# Optimizing Tracheal Oxygen Tension and Diffusion Ratio When Choosing High-Flow Oxygen Therapy or CPAP for the Treatment of Hypoxemic Respiratory Failure: Insights from Ex Vivo Physiologic Modelling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}), a science fiction hero invents the machine to convert CO

_{2}to equal parts oxygen (O

_{2}) and equal parts diamond (C). The wise men of the time harvest the O

_{2}and survive, while the foolish masses war over the diamond deposits and perish. Oxygen is vital to our existence because it provides a key ingredient to cellular respiration, and in mammals, the overwhelming physiological method for acquiring O

_{2}stores is through breathing.

_{2}transport system from the air to the tissues is impaired, clinicians may employ an O

_{2}therapy device with the aim of increasing tissue oxygenation. A necessary preliminary to this is to increase (and optimize) tracheal oxygen tension. The clinician will of course also wish to optimize alveolar oxygenation as well as other downstream factors (for example, gas exchange and cardiac output) that enhance tissue oxygen delivery.

_{2}therapy options in terms of oxygen diffusion of blood against the amount of O

_{2}used in treatment referenced as a ratio to no treatment.

## 2. Methods

#### 2.1. Physiologic Model

#### 2.1.1. Fick’s Law

- $\frac{d{O}_{2}}{dt}$ is the transport rate of O
_{2}; - $d$ is a diffusion coefficient;
- ${A}_{sa}$ is the alveolar surface area;
- $dP$ is the difference in tension between the alveolar oxygen and the partial pressure of oxygen in the venous blood of the pulmonary artery (A—a gradient);
- $T$ is the membrane thickness.

_{2}therapy devices:

- The increase in ${P}_{A}{O}_{2}$ relative to room air from inhaling pressurized, oxygen-enriched air;
- An increase or recruitment in alveolar surface area from positive applied pressure (continuous positive airway pressure (CPAP) or positive end expiratory pressure (PEEP)).

- ${A}_{sa\_untreated}$ is the alveolar surface area before CPAP is applied;
- $FRC$ is the functional residual lung capacity, and it is assumed that most respiration will occur at this lung volume;
- $CPAP$ is the pressure applied;
- ${C}_{lung}$ is the static lung compliance considered to be constant for non-atelectatic or non-distended lungs. Only the lung compliance is considered and assumed be approximately 40 mL/cm H
_{2}O [2]. The chest wall compliance is not considered when computing the relative increase in alveolar surface area.

#### 2.1.2. Alveolar Gas Equation

- ${F}_{i}{O}_{2}$ is the volume fraction of oxygen in the inhaled gas;
- ${P}_{atm}$ is the atmospheric pressure;
- ${P}_{app}$ is any applied pressure support, PEEP, or CPAP from respiratory equipment;
- ${P}_{{H}_{2}O}$ is the water vapor pressure in the gas within the alveolus;
- ${P}_{a}C{O}_{2}$ is the arterial partial pressure of $C{O}_{2}$;
- $R$ is the respiratory quotient (typically 0.8).

#### 2.2. Treatment Effectiveness Model Expressed as a Diffusion Ratio

_{2}therapy divided by the initial rate of diffusion assuming no therapy (patient breathing room air).

- $maximumof\frac{d{O}_{2}}{dt}treated$ occurs when enriched ${\mathrm{P}}_{\mathrm{A}}{\mathrm{O}}_{2}$ is presented to hypoxemic ${\mathrm{P}}_{\mathrm{v}}{\mathrm{O}}_{2}$ with PEEP;
- $maximumof\frac{d{O}_{2}}{dt}untreated$ occurs when room air is presented to hypoxemic ${\mathrm{P}}_{\mathrm{v}}{\mathrm{O}}_{2}$ without PEEP.

#### 2.2.1. Note Regarding the Clinical Meaning of $\mathrm{Diffusion}\mathrm{Ratio}\%$

#### 2.2.2. Patient Model

_{2}O/L/s, C = 40 mL/cm H

_{2}O.)

#### 2.3. Modeling the HFNT Device

- (a)
- Providing supplemental oxygen to increase ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ and thus increase ${P}_{A}{O}_{2}$ [11];
- (b)
- Applying high flow directly to the airway through the nares to provide a small amount of PEEP [12] to expand the gas exchange surface.

- (1)
- The cannula flow rate;
- (2)
- The fraction of inhaled oxygen, ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$, in the cannula ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$.

#### 2.3.1. Device ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ vs. Tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$

#### 2.3.2. Estimating Tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ for HFNT

#### 2.3.3. Heatmap Color Convention for Figures in this Article

## 3. Results

#### 3.1. Tracheal ${F}_{i}{O}_{2}$ Estimation during HFNT

#### 3.2. Effectiveness of HFNT Treatment vs. No Treatment (Diffusion Ratio)

#### 3.3. HFNT Setting Recommendations

**1a. Set the desired**${\mathit{F}}_{\mathit{i}}{\mathit{O}}_{\mathbf{2}}$

**.**

**2a. Set the Flow ≥ PIF.**

#### 3.4. Analysis of HFNT without a Blender

#### 3.4.1. Tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ Model for HFNT without a Blender

#### 3.4.2. Guidelines for Setting HFNT with Bleed-In Oxygen

**1a. Increase the Flow setting to match PIF *.**

**2a. Provide a bleed-in**${\mathit{O}}_{\mathbf{2}}$

**rate by**

**2b.**$tracheal{F}_{i}{O}_{2}\frac{0.79{O}_{2}Flow+0.21Flow}{Flow}$

#### 3.5. Comparison of HFNT to CPAP with Oxygen

_{2}O begin to expand the alveolar surface area and contribute to higher ${P}_{A}{O}_{2}$. It is also apparent that the HFNT is superior in efficacy at the same ${O}_{2}$ flow rate when compared with CPAP machines when ${O}_{2}$ is added at the device.

^{3}HFNT with and without a blender has the same efficacy vs. ${O}_{2}$ consumption despite the differences in setup because the delivery method is the same.

## 4. Discussion

#### 4.1. Significance of the Findings

#### 4.2. Critique of the Method

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A graphical illustration of the diffusion of oxygen at different efficacy levels compared to untreated patients. The diffusion ratio or maximum rate of diffusion is 800% at ${F}_{i}{O}_{2}$ = 1 and 200% at ${F}_{i}{O}_{2}$ = 0.3 when compared to breathing room air without treatment. This efficacy refers to the rate at which oxygen is transferred from the alveolus to the venous blood in the pulmonary artery at the initial exposure of the air to the hypoxemic blood across a membrane. The figure illustrates that for higher efficacy, the ${P}_{a}{O}_{2}$ will reach normoxia sooner or more likely during tidal breathing during treatment.

**Figure 2.**This figure illustrates four differing breath waveforms used throughout this analysis. Flow ($\mathrm{Liters}/\mathrm{min}$) is shown in the upper chart of each panel and volume $\left(\mathrm{Liters}\right)$ in the lower chart. The breath sizes range from a shallow 200 mL breath to a normal 500 mL tidal breath. The peak inspiratory flow is listed for each breath. It will become clearer below why the peak inspiratory flow is highly relevant to the clinical effectiveness of the HFNT treatment.

**Figure 3.**The derivation of tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ considering the actual patient flow and the dilution of the oxygen when patient flow may become greater than the cannula flow.

**Figure 4.**The relationship between the settings and the tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ for HFNT on a shallow breath: 200 mL, PIF = 18 LPM. When the flow setting is above the peak inspiratory flow (PIF), the tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ is equal to the device ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$, and no change in FiO

_{2}is expected in any column above the PIF. The numbers contained within the table are kept small; see the color convention to represent the number, described in Section 2.3.2.

**Figure 5.**A side-by-side comparison ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ for the four breath sizes shows that as breath size increases in depth, and PIF increases, the flow setting must be above the maximum breath’s PIF to maintain the set ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ for all breaths. The green line in each chart above represents the PIF for that size breath. The tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ increases below the green line and remains constant in each column above the green line, indicating that setting flow equivalent to PIF is sufficient to achieve the desired ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$. The color convention is described in Section 2.3.2. These charts are meant to show qualitatively, as breaths get larger at the same settings, the charts become more bluish, indicating that tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ is lower at the same setting when breath depth increases.

**Figure 6.**A side-by-side comparison ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ for a consistent breath size (400 mL, with constant PIF, 36 LPM) at different respiratory rates (10, 15, 20 and 25 breaths per minute (BPM)). The four charts are completely identical, and this teaches that respiratory rate and therefore also minute ventilation does not impact ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ during treatment with HFNT.

**Figure 7.**A chart representing the effectiveness of HFNT versus no treatment. The percentage (%) indicates the maximum diffusion rate induced to hypoxemic blood with HFNT treatment at a particular setting as a ratio to the maximum diffusion rate from breathing room air without intervention. This figure’s overall characteristic correlates to the heatmaps for tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ in Figure 6, indicating an ANOVA of treatment efficacy is primarily associated with ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$.

**Figure 8.**The values in Figure 7 are shown as a surface plot. Effectiveness of the treatment is maximized with increasing the set flow and increasing ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$. If the set flow is below the PIF (36 LPM), we see the diffusion ratio of the treatment is diminished toward no treatment (100%).

**Figure 9.**The rotated surface of Figure 8 illustrates how small the diffusion rate benefit is from the small additional PEEP described by Parke et al. [14] due to increasing flow. This is indicated because the surface is flat in the vertical dimension when the flow setting is above the PIF. The diffusion ratio increases as the flow setting is increased to the PIF (36 LPM here), and then, no more benefit at any ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ setting is incurred from increasing flow above the PIF. This implies that increasing total flow above PIF is simply an unnecessary expenditure of oxygen supplies without perceived clinical benefit to the patient.

**Figure 10.**The effectiveness surfaces are drawn together as breath size (PIF) varies. A comparison of HFNT effectiveness at different settings shows that as breaths get larger, the effectiveness of the treatment at the same settings is diminished unless the flow setting is sufficiently large to support the greatest PIF. If the maximum PIF is supported, the effectiveness is maintained; however, there is no additional benefit indicated with increases in flow above the PIF (shown by the flat surface in the vertical dimension on the right side of the plot above). Therefore, the model shows that effectiveness is optimized at a given ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ setting when the flow is set at or above the PIF.

**Figure 11.**In this figure, the two clinical inputs for HFNT are the set flow and the bleed-in O

_{2}flow. The model applies a time-varying patient flow waveform, ${Q}_{p}\left(t\right)$, and estimates tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ based on the mixing of the treatment flow and the entrained room air with the additional dilution occurring when the flow setting is greater than the bleed-in O

_{2}flow.

**Figure 12.**Applying HFNT to a shallow breath with a peak inspiratory flow (PIF) of 18 LPM illustrates clearly how to maximize the tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ with settings. ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ is maximized at each fixed ${\mathrm{O}}_{2}$ flow rate when the total flow is equal to the PIF. Increasing the total flow setting dilutes the device ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ and therefore the tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$.

**Figure 13.**An illustration of all four ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ charts for the four candidate breaths shows how both total flow settings and ${\mathrm{O}}_{2}$ flow rate must increase with breath size. The deeper breaths with higher PIF require higher settings to achieve the desired tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$. Here also note, indicated by the color trends on the charts, that increasing the flow setting always dilutes the tracheal ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$.

**Figure 14.**The complex relationship between settings and ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ values is shown by this chart for HFNT with bleed-in oxygen. For this 300 mL breath, the ability to maintain an ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ is achieved with increasing total flow and ${\mathrm{O}}_{2}$ flow bleed-in rate together. The PIF for the 300 mL breath is 25 LPM after the total flow equal or exceeds PIF, ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$, and the relationship can be determined by a ratio of the device settings. When flow is less than PIF, the ${\mathrm{F}}_{\mathrm{i}}{\mathrm{O}}_{2}$ calculation requires knowledge of the breath pattern.

**Figure 15.**This figure illustrates a comparison of the diffusion efficacy with variable settings for HFNT

^{3}, CPAP plus ${O}_{2}$ entrained at the mask, and ${O}_{2}$ added to the back of the CPAP. The diffusion efficiency describes the maximum diffusion rate of ${O}_{2}$ in hypoxemic arterial blood for each device/settings combination compared to no treatment. The comparison shown here uses the breath size of 500 mL and plots in one dimension the flow of oxygen used in the therapy. The flow of oxygen is not constant in HFNT; however, it was computed as an average flow used by the HFNT blender during the breath. In the second dimension, the CPAP pressure or the flow setting from HFNT is plotted on the same scale, reminding the reader that the PEEP and total flow are correlated in HFNT. This third dimension indicates effectiveness according to equation (4). The red and yellow surfaces describing the effectiveness of the CPAP with ${O}_{2}$ entrained at the mask (red) and HFNT (yellow) are similar, while CPAP is below a nominal 15 cm H

_{2}0. The blue surface describes the least-effective method: CPAP with ${O}_{2}$ entrained at the device.

Parameter | Correlation to Oxygen Diffusion | Impact | Treatment Method |
---|---|---|---|

${F}_{i}{O}_{2}$ | Significant, ${F}_{i}{O}_{2}$ application can increase ${P}_{A}{O}_{2}$ by a factor of 5 | ${O}_{2}$ therapy | |

${P}_{atm}$ | Small impact to ${P}_{A}{O}_{2}$ in most inhabitable areas, but low atmospheric pressure can lead to altitude sickness | hyperbaric chamber or moving the patient to sea level | |

${P}_{app}$ | Small impact to ${P}_{A}{O}_{2}$ as applied pressures are insignificant in relation to atmospheric pressure; however, the applied pressure also aids diffusion by increasing surface area. | CPAP, PEEP, or MV | |

${P}_{{H}_{2}O}$ | $\mathrm{Humidity}\mathrm{lowers}{P}_{A}{O}_{2}$, but is necessary especially with HFNT to prevent injury and dehydration. | Active or Passive heated humidification, natural humidification through mucosal membranes or HME | |

${P}_{a}C{O}_{2}$ | $\mathrm{Poor}\mathrm{ventilation}\mathrm{slightly}\mathrm{reduces}{P}_{A}{O}_{2}$ | Inspiratory Pressure Support or Expiratory Pressure therapy to aid obstructive disease | |

$R$ | Does not vary far from typical values of 0.8 | Dietary changes |

Parameter | Symbol | Value Used | Reference |
---|---|---|---|

Functional Residual Capacity | FRC | 3 L | [3] |

Alveolar SA untreated | ${A}_{SA\_untreated}$ | 118 m^{2} | [4] |

Atmospheric Pressure | ${P}_{atm}$ | 99 kPa ^{1} | [5] |

Alveolar Water Vapor Pressure | ${P}_{{H}_{2}O}$ | 47.08 mm Hg | [6] |

Arterial CO_{2} Pressure | ${P}_{a}C{O}_{2}$ | 46 mm Hg | [1] |

Respiratory Quotient | R | 0.8 | [1] |

Venous O_{2} Pressure in the Pulmonary Artery during Hypoxemia | ${P}_{v}{O}_{2}$ | 32 mm Hg | [7] |

^{1}Atmospheric Pressure is calculated from a 194 m elevation and using the relationship ${P}_{atm}=101325{\left(1-0.0000225577\ast Elevation\right)}^{5.2588}$.

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**MDPI and ACS Style**

Truschel, B.; Polkey, M.I.
Optimizing Tracheal Oxygen Tension and Diffusion Ratio When Choosing High-Flow Oxygen Therapy or CPAP for the Treatment of Hypoxemic Respiratory Failure: Insights from Ex Vivo Physiologic Modelling. *J. Clin. Med.* **2023**, *12*, 2878.
https://doi.org/10.3390/jcm12082878

**AMA Style**

Truschel B, Polkey MI.
Optimizing Tracheal Oxygen Tension and Diffusion Ratio When Choosing High-Flow Oxygen Therapy or CPAP for the Treatment of Hypoxemic Respiratory Failure: Insights from Ex Vivo Physiologic Modelling. *Journal of Clinical Medicine*. 2023; 12(8):2878.
https://doi.org/10.3390/jcm12082878

**Chicago/Turabian Style**

Truschel, Bill, and Michael I. Polkey.
2023. "Optimizing Tracheal Oxygen Tension and Diffusion Ratio When Choosing High-Flow Oxygen Therapy or CPAP for the Treatment of Hypoxemic Respiratory Failure: Insights from Ex Vivo Physiologic Modelling" *Journal of Clinical Medicine* 12, no. 8: 2878.
https://doi.org/10.3390/jcm12082878