class Codes: A61B 5/087 Measuring breath flow
• CPC Class Codes: A61B 5/411 Detecting or monitoring allergy or intolerance reactions to an allergenic agent or substance

Abstract

The invention provides an estimation of key flow-independent parameters characteristic of NO exchange in the lungs, namely: 1) the steady state alveolar concentration, C_alv,ss; 2) the maximum flux of NO from the airways, J_NO,max; and 3) the diffusing capacity of NO in the airways, D_NO,air. The parameters were estimated from a single exhalation maneuver comprised of a pre-expiratory breathhold, followed by an exhalation in which the flow rate progressively decreased. The mean values for J_NO,max, D_NO,air, and C_alv,ss do not depend on breathhold time for breathhold times greater than approximately 10 seconds. A priori estimates of the parameter confidence intervals demonstrates that a breathhold no longer than 20 seconds may be adequate, and that J_NO,max be can estimated with the smallest uncertainty, and D_NO,air the largest.

Claims

1. A method for determining flow independent parameters characteristic of nitrogen monoxide exchange and of lung function in a subject during one or more exhalations during which flow rate of exhalation varies in time comprising:

exhaling into a mouthpiece in which the resistance to airflow can vary in time and;

measuring exhaled nitrogen monoxide concentration, C_exh, from said subject as a function of time; and

simultaneously measuring volumetric exhalation flow rate, , as a function of time with measurement of exhaled nitrogen monoxide concentration;

backwards integrating said volumetric exhalation flow rate, , over time to convert exhalation time to residence time of each exhaled bolus of gas in said airway compartment of said subject; and

selecting said flow independent parameters to fit said measured nitrogen monoxide concentration as a function of time given residence time obtained by backwards integration.

2. The method of claim 1 further comprising:

estimating V_air, which is the volume of said airway compartment of said subject, and;

measuring V_ds which is the dead space volume or volume expired prior to observing an NO signal, and

where backwards integrating said exhalation flow rate, , over time to convert exhalation time to residence time of each exhaled bolus of gas in an airway compartment in said subject is performed in a computer according to a Case I or Case II integration where;

$\begin{array}{cc}\mathrm{Case}<br><br>\text{\hspace{1em}<br><br>}<br><br>I<br><br>\left(\mathrm{Phase}<br><br>\text{\hspace{1em}<br><br>}<br><br>I<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{of}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{exhalation}\right);<br><br>& {\int <br><br>}_{t-{\mathrm{\tau <br><br>}}_{\mathrm{res}<br><br>\left(t\right)}}^{t+t_{\mathrm{ds}}}<br><br>V_E^{\&<br><br>}<br><br>\left(t^{\mathrm{\prime <br><br>}}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>t^{\mathrm{\prime <br><br>}}=0\\ \mathrm{Case}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}<br><br>\left(\mathrm{Phase}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{III}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{of}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{exhalation}\right);<br><br>& {\int <br><br>}_{t-{\mathrm{\tau <br><br>}}_{\mathrm{res}<br><br>\left(t\right)}}^{t+t_{\mathrm{ds}}}<br><br>V_E^{\&<br><br>}<br><br>\left(t^{\mathrm{\prime <br><br>}}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>t^{\mathrm{\prime <br><br>}}=V_{\mathrm{air}}+V_{\mathrm{ds}}\end{array}$

where t is time, t_ds is convective transport delay time in the dead space volume, T_res;

is residence time of each differential gas bolus in said airway compartment.

3. The method of claim 2 where selecting said flow independent parameters to fit said measured nitrogen monoxide concentration as a function of time given residence time obtained by backwards integration comprises estimating three flow independent parameters C_alv,ss, D_NO,air, J_NO,max from C_exh as a function of T_res(t), where C_alv,ss is the steady state alveolar concentration of nitrogen monoxide, D_NO,air is the diffusing capacity of nitrogen monoxide in said airway compartment, J_NO,max is the maximum total molar flux of nitrogen monoxide from the airway wall, C_exh is the exhaled concentration of nitrogen monoxide, and T_res(t) is the residence time of each differential gas bolus in said airway compartment as a function of time, t.

4. The method of claim 3 where estimating said three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max from C_exh as a function of T_res(t), comprising performing said estimation by relating said three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max and C_exh to measured exhaled concentration in a computer in the relationship given by:

$C_{\mathrm{exh}}<br><br>\left(t+t_{\mathrm{ds}}\right)=\left(C_{\mathrm{in}}<br><br>\left(t-{\mathrm{\tau <br><br>}}_{\mathrm{res}}\right)-\frac{J_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\max }}{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}\right)<br><br>{\mathrm{e<br><br>}}^{-\frac{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}{V_{\mathrm{air}}}<br><br>{\mathrm{\tau <br><br>}}_{\mathrm{res}}<br><br>\left(t\right)}+\frac{J_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\max }}{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}$

where C_in is the inlet concentration of nitrogen monoxide to said airway compartment.

5. The method of claim 1 where selecting said flow independent parameters to fit said measured nitrogen monoxide concentration as a function of time given residence time obtained by backwards integration comprises estimating three flow independent parameters C_alv,ss, D_NO,air, J_NO,max from C_exh as a function of T_res(t), where C_alv,ss is the steady state alveolar concentration of nitrogen monoxide, D_NO,air is the diffusing capacity of nitrogen monoxide in said airway compartment, J_NO,max is the maximum total molar flux of nitrogen monoxide from the airway wall, C_exh is the exhaled concentration of nitrogen monoxide, and T_res(t) is the residence time of each differential gas bolus in said airway compartment as a function of time, t.

6. The method of claim 5 where estimating said three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max from C_exh as a function of T_res(t), comprises performing said estimation by relating said three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max and C_exh to measured exhaled concentration in a computer in the relationship given by:

$C_{\mathrm{exh}}<br><br>\left(t+t_{\mathrm{ds}}\right)=\left(C_{\mathrm{in}}<br><br>\left(t-{\mathrm{\tau <br><br>}}_{\mathrm{res}}\right)-\frac{J_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\max }}{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}\right)<br><br>{\mathrm{e<br><br>}}^{-\frac{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}{V_{\mathrm{air}}}<br><br>{\mathrm{\tau <br><br>}}_{\mathrm{res}}<br><br>\left(t\right)}+\frac{J_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\max }}{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}$

where C_in is the inlet concentration of nitrogen monoxide to said airway compartment.

7. The method of claim 1 where measuring nitrogen monoxide concentration as a function of time comprises performing said measurement of said exhaled bolus of gas with a distribution of residence times ranging from approximately 0.5 seconds to a minimum of approximately 10 seconds for an adult sized lung after a breathold.

8. The method of claim 1 where measuring nitrogen monoxide concentration as a function of time and simultaneously measuring volumetric exhalation flow rate, , as a function of time comprises performing said measurements with a distribution of residence times ranging from approximately 0.5 seconds to approximately a minimum of 10 seconds for an adult sized lung after a breathhold.

9. The method of claim 1 where measuring nitrogen monoxide concentration as a function of time and simultaneously measuring volumetric exhalation flow rate, , as a function of time comprises performing said measurements with a residence time of said exhaled bolus of gas of at least ten seconds by performing a preexpiratory breathhold.

10. The method of claim 9 where performing said pre-expiratory breathhold comprises performing a breathhold of duration between 10-45 seconds.

11. The method of claim 1 where exhaling into said mouthpiece with variable resistance to airflow comprises providing an approximately exponentially decreasing flow of exhalation in time.

12. The method of claim 1 where exhaling into said nitrogen monoxide concentration analyzer comprises providing an uniform distribution of residence time and a minimal acceleration of said exhaled bolus of gas in said airway compartment.

13. The method of claim 1 where exhaling into said nitrogen monoxide concentration analyzer comprises establishing said residence time for each differential bolus of gas as an approximate linear function of time, t.

14. The method of claim 13 where establishing said residence time for each differential bolus of gas as a linear function of time, t, comprises exhaling such that

=1/(⁻

1+ct)

is approximated, where is the time dependent rate of exhalation, is the initial flow rate of exhalation and c is a linear multiplier.

15. The method of claim 1 where selecting said flow independent parameters to fit said measured nitrogen monoxide concentration as a function of time given residence time obtained by backwards integration comprises optimizing said flow independent parameters by performing a nonlinear least square minimization of C_exh.

16. The method of claim 15 where optimizing said flow independent parameters by performing a nonlinear least square minimization of C_exh comprises minimizing a sum of two terms:

1) the squared residual in the average concentrations in Phase I and II weighted by the number of data points, and

     2) the sum of the squared residual of C_exh in Phase III of the exhalation profile according to the following relationship;

$\begin{array}{cc}{R}_{\mathrm{LS}}=n_{I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}·<br><br>{\left(\left(\underset{i=1}{\overset{n_{I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{exh},\text{\hspace{1em}<br><br>}<br><br>i}^{*}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>V_{I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}\right)/V_{I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}-\left(\underset{i=1}{\overset{{\text{\hspace{1em}<br><br>}}^n<br><br>I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{exh},\text{\hspace{1em}<br><br>}<br><br>i}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>V_{I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}\right)/V_{I,\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}}\right)}^2+\underset{i=1}{\overset{n_{\mathrm{III}}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\left(C_{\mathrm{exh},\text{\hspace{1em}<br><br>}<br><br>i}^{*}-C_{\mathrm{exh},\text{\hspace{1em}<br><br>}<br><br>i}\right)}^2& \left(7\right)\end{array}$

where n_I,II and V_I,II are the number of data points and volume in Phase I and II respectively, n_III and V_III are the number of data points and volume in Phase III, C*_exh is the model-predicted concentration, and Δ

V_I,II is the change in volume between consecutive data points, (*dt), in Phase I and II respectively.

17. The method of claim 1 where exhaling into a mouthpiece in which in which flow rate and nitrogen monoxide concentration are simultaneously measured includes tidal breathing by said subject.

18. An apparatus for determining flow independent parameters of lung function in a subject during one exhalation during which flow rate of exhalation varies in time comprising:

a sampling line into which said subject exhales;

a nitrogen monoxide analyzer coupled to said sampling line to measure exhaled nitrogen monoxide concentration, C_exh, from said subject as a function of time;

a flow meter coupled to said sampling line to measure to measure volumetric exhalation flow rate, , as a function of time; and

a computer coupled to said nitrogen monoxide analyzer and to said flow meter to backwards integrate said volumetric exhalation flow rate, , over time to convert exhalation time to residence time of each exhaled bolus of gas in said airway compartment of said subject; and

to select said flow independent parameters to fit said measured nitrogen monoxide concentration as a function of time given residence time obtained by backwards integration.

19. The apparatus of claim 18 where said flowmeter measures V_ds which is the dead space volume or volume expired prior to observing a NO signal, and where said computer is arranged and configured to backwards integrate said exhalation flow rate, , over time to convert exhalation time to residence time of each exhaled bolus of gas in an airway compartment in said subject is performed in a computer according to a Case I or Case II integration where:

$\begin{array}{cc}\mathrm{Case}<br><br>\text{\hspace{1em}<br><br>}<br><br>I<br><br>\left(\mathrm{Phase}<br><br>\text{\hspace{1em}<br><br>}<br><br>I<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{of}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{exhalation}\right);<br><br>& {\int <br><br>}_{t-{\mathrm{\tau <br><br>}}_{\mathrm{res}<br><br>\left(t\right)}}^{t+t_{\mathrm{ds}}}<br><br>V_E^{\&<br><br>}<br><br>\left(t^{\mathrm{\prime <br><br>}}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>t^{\mathrm{\prime <br><br>}}=0\\ \mathrm{Case}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{II}<br><br>\left(\mathrm{Phase}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{III}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{of}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{exhalation}\right);<br><br>& {\int <br><br>}_{t-{\mathrm{\tau <br><br>}}_{\mathrm{res}<br><br>\left(t\right)}}^{t+t_{\mathrm{ds}}}<br><br>V_E^{\&<br><br>}<br><br>\left(t^{\mathrm{\prime <br><br>}}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>t^{\mathrm{\prime <br><br>}}=V_{\mathrm{air}}+V_{\mathrm{ds}}\end{array}$

where t is time, t_ds is convective transport delay time in the dead space volume, T_res;

is residence time of each differential gas bolus in said airway compartment.

20. The apparatus of claim 18 where said computer is arranged and configured to estimate three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max from experimentally determined C_exh as a function of T_res(t), where C_alv,ss is the steady state alveolar concentration of nitrogen monoxide, D_NO,air is the diffusing capacity of nitrogen monoxide in said airway compartment, J_NO,max is the maximum total molar flux of nitrogen monoxide from the airway wall, C_exh is the exhaled concentration of nitrogen monoxide, and T_res(t) is the residence time of each differential gas bolus in said airway compartment as a function of time, t.

21. The apparatus of claim 20 where said computer is arranged and configured to estimate three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max from experimentally measured C_exh as a function of T_res(t), where C_alv,ss is the steady state alveolar concentration of nitrogen monoxide, D_NO,air is the diffusing capacity of nitrogen monoxide in said airway compartment, J_NO,max is the maximum total molar flux of nitrogen monoxide from the airway wall, C_exh is the exhaled concentration of nitrogen monoxide, and T_res(t) is the residence time of each differential gas bolus in said airway compartment as a function of time, t.

22. The apparatus of claim 21 where said computer performs said estimation by relating said three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max and experimentally measured C_exh in a computer in the relationship given by:

$C_{\mathrm{exh}}<br><br>\left(t+t_{\mathrm{ds}}\right)=\left(C_{\mathrm{in}}<br><br>\left(t-{\mathrm{\tau <br><br>}}_{\mathrm{res}}\right)-\frac{J_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\max }}{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}\right)<br><br>{\mathrm{e<br><br>}}^{-\frac{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}{V_{\mathrm{air}}}<br><br>{\mathrm{\tau <br><br>}}_{\mathrm{res}}<br><br>\left(t\right)}+\frac{J_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\max }}{D_{\mathrm{NO},\text{\hspace{1em}<br><br>}<br><br>\mathrm{air}}}$

where C_in is the inlet concentration of nitrogen monoxide to said airway compartment.

23. The apparatus of claim 22 where said computer performs said estimation by relating said three flow-independent parameters C_alv,ss, D_NO,air, J_NO,max and experimentally measured C_exh in a computer in the relationship given by:

$C_{\mathrm{exh}}<br><br>\left(t+t_{\mathrm{ds}}\right)=\left(C_{i<br><br>\text{\hspace{1em}<br><br>}<br><br>n}<br><br>\left(t-{\mathrm{\tau <br><br>}}_{\mathrm{res}}\right)-\frac{J_{\mathrm{NO},\max }}{D_{\mathrm{NO},\mathrm{air}}}\right)<br><br>{\mathrm{e<br><br>}}^{-\frac{D_{\mathrm{NO},\mathrm{air}}}{V_{\mathrm{air}}}<br><br>{\mathrm{\tau <br><br>}}_{\mathrm{res}}<br><br>\left(t\right)}+\frac{J_{\mathrm{NO},\max }}{D_{\mathrm{NO},\mathrm{air}}}$

where C_in is the inlet concentration of nitrogen monoxide to said airway compartment.

24. The apparatus of claim 18 where said nitrogen monoxide analyzer performs said measurements on said exhaled bolus of gas with a distribution of residence times ranging from approximately 0.5 to a minimum of approximately 10 seconds for an adult sized after a breathhold.

25. The apparatus of claim 18 where said nitrogen monoxide analyzer performs said measurements on said exhaled bolus of gas with a residence time of at least one second after a pre-expiratory breathhold.

26. The apparatus of claim 18 where said nitrogen monoxide analyzer performs said measurements on said exhaled bolus of gas with a residence time of at least ten seconds after a pre-expiratory breathhold.

27. The apparatus of claim 26 where said nitrogen monoxide analyzer performs said measurements on said exhaled bolus of gas with a distribution of residence times between approximately 0.5 and 3 seconds for an adult sized lung after expulsion of air in the airway during a pre-expiratory breathhold of 10, 20, 30 or 45 seconds.

28. The apparatus of claim 18 where said nitrogen monoxide analyzer is provided with an approximately exponentially decreasing flow of exhalation.

29. The apparatus of claim 18 where said nitrogen monoxide analyzer is provided with an approximate uniform distribution of residence time and a minimal acceleration of said exhaled bolus of gas in said airway compartment.

30. The apparatus of claim 18 where said nitrogen monoxide analyzer is provided with differential boluses of gas with a residence time which is an approximate linear function of time, t.

31. The apparatus of claim 30 where said nitrogen monoxide analyzer is provided with differential boluses of gas with a residence time such that

=1/(⁻

1+ct)

is approximated, where is the time dependent rate of exhalation, is the initial flow rate of exhalation and c is a linear multiplier.

32. The apparatus of claim 18 where said computer is arranged and configured to optimize said flow independent parameters by performing nonlinear least square minimization of C_exh.

33. The apparatus of claim 32 where said computer is arranged and configured to optimize said flow independent parameters by performing a nonlinear least square minimization of C_exh comprises minimizing a sum of two terms:

1) the squared residual in the average concentrations in Phase I and II weighted by the number of data points, and

     2) the sum of the squared residual of C_exh in Phase III of the exhalation profile according to the following relationship;

$\begin{array}{cc}{R}_{\mathrm{LS}}=n_{I,\mathrm{II}}·<br><br>{\left(\left(\underset{i=1}{\overset{n_{I,\mathrm{II}}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{exh},i}^{*}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>V_{{\text{\hspace{1em}<br><br>}}_{I,\mathrm{II}}}\right)/V_{{\text{\hspace{1em}<br><br>}}_{I,\mathrm{II}}}-\left(\underset{i=1}{\overset{n_{I,\mathrm{II}}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{exh},i}·<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>V_{{\text{\hspace{1em}<br><br>}}_{I,\mathrm{II}}}\right)/V_{{\text{\hspace{1em}<br><br>}}_{I,\mathrm{II}}}\right)}^2+\underset{i=1}{\overset{n_{I,\mathrm{II}}}{\sum <br><br>}}<br><br>{(\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{exh},i}^{*}-C_{\mathrm{exh},i})}^2& \left(7\right)\end{array}$

where n_I,II and V_I,II are the number of data points and volume in Phase I and II respectively, n_III and V_III are the number of data points and volume in Phase III, C*_exh is the model-predicted concentration, and Δ

V_I,II is the change in volume between consecutive data points, (*dt), in Phase I and II respectively.

34. The apparatus of claim 18 where said nitrogen monoxide concentration analyzer samples tidal breathing by said subject.