Method for measuring airway resistance

Abstract

A method of characterizing the respiratory properties of a conscious living organism from a single respiratory waveform containing thoracic and nasal flow signal components is described that includes acquiring a single box flow waveform containing thoracic and nasal flow signal components, measuring the areas of peaks of the waveform, and characterizing respiratory properties from the peak areas. A method is also described for characterizing the respiratory function of a conscious living subject by acquiring separate thoracic and nasal respiratory waveforms, determining the phase shifts between the waveforms at first and second time spaced points, determining the net inspired volume between the points, and characterizing respiratory function using the phase shift and net inspired volume.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph of a single breath showing the nasal and thoracic flow.

FIG. 2 is graph of a single breath showing nasal and thoracic flow with increased airway resistance.

FIG. 3 is a graph of the difference in nasal and thoracic flows of the graphs of FIGS. 1 and 2.

FIG. 4 is a graph of a Box Flow signal illustrating calculation of the index of airway resistance.

DETAILED DESCRIPTION OF THE INVENTION

Calculation of Index of Airway Resistance from a Single Waveform

FIGS. 1 and 2 graphically illustrate the phase shift between separately acquired signals for nasal and thoracic flow resulting from airway resistance. Inspiration is positive and expiration is negative. The nasal flow signal has about the same shape as the thoracic flow signal, but is smaller and slightly delayed. FIG. 2 shows a longer delay between the nasal and thoracic flow signals, indicating increased airway resistance.

FIG. 3 shows the resulting Box Flow signals produced from the graphs in FIGS. 1 and 2. That is, the Box Flow signal (A) is produced from the flows shown in FIG. 1, and Box Flow signal (B) is produced from the flows shown on the graph in FIG. 2. Notice that Box Flow signal (B) has higher peaks and valleys which correlate with a longer delay.

One way to compute the phase shift between the nasal and thoracic flows is to first scale the nasal flow waveform so that its peak-to-peak magnitude is equal to the peak-to-peak magnitude of the thoracic flow. Then calculate a new waveform (scaled difference) by subtracting the scaled nasal flow from the thoracic flow. The time delay between the two flow signals can be measured by integrating a small region (small compared to a respiratory cycle, say 10% or less) on the scaled difference waveform, and dividing that result by the differences in thoracic flow from the start to the end of that integrated region. From the time delay, it is a simple matter to compute the phase shift. In summary, the scaled difference can be used to measure phase shift.

A phase shift can be calculated within almost any region of a single breath as long as the starting and ending flows are not equal. (If the starting and ending flows are the same, then the quotient will have a zero in the denominator.) However, some regions are better than others for practical computational reasons. For example, because a computer can represent a flow value along the signal with a specific finite number resolution, it is desirable that the starting and ending flow are as far apart as possible. This reason can also be applied to computing the difference between the nasal and thoracic flows. Assuming the phase shift is uniform, the difference between the nasal and thoracic flow is greatest where the slope of the flow signals is steepest.

As a result, the two best regions to measure the phase shift are regions surrounding the transition from inspiration-to-expiration and from expiration-to-inspiration. And since the subject may hesitate at the end of expiration, the transition from inspiration-to-expiration is best.

Since the Box Flow signal is the difference between the nasal and thoracic flows, it responds to changes in phase shift. And since it is the unscaled difference between the nasal and thoracic flows, it responds to amplitude difference between nasal and thoracic flows. A peak may be expected at the transition from inspiration-to-expiration due to the phase shift between the nasal and thoracic flows. We can also see a similar, but opposite-going peak at the transition from expiration-to-inspiration.

As described above, resistance information is readily available on the Box Flow signal at the transition from inspiration-to-expiration and from expiration-to-inspiration. This information is manifested by a peak surrounding that transition region. The area under this peak can be shown to be related to the developed pressure within the lung required to move the air either in or out. Also, the area under this peak is similar to the area computed between the nasal and thoracic waveforms in the double chamber application, which is an element in the computation of specific airway resistance. While not being purely related to resistance, or lung pressure, this peak is at least sensitively responsive to airway resistance.

Example Index of Airway Obstruction

In order to calculate the index of airway resistance (I_pr) as a measurement of airway resistance from the peaks in graph (B) of FIG. 3, three areas are measured: an area during inspiration (A₂), and an area during expiration (A₃), and the area of the Box Flow negative peak which occurs between inspiration and expiration (A₁). The duration of each area is identical as determined by measuring the time (T_p) from the Box Flow zero to the Box Flow minimum within the negative peak. The duration is twice this measured time.

The area during inspiration (A₂) is measured immediately before the zero crossing. The area during expiration (A₃) is measured after the Box Flow negative peak (A₁). Specifically, A₃ begins T_p past A₁. The index of airway resistance is then measured in accordance with the following equation:

$I_{\mathrm{pr}}=\frac{A_1\times 2\times T_p}{A_2+A_3}$

Calculation of Functional Residual Capacity from a Single Waveform

Peak information can also be used to estimate functional resistance capacity (FRC). To estimate the subject's FRC, we start with the following equation, and simplify it:

${\stackrel{.}{V}}_b\left(t\right)\approx {\stackrel{.}{V}}_a\left(t\right)\left(1-\frac{T_{c,n}P_a\left(t\right)}{T_aP_c}\right)-V_a\left(t\right){\stackrel{.}{P}}_a\left(t\right)\frac{T_{c,n}}{T_aP_c}$

Where:

• {dot over (V)}_b(t) is the flow of air out of the chamber (named the Box Flow),
• {dot over (V)}_a(t) is the flow of air into the animal,
• V_a(t) is the volume of air in the lungs,
• T_c is the chamber temperature during inspiration,
• T_n is the nasal temperature during expiration,
• T_a is the subject's body temperature,
• P_c is the dry air pressure within the chamber,
• P_a(t) is the dry air pressure within the lungs, and

Making all these assumptions, if we integrate the peaks that occur, then we can estimate FRC as follows:

$\begin{array}{c}\frac{{\mathrm{Peak}}_{\mathrm{Exp}-\mathrm{to}-\mathrm{Insp}}}{{\mathrm{Peak}}_{\mathrm{Insp}-\mathrm{to}-\mathrm{Exp}}}\approx \frac{K_2\left(\mathrm{FRC}\right)\int {\stackrel{.}{P}}_l\left(t\right)t_{\mathrm{Inspiration}}}{-K_2\left(\mathrm{FRC}+V_T\right)\int {\stackrel{.}{P}}_l\left(t\right)t_{\mathrm{Expiration}}}\\ \approx \frac{\mathrm{FRC}}{\mathrm{FRC}+V_T}\\ =W\end{array}$

W is the ratio of the area peak under each peak. The value can be easily derived from the box flow signal. And as shown above, this ratio is related to the ratio of the subject's pulmonary volume at the start of inspiration to the pulmonary volume at the end of inspiration.

With an estimation of V_T (tidal volume), FRC can be estimated by the following:

$\mathrm{FRC}=\frac{W•V_T}{W-1}$

Estimating FRC and Airway Resistance Using Separate Nasal and Thoracic Flows

It is known from A Noninvasive Technique For Measurement Of Changes In Specific Airway Resistance, Pennock et al., J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 46(2): 399-406, (1979), that the following relationship is true:

tan θ=2πfR_awC

where:

• θ is the phase shift between the nasal and thoracic flows
• C is the compressibility of the lung
• R_aw is the airway resistance
• f is the frequency of breathing

$C=\frac{V}{P}$

If the expansion or contraction is isothermal (and it is because it takes place at subject's body temperature), then the following relationship is true:

$C=\frac{V_{\mathrm{tgv}}}{P_a}$

where:

• V_tgv is the thoracic gas volume
• P_a is the dry gas pressure in the lung
• θ is the phase shift between the nasal and thoracic flows. This phase shift can be measured by determining the time (in seconds) that the nasal flow lags behind the thoracic flow and the frequency of breathing in Hertz.

θ=2πfd

where:

• d is the time in seconds that the nasal flow lags behind the thoracic flow
• f is the frequency of breathingApplying these other equations, we can rewrite the original equation:

$\tan \theta =\frac{2\pi {\mathrm{fR}}_{\mathrm{aw}}V_{\mathrm{tgv}}}{P_a}$

The thoracic gas volume (V_tgv) is different at the start of inspiration than it is at the end of inspiration. And this difference can easily be measured by integrating the thoracic flow signal. This value is routinely reported as the tidal volume (V_T).

$\tan {\theta }_{\mathrm{start}}=\frac{2\pi {\mathrm{fR}}_{\mathrm{aw}}\left(\mathrm{FRC}\right)}{P_a}$ $\tan {\theta }_{\mathrm{end}}=\frac{2\pi {\mathrm{fR}}_{\mathrm{aw}}\left(\mathrm{FRC}+V_T\right)}{P_a}$

Knowing these two equations, an equation can be derived both for FRC and R_aw.

To simplify the following derivations, substitute the tangent terms as follows:

$D_{\mathrm{start}}=\tan {\theta }_{\mathrm{start}}$ $D_{\mathrm{end}}=\tan {\theta }_{\mathrm{end}}$ $\mathrm{FRC}=\frac{D_{\mathrm{start}}P_a}{2\pi {\mathrm{fR}}_{\mathrm{aw}}}$ $\begin{array}{c}{D}_{\mathrm{end}}=\frac{2\pi {\mathrm{fR}}_{\mathrm{aw}}\left[\frac{D_{\mathrm{start}}P_a}{2\pi {\mathrm{fR}}_{\mathrm{aw}}}+V_T\right]}{P_a}\\ =D_{\mathrm{start}}+\frac{2\pi {\mathrm{fR}}_{\mathrm{aw}}V_T}{P_a}\end{array}$ $R_{\mathrm{aw}}=\frac{\left[D_{\mathrm{end}}-D_{\mathrm{start}}\right]P_a}{2\pi {\mathrm{fV}}_T}$ $\mathrm{FRC}=\frac{D_{\mathrm{start}}V_T}{\left[D_{\mathrm{end}}-D_{\mathrm{start}}\right]}$

Certain modifications and improvements will occur to those skilled in the art upon a reading of the foregoing description. It should be understood that all such modifications and improvements have been deleted herein for the sake of conciseness and readability but are properly within the scope of the following claims.

Claims

1. A method of characterizing the respiratory properties of a conscious living organism from a single respiratory waveform that includes thoracic and nasal flow signal components comprising: a) acquiring a single box flow waveform that includes thoracic and nasal flow signal components;b) measuring area of peaks of said waveform; andc) characterizing respiratory properties from said peak areas.

2. The method of claim 1, wherein said waveform is acquired using a whole body plethysmograph.

3. The method of claim 1, wherein said area peaks include the area of the peak between inspiration and expiration.

4. The method of claim 1, including measuring an area of the signal during inspiration, measuring an area of the signal during expiration, and measuring an area of the signal between inspiration and expiration, said areas having the same time duration.

5. The method of claim 1, wherein said respiratory property is calculated as the index of airway resistance using the equation:

6. A method of characterizing the respiratory properties of a conscious living organism as the index of airway resistance Ipr from a single respiratory waveform that includes thoracic and nasal flow signal components comprising: a) acquiring a single box flow waveform that includes thoracic and nasal flow signal components;b) measuring an area of the waveform during inspiration, measuring an area of the signal during expiration, and measuring an area of the signal between inspiration and expiration, said areas having the same time duration; andc) calculating Ipr from the relationship and volumes of said areas.

7. The method of claim 6, wherein said waveform is acquired using a whole body plethysmograph.

8. The method of claim 6, wherein Ipr is calculated as the index of airway resistance using the equation:

9. The method of claim 1, wherein said respiratory property is functional residual capacity, and said property is calculated as the ratio of the area of the peak from expiration to inspiration divided by the area of the peak from inspiration to expiration.

10. A method of characterizing the respiratory function of a conscious living subject comprising: a) acquiring separate thoracic and nasal respiratory waveforms;b) determining the phase shifts between said waveforms at first and second time spaced points;c) determining the net inspired volume between said points; andd) characterizing respiratory function using the phase shifts and net inspired volume.

11. The method of claim 10, wherein said first point is at the transition from expiration to inspiration.

12. The method of claim 10, wherein said second point is at the transition from inspiration to expiration.

13. The method of claim 10, wherein said respiratory function is characterized by dividing the difference in the phase shifts by the net inspired volume.

14. The method of claim 10, wherein said net inspired volume is equal to the total inspired volume between said points minus the total expired volume between said points.

15. The method of claim 10, further including the step of measuring the subject's respiratory rate and using said respiratory rate with said phase shifts and net inspired volume to characterize said respiratory function.

16. The method of claim 10, further including the step of measuring the subject's lung pressure and using said pressure measurement with said phase shifts and net inspired volume to characterize said respiratory function.

17. The method of claim 10, wherein the respiratory function is airway resistance (Raw), characterized by the equation:

18. The method of claim 10, wherein the respiratory function is functional residual capacity FRC characterized by the equation:

19. A method of characterizing the respiratory function of a conscious living subject comprising: a) acquiring separate thoracic and nasal respiratory waveforms;b) determining the a first phase shift between said waveforms at the transition from expiration to inspiration and a second phase shift between said waveforms at the transition from inspiration to expiration;c) determining the net inspired volume between said first and second phase shifts; andd) dividing the difference in the phase shifts by the net inspired volume.

20. The method of claim 19, further including the steps of measuring the subject's respiratory rate and the subject's lung pressure and using said respiratory rate and the pressure with said phase shifts and net inspired volume to characterize said respiratory function.