Scholarly article on topic 'A Model Analysis of Arterial Oxygen Desaturation during Apnea in Preterm Infants'

A Model Analysis of Arterial Oxygen Desaturation during Apnea in Preterm Infants Academic research paper on "Medical engineering"

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Academic research paper on topic "A Model Analysis of Arterial Oxygen Desaturation during Apnea in Preterm Infants"

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A Model Analysis of Arterial Oxygen Desaturation during Apnea in Preterm Infants

Scott A. Sands1, Bradley A. Edwards1, Vanessa J. Kelly1, Malcolm R. Davidson2, Malcolm H. Wilkinson1, Philip J. Berger1*

1 Ritchie Centre for Baby Health Research, Monash Institute of Medical Research, Monash University, Victoria, Australia, 2 Department of Chemical and Biomolecular Engineering, Faculty of Engineering, University of Melbourne, Victoria, Australia


Rapid arterial O2 desaturation during apnea in the preterm infant has obvious clinical implications but to date no adequate explanation for why it exists. Understanding the factors influencing the rate of arterial O2 desaturation during apnea (SaO2) is complicated by the non-linear O2 dissociation curve, falling pulmonary O2 uptake, and by the fact that O2 desaturation is biphasic, exhibiting a rapid phase (stage 1) followed by a slower phase when severe desaturation develops (stage 2). Using a mathematical model incorporating pulmonary uptake dynamics, we found that elevated metabolic O2 consumption accelerates SaO2 throughout the entire desaturation process. By contrast, the remaining factors have a restricted temporal influence: low pre-apneic alveolar PO2 causes an early onset of desaturation, but thereafter has little impact;reduced lung volume, hemoglobin content or cardiac output, accelerates SaO2 during stage 1, and finally, total blood O2 capacity (blood volume and hemoglobin content) alone determines SaO2 during stage 2. Preterm infants with elevated metabolic rate, respiratory depression, low lung volume, impaired cardiac reserve, anemia, or hypovolemia, are at risk for rapid and profound apneic hypoxemia. Our insights provide a basic physiological framework that may guide clinical interpretation and design of interventions for preventing sudden apneic hypoxemia.

Citation: Sands SA, Edwards BA, Kelly VJ, Davidson MR, Wilkinson MH, et al. (2009) A Model Analysis of Arterial Oxygen Desaturation during Apnea in Preterm

Infants. PLoS Comput Biol 5(12): e1000588. doi:10.1371/journal.pcbi.1000588

Editor: Kim Prisk, University of California, San Diego, United States of America

Received July 28, 2009; Accepted October 30, 2009; Published December 4, 2009

Copyright: © 2009 Sands et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: We received no funding for this work.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail:


Apnea and its accompanying arterial O2 desaturation are common clinical complications in preterm infants, occurring in more than 50% of very low birth weight infants [1]. In preterm infants, apnea causes a reduction in heart rate [2] and cerebral perfusion [3], often requires mechanical ventilation, and is associated with neurodevelopmental impairment [4]. Apnea-related hypoxemia is of major concern in light of evidence that repetitive hypoxia in newborn animals results in irreversibly-altered carotid body function [5], raising the possibility of impaired ventilatory control, and causes neurocognitive and behavioural deficits [6]. Respiratory arrest and hypoxemia are also strongly implicated in sudden infant death syndrome (SIDS) [7,8] where the speed at which hypoxemia develops is considered to be particularly dangerous.

In preterm infants, the rate of arterial O2 desaturation (Sao2) can be highly variable and rapid, with average rates as high as 4.3% s during isolated apneas [9]. An earlier framework to describe SaO2 proposed that metabolic O2 consumption relative to alveolar volume determines the speed at which alveolar PO2 falls [10]; it was envisaged that Sao2 is then a function of falling Po2 and the slope of the oxy-hemoglobin dissociation curve. However, such a model assumes that the rate of alveolar depletion of O2, denoted pulmonary O2 uptake (VpO2), is equal to tissue O2 consumption during apnea (see Methods - Theory). Previous

studies in adults have shown that Vpo2 falls from metabolic consumption during apnea [11], and our previous modeling studies in lambs showed that the difference between VpO2 and metabolic O2 consumption has a crucial role in determining Sao2 during recurrent apneas [12]. We found that apneic changes in VpO2 cause desaturation to occur in 2 stages. During stage 1, lung O2 stores are depleted, and VpO2 falls below metabolic consumption. During stage 2, VpO2 is close to zero, and tissue O2 needs are provided by depletion of blood O2 stores.

To date, no complete theoretical analysis of the factors influencing desaturation during apnea has been published. The only available study [13] has a number of critical limitations. First, the model incorporated a constraint of a fixed difference between SaO2 and mixed-venous saturation; thus dynamic changes in VpO2 could not occur and their influence on SaO2 could not be examined. Second, no assessment was made of the impact of cardiorespiratory factors on the two stages of O2 desaturation. Third, in focusing on adults, the study did not examine profound desaturation to levels well below 60% as can often occur in preterm infants [9,14].

Accordingly, the aim of the current study was to quantify the importance of cardiorespiratory factors relevant to Sao2 during apnea, with particular reference to the preterm infant. Using a model that permits variation of Vpo2 during apnea, we examine a number of factors known to influence Sao2, such as lung volume [15], metabolic O2 consumption [16] and pre-apneic arterial oxygenation [17] as well as factors that are particularly pertinent for

Author Summary

When breathing stops, the flow of O2 into and the flow of CO2 out of the body cease. Such an event, termed an apnea, can be especially dangerous in preterm infants in whom it can lead to a rapid decline in arterial O2 saturation, reaching rates of 3-8% per second, rapidly reducing O2 to a level that could lead to neurological damage. Despite extensive experimental research, we have a poor mechanistic understanding of the causes of rapidly developing hypoxemia. We describe a new mathematical model that allows examination of the importance of the major cardiorespiratory factors that are likely to influence the speed at which arterial hypoxemia worsens during apnea. We found that high metabolic rate as well as reduced pre-apneic ventilation, lung volume, cardiac output, hemoglobin content, blood O2 affinity, and blood volume accelerate the development of hypoxemia during apnea. Importantly, the cardiorespiratory factors that contribute to rapid hypoxemia are all pertinent to the preterm infant during early postnatal development. Thus the newborn is highly susceptible to rapid and severe desaturation, potentially explaining the propensity of preterm infants, particularly those with apnea, to neurological impairment.

the developing newborn, including anemia, hypovolemia, reduced O2 affinity, and chronically and acutely reduced cardiac output. We use the results to develop a conceptual framework for the interpretation of mechanisms underlying rapid Sao2 during apnea.


Overview of the two-compartment model for gas exchange

To determine the independent influence of clinically relevant cardiorespiratory factors on Sao2 during a single isolated apnea, we used a two-compartment lung-body mathematical model which incorporated realistic blood O2 stores and gas exchange dynamics (Figure 1), as described in Methods - Mathematical model (a full list of symbols is provided in Table 1). We used published parameters for healthy preterm infants born at ~30 wk gestational age (Table 2); the values represent measurements taken at approximately term equivalent age when surprisingly rapid desaturation has been observed [9]. We also derive analytic solutions for SaO2 to quantify the importance of cardiorespiratory factors on Sao2 to obtain a detailed view of the arterial O2 desaturation process, as described in Methods - Theory.

Pulmonary gas exchange dynamics during apnea

To examine changes in O2/CO2 exchange during apnea, a single apnea was imposed on the model. During apnea, changes in alveolar O2 and CO2 stores are not constant (Figure 2); importantly, alveolar PO2 (PAo2) did not continue to fall at its initial rate as governed by metabolic O2 consumption (VO2), but instead the rate of fall in Pa02 was reduced as it approached mixed venous Po2 (Pvo2), an observation also reflected in the falling VPo2. As a result, two distinct phases for O2 depletion can be seen, which we refer to as stage 1 and stage 2 [12]. During stage 1, PAo2 fell rapidly and Vpo2 decreased and became dissociated from Vo2; during stage 2, with Vpo2 greatly reduced, both PAo2 and Pvo2 fell together at a reduced rate. The two distinct phases were also observed for alveolar and arterial Pco2 (PAco2, Paco2) although stage 1 for CO2 was substantially shorter than that for O2. Such an

Figure 1. Model schematic representing O2 uptake, transport and consumption. O2 stores are represented by the alveolar, arterial, and venous compartments. Two dynamically-independent levels of O2 uptake are denoted: pulmonary O2 uptake (Vpo2) and metabolic consumption (Vo2). R-L shunt is also included. Ta is the arterial transit time. Symbols are described in Table 1. doi:10.1371/journal.pcbi.1000588.g001

effect results from the earlier fall in pulmonary CO2 uptake (VPco2) relative to the fall in Vpo2 (Figure 2A) and is reflected in the reduction in respiratory exchange ratio (V pco2 /V po2) (Figure 2B). Consequently, a more rapid fall in PAo2 was observed compared with the rise in PAco2(see Methods - Derivation of equations), such that Pao2 fell by 100 mmHg in the time Paco2 rose by just 14 mmHg (Figure 2C).

Time-course of Sao2 during apnea

The time-course of Sao2 is complex (Figure 3), a consequence of the nonlinear O2-dissociation curve in combination with the fall in Vpo2. At apnea onset, Sao2 started to fall with a rate equivalent to that predicted by Equation 12, where Sao2 = 0.5% s{1 (Figure 3). During apnea, changes in the slope of the O2-dissociation curve (bHbo2) and Vpo2 dominated the time-course of desaturation as hypoxemia progressed. As Sao2 started to fall after apnea onset, bHbo2 increased with little change in Vpo2, resulting in a proportional increase in Sao2. However, as arterial hypoxemia developed, there was a concurrent decline in Vpo2. As Sao2 is directly proportional to the product bHbo2 x Vpo2 (Equation 11) it follows that during apnea, the peak Sao2 of 3.5% s 1 occurred when bHbo2 x Vpo2 reached a maximum. This occurred when neither Vpo2 nor bHbo2 was at its maximum (both ~50% of peak). Finally, with Vpo2 greatly reduced during stage 2, Sao2 remained at a constant level (Sao2 = 1.7% s-1), close to that predicted by Equation 13 (1.8% s"1).

Factors influencing Sao2

The following parameters were individually varied from their 'normal' values to quantify their influence on Sao2: resting Pao2 ,

Table 1. Mathematical symbols. Table 1 Cont'

Pvap Alveolar water vapour partial pressure, 47 mmHg

lung volume (Vl), metabolic O2 consumption (Vo2), blood hemoglobin content (Hb), cardiac output (Qt), R-L shunt fraction (Fs), and the Po2 at 50% saturation (P50). All other parameters were kept constant to remove confounding effects, unless specified otherwise.

To quantify SaO2 we used 3 different measures. First, since apnea is considered clinically significant if it lasts for > 10 s and is accompanied by bradycardia or O2 desaturation [18], we calculated the average rate of fall in Sao2 between apnea onset and 10 s later (SaO°2s); such a measure describes the immediacy of onset of desaturation and is analogous to the practical measurement of average Sao2 used in many clinical studies [9,15,19,20]. Second, we determined the peak instantaneous SaO2 during apnea

Table 2. Typical parameters for the preterm infant at term equivalent age.

Pan Rate of change in alveolar N2 partial pressure

QbCO2 Blood volume for CO2

QbO2 Blood volume for O2

Qv Venous (and tissue) volume

Qvco2 Venous (and tissue) volume for CO2

QVO2 Venous (and tissue) volume for O2

Q t Cardiac output

Q p Pulmonary blood flow

RER Respiratory exchange ratio (VpCO2/VpO2)

So2 O2 saturation

Sao2 Arterial O2 saturation

ScO2 End-capillary arterial O2 saturation

SV02 Mixed venous O2 saturation

S ao2 Rate of arterial O2 desaturation

S a002s Average SaO2 from t = 0-10 s during apnea

Parameter Value Reference/s

Lung volume (Vl) 20 ml kg"1 [31,54]

Metabolic O2 consumption (Vo2) 10 ml min"1 kg"1 [55,39,40]

Cardiac output (Q_ T) 250 ml min"1 kg"1 [56]

Hemoglobin content (Hb) 8 g dl"1 [22]

P50 24 mmHg [22]

Blood volume (Qb) 80 ml kg"1 [57]

P50 is the partial pressure at 50% saturation. Vl is taken from data on functional residual capacity. For all simulations unless otherwise stated: respiratory exchange ratio (RER) was assumed to be 0.8; shunt fraction (Fs) was adjusted to 8.7% to achieve a resting PaO2 of 72 mmHg as is typical for normal healthy infants [58]; resting alveolar ventilation (V1 = 168 ml min"1kg"1 under normal conditions) was set to achieve resting PaO2 = 100 mmHg. doi:10.1371/journal.pcbi.1000588.t002

Figure 2. Pulmonary gas exchange during apnea. (A) Rate of pulmonary O2/CO2 exchange. VpO2 and VpCO2 fall from resting levels during apnea. (B) Net alveolar-capillary gas uptake (Vptotal = VpO2 — VpCO2) and respiratory exchange ratio (RER~VpCO2/VpO2)during apnea. (C) Changes in alveolar, arterial and mixed venous PO2 /PCO2 during apnea. Contrast the time-course in Pao2 and Paco2 as they fall/rise towards PvO2 /PvCO2. (*) represents the fall in PAo2 if Vp^ was assumed equal to VO2. S1 = stage 1; S2 = stage 2. doi:10.1371/journal.pcbi.1000588.g002

(Sa(O2ak), the value during the linear portion of arterial desaturation [10,21] which we find is not confounded by resting SaO2. Third, we report a measure of SaO2 during stage 2 apnea (SaOa®22). To quantify the sensitivity of SaO2 to changes in each cardiorespira-tory factor, we defined the term impact ratio as the ratio of proportional increase in SaO2 to a small increase from the normal value of each factor. For example, an impact ratio of 1 indicates a one-to-one increase in SaO2 with an increase in the factor, and a

negative ratio indicates an inverse relationship. The impact of each cardiorespiratory factor on SaO°2s, SaO2a , and SaOag2 is summarised in Table 3.

Resting PAo2 . Changes in PAo2, achieved via reduced resting ventilation or increasing inspired O2 (Fi02), had a substantial effect on the onset of desaturation. Reduced pre-apneic PAo2 dramatically increased SaO°2s (Figure 4A), but had little effect on S aO22ak or SaOa®2 . In contrast, increasing pre-apneic Pa02 with the application of supplemental O2 achieved the opposite, essentially right-shifting or delaying the arterial desaturation curve, where one second of delay can be achieved by an increase in Pio2 (DPio2) of ~ 7 mmHg, or DFi02 of ~ 1% (see Methods - Derivation of equations). These results occurred despite only a minor influence being visible on resting Sao2. For example, a reduction of Pa02 from 100 to 60 mmHg caused a 6% reduction in resting SaO2 but at the

ßHb02xVp02 1

- 5 - 4 T cr c

- 3 - 2 X < "O o

Time (s)

Figure 3. The time course of SaO2 during apnea. Panel (A) shows the increase in the slope of the oxy-hemoglobin dissocation curve at the level of alveolar PO2 (^hbo2), and the fall in pulmonary oxygen uptake (VpO2) that occurs during apnea. Panel (B) shows that changes in the product bhbo2 xVpO2 explain the time course of the instantaneous slope of arterial O2 desaturation (SaO2) during apnea. Note that the peak S>aO2 occurs when VpO2 is substantially less than its resting value. Note also that the rate of fall of mixed-venous saturation (SvO2) and S_ ao2 become equal and constant after 20 s. doi:10.1371/journal.pcbi.1000588.g003

same time led to a more than 2-fold elevation in S aO0s (Figure 4B). Additionally, a severe reduction in PAo2 , to below 70 mmHg, was required to elevate S aO2ak.

Lung volume (Vl) and blood volume (Qb). SaO°s and

S aO2ak were inversely related to Vl during stage 1 (Figure 5A, B), but changes in Vl had no influence on Sa^a®2 . In direct contrast,

reduced Qb strongly increased SaOag2 2, but had no effect on stage

Table 3. Impact ratios describing the effect of cardiorespiratory factors on SaO2.

Parameter alteration S a£s S aOf S as¿ase2

Resting PAO2 -3.97 -0.35 -0.01

Lung volume (Vl) -2.24 -0.82 -0.09

Blood volume (Qb) -0.01 -0.06 -0.68

O2 consumption (VO2) CC +2.29 +1.00 +1.00

O2 consumption (VO2) nCC +2.73 +1.92 +1.00

Hemoglobin content (Hb) nCC -0.38 -1.00 -0.89

Hemoglobin content (Hb) CC +0.01 -0.10 -0.89

P50 +1.37 -0.68 -0.11

Cardiac output (Qt, resting) -0.39 - 0.90 0.00

Cardiac output ((Qt, transient) +1.45 - 0.06 0.00

Shunt Fraction (Fs) -0.01 +0.01 0.00

Impact ratio is defined as the ratio of proportional increase in Sao to the proportional increase in each factor, based on small changes around normal values. An impact ratio of 1 indicates a one-to-one increase in SaO2 >with an increase in the factor, and a negative ratio indicates an inverse relationship. CC = cardiac compensated, nCC = cardiac uncompensated. doi:10.1371/journal.pcbi.1000588.t003

Figure 4. Impact of pre-apneic alveolar Po (ventilation, supplemental O2) on Sao. (A) Effect of three levels of alveolar PO/(Pa02), (i)

100 mmHg, (ii) 80 mmHg and (iii) 60 mmHg, on arterial (SaO/) and mixed venous (SvO/) O2 desaturation during apnea. Note that arterial O2 desaturation is substantially right-shifted with increased Pa0/. (B) Sensitivity of SaO/ to changes in pre-apneic Pa0;(Fi02). Note that reduced Pa0/ has a major impact on S a0°s but little impact on S aoa8ei; the influence on S aoe2ak is small in the normal range b ut b ecomes stronger at low/ Pa0/. n ='normal' 'values; S1, stage 1 slope; S2, stage 2 slope. doi:10.1371/journal.pcbi.1000588.g004

1 desaturation as reflected in no change in SaO2ak or SaO°2s (Figure 5C, D). 2 2

Metabolic O2 consumption (V o2). To examine the impact of changing VO2 on SaO2, independent of resting Svo., QT was adjusted to maintain resting Svo. constant, where AQT(%) = AVo2(%); we refer to this procedure as 'cardiac compensation'. Under this condition, elevated VO2 caused a directly proportional increase in SaO2 throughout stages 1 and 2 (Figure 6A, B). Without cardiac compensation, the effect of increased VO2 on SaO2 during stage 1 was magnified, as shown by the further increase in SaO22ak (Figure 6A, B).

Hemoglobin content (Hb) and oxygen affinity (P50). Reduced hemoglobin content (Hb) increased SaO2ak and SaOag2 2 but had little effect on SaO°2s (Figure 7A, B). The increase in SaO2ak occurred with an increase in the peak of the product bHbo. x VpO2 as VPO2 was higher at each level of SaO2. The simulation was repeated with cardiac compensation for the reduction in hemoglobin content, where AQt(%)= 1/AHb(%), to maintain constant resting Svo.. Following such compensation, no changes in SaO2ak or SaO°2s were observed but reduced Hb continued to increase SaOf22. In examining the influence of P50, P90 was adjusted in equal proportion on the basis of published data [22]. Increased P50 increased the immediate SaO2, increased SaO°2s, decreased SaO2ak and had no effect on SaOag2 (Figure 7C, D).

Cardiac output (Qt). Reduced resting QT increased SaO2ak, but had little impact on SaO°s or SaOage2 (Figure 8A, B). As with

Hb, the increase in SaO2ak with reduced resting Qt occurred with an increase in the peak of the product bHbo. x Vpo.. To differentiate between the influence on Sao. of an acute reduction in cardiac output, i.e. when bradycardia accompanies apnea, rather than a chronic reduction, we reduced cardiac output in a step-wise manner from the baseline value at the time of apnea onset. In constrast to the effect of reduced resting Qt, a transient

reduction in Qt decreased SaO°2s, but had a negligible impact on SaO2ak or SaOf22 (Figure 8C, D).

Resting R-L shunt fraction (Fs). Increased Fs reduced resting Sao. and Svo. but had no effect on SaO°2s, SaO2ak, or S aOf22 (Figure 9A, B). 2 2


Our model analysis of the rate of arterial O2 desaturation during apnea demonstrates that pre-apneic ventilation, lung volume, cardiac output, hemoglobin content and blood volume exert unique effects on Sao. throughout the time-course of desaturation, while metabolic O2 consumption is uniformly influential throughout the process. Our analysis reveals that lung volume and the slope of the O2-dissociation curve are important early in the process, during what we refer to as stage 1 [12], but not stage 2. For the first time, our study reveals that reduced cardiac output and hemoglobin content, and as a consequence resting mixed-venous saturation, substantially accelerate peak Sao.. Finally, low blood volume and hemoglobin content, and therefore a low total blood O2 capacity, increase the speed of desaturation, but only in stage 2. In addition to infants with elevated metabolic needs and low lung volume, those with anemia, cardiac dysfunction, or hypovolemia, which are common complications of prematurity, are at heightened risk of rapid and profound arterial desaturation during apnea.

Methodological considerations

To evaluate the independent effects of cardiorespiratory factors on Sao. we used a two-compartment model, incorporating both alveolar and blood gas stores. The inclusion of a realistic blood store was crucial to reveal that changes in Vpo2 occur as a consequence of arterial and mixed-venous saturation falling

Figure 5. Impact of lung volume (Vl) and blood volume (Qb) on Sao. (A) Effect of three levels of Vl, (i) 30, (ii) 20 and (iii) 10 ml kg , on arterial (Sao2) and mixed venous (SvO2) O2 desaturation during apnea. (B) Sensitivity of S>aO2 to changes in VL. Note that reduced VL has a strong

impact on Sagf and SaO°s but no impact on SaO^822. (C) Effect of three levels of Qb, (iv) 120, (v) 80 and (iv) 40 ml kg \ on SaO2 and SvO2 during apnea. (D) Sensitivity of SaO2 to changes in Qb. Note that reduced Qb has little impact on Sa§2*k or SaO°2s but has a large impact on SaO^82 2. n ='normal' values; S1, stage 1 slope; S2, stage 2 slope. doi:10.1371/journal.pcbi.1000588.g005

asynchronously during apnea (Figure 3). Our approach allowed us to extend the previous framework based on the assumption of constant VpO2 [23], which prevented the recognition that a steep O2-dissociation curve and low lung volume do not accelerate SaO2 beyond stage 1. Furthermore, the varying VpO2 permitted recognition that cardiac output, hemoglobin content, and blood volume have a major influence on Sao2.

In the current study, the typical value of SaO2 found using our model was 3.5% s 1 whereas Poets and Southall [9] using beat-by-beat oximetry in preterm infants reported a mean value for Sao2 =4.3%s-1 during isolated apneas. Reasons for our lower value may lie with our simplifying assumptions. Notably, we assumed a homogenous lung compartment and complete gas

mixing and as such, the model incorporated neither limitation of alveolar-capillary diffusion nor an uneven ventilation-perfusion distribution, two factors that could cause an increase in SaO2. In addition, we assumed a constant lung volume during apnea, equal to published values of functional residual capacity, whereas it is known that lung volume can fall during apnea [15,24]; based on our data, a fall in lung volume to 15.5 ml min 'kg 1 immediately after apnea onset would achieve SaO2 of 4.3% s 1 (Figure 5B).

A final assumption implicit in our model is that all O2 transfer to the blood occurs via the pulmonary circulation. However, in very preterm infants there is evidence ofpercutaneous respiration in the first few days of life in both room air and with supplemental O2 [25]. With whole body exposure of 90% O2 to the newborn skin, it

Figure 6. Impact of metabolic O2 consumption (VO2) on SaO2. Panel (A) shows the effect of doubling VO2 on arterial (SaO2) and mixed venous (SvO2) O2 during apnea; (i) 10 ml min 21kg 2 \ (ii) 20 ml min 2 qkg 2 1 with cardiac compensation (CC), and (iii) 20 ml min 2 qkg 2 1 with no CC (nCC). Note that with CC, increased VO2, from (i) to (ii), elevated SaO2 uniformly at all levels of SaO2 during both stages 1 and 2; note that the level of SaO2 at the inflection point (shown by short black lines) is unchanged. With nCC (iii), increased V^ caused a reduced resting Svo2 and lower SaO2 inflection, and greater Sa02 during stage 1, compared to (ii). (B) Sensitivity of Sa02 to changes in V02. Note that with increased V02: a uniform increase in SaO^ occurred with CC, and a more-than-proportional increase was seen with nCC; Sa0°s is elevated in both cases, but more so with nCC; a uniform increase in SaO^822 is shown regardless of CC. n ='normal' values; S1, stage 1 slope; S2, stage 2 slope. doi:10.1371/journal.pcbi.1000588.g006

has been calculated that Vp02 can be reduced by 8-10% [26], likely via an increased resting mixed-venous saturation; our study demonstrates that such an effect would decrease Sa02 during apnea.

Pulmonary gas exchange dynamics during apnea

Our study is consistent with previous observations that Vp02 and VpC02 rapidly decline during apnea from their steady-state values [11], with VpC02 falling faster than Vp0j. The relatively low blood capacitance for O2 compared with that for CO2 results in the resting alveolar-mixed-venous partial pressure difference being ~ 12-fold greater for O2 than for CO2. Consequently, when apnea begins ~12 times more O2 than CO2 must diffuse across the lung to obliterate the alveolar-mixed-venous partial pressure difference. The slower fall in Vp02 vs. VpC02 provides for a faster depletion of alveolar O2 vs. CO2 stores; such an effect results in complete desaturation of arterial blood in the time PaCO2 rises by just 14 mmHg. These findings lead us to conclude that short-term O2 homeostasis is more unstable than CO2 homeostasis and thus that the danger of isolated apneas in infants is likely to be mediated via hypoxemia rather than hypercapnia.

Factors influencing Sao2

Our study provides for the first time a comprehensive analysis of the factors that determine arterial desaturation during apnea in preterm infants. We show that resting oxygenation in the form of alveolar PO2 has the greatest influence on desaturation at apnea onset. When apnea begins at an increasingly lower alveolar Po2 , Sao2 more quickly reaches its maximum because Po2 rapidly arrives at the steepest part of the O2-dissociation curve. This effect explains the inverse relationship between mean Sao2 and pre-apneic Sa02 during apnea [17], but as we show the peak slope

itself is negligibly affected by reduced resting PO2 within the normal range.

We demonstrate that Sa02 is inversely related to lung volume during stage 1 of apnea as a result of the greater reduction in alveolar Po2 in poorly inflated lungs per unit of O2 transferred into the pulmonary capillaries. This analysis is consistent with the inverse correlation between Sa02 and lung volume [15], with the view that active upper airway closure maintains lung volume and slows Sa02 [27,28], and with our recent report that the application of continuous positive airway pressure effectively slows Sa02 in lambs [29]. However, once stage 2 begins, the blood becomes the principal source of O2 and thus the only store which influences Sa02.

A novel finding from our study is that reduced resting mixed-venous saturation, caused by either a reduced cardiac output or reduced hemoglobin content, strongly elevates peak Sa02, independent of metabolic O2 consumption. We show that reduced resting mixed-venous saturation accelerates Sao2 via an increase in the peak value of bHbo2 x Vp02; in other words, low mixed-venous saturation provides for a greater pulmonary O2 uptake even in the presence of a developing arterial hypoxemia, and thereby increases Sao2. A role for hemoglobin in determining Sao2 is consistent with the finding that elevated hemoglobin content in adults slows Sa02 during apnea [21]. In contrast, blood transfusion to raise hemoglobin content in anemic preterm infants, a common clinical therapy, has little or no impact on the severity of apneic desaturation [30]. Our proposed explanation for the lack of benefit of raising hemoglobin content via transfusion is that it also reduces heart rate [30] and cardiac output. Thus, in the newborn, the rise in mixed-venous saturation expected after transfusion is counteracted by a tendency for mixed-venous saturation to fall as a result of reduced cardiac output. An investigation that failed to find an effect of cardiac output on Sa02 [23] did not account for our

Figure 7. Impact of hemoglobin content (Hb) and O2 affinity (P50) on SaO;. (A) Effect of three levels of Hb, (i) 12 g dP1, (ii) 8 g dP1 and (iii) 4 g dP1, on arterial (SaO;) and mixed venous (Sv^) O2 desaturation during apnea. Note the fall in Sao2 at the inflection point (shown by short black lines). Note also that the reduced Hb has little impact on desaturation above SaO; ~ 80%. (B) Sensitivity of SaO; to changes in Hb. (C) Effect of three levels of P50, (iv) 18 mmHg, (v) 24 mmHg, and (vi) 36 mmHg, on SaO;. (D) Sensitivity of SaO; to changes in P50. n ='normal' values; S1, stage 1 slope; S2, stage 2 slope.


finding that pre-apneic and transient changes in cardiac output have opposing influence on Sao2. Importantly, we find that a transient fall in cardiac output, characteristic of bradycardia during apnea in preterm infants [2], conserves alveolar O2 via reduced VpO2 and thus reduces SaO2 (see Equations 10 and 11). Consistent with this finding, apneic bradycardia prevents a rapid fall in SaO2 in adults [21].

We found that each of the factors examined exerts a unique and therefore recognisable influence on the time course of the desaturation process (Figure 10). Low alveolar PO2 can be recognised by a left-shift of the desaturation trajectory so that desaturation begins sooner following the onset of apnea. A steep desaturation slope in the early phase of stage 1 points to a low

ratio of lung volume to metabolic O2 consumption. In the late phase of stage 1, when desaturation proceeds in a linear fashion, a low resting mixed-venous saturation accelerates SaO2 and leaves the fingerprint of a low inflection point in arterial O2 desaturation; low resting mixed-venous saturation reflects low cardiac output or hemoglobin content with respect to O2 consumption. Lastly rapid SaO2 during stage 2 signifies a low total blood O2 capacity with respect to O2 consumption which would point to either low blood volume or anemia. The presence of a constant R-L shunt, while having no influence on SaO2, causes a parallel downwards shift in the desaturation trajectory. The unique impact of different factors on the desaturation curve may be used to guide preventive clinical intervention.

Figure 8. Impact of cardiac output (Qt) on Sa^,. (A) Effect of three levels of resting Qt, (i) 375 ml min 2 1kg 2 1, (ii) 250 ml min 2 1kg 2 1, and (iii) 125 ml min 2 1kg 2 1, on arterial (SaO2) and mixed venous (SvO2) O2 during apnea. Note that reduced Qt elevates SaO2, associated with a reduction in resting SvO2 and reduction in SaO2 at the stage 1-2 transition or inflection point (shown by short black lines). (B) Sensitivity of SaO2 to changes in Qt. Note the strong influence of (Qt on SaOe2ak, but negligible effect on SaO°2s and Saj^822. (C) Simulations in (A) repeated for a step change in (Qt at apnea onset by (iv) +125 ml min21kg21 (e.g. tachycardia), (v) 0 ml min2 21kg 1, and (vi) 2125ml min 1kg 1 (e.g. bradycardia), following resting Qt~25° ml min^kg"1. Note that the transient effect of (Qt is opposite to the resting effect of Qt on arterial desaturation during apnea. (D) Sensitivity of SaO2 to acute changes in (Qt during apnea. Note the strong influence of a step-change in (Qt on SaO°s, but negligible effect on SaO,ak and SaOa®2 . n ='normal' values.


Clinical significance

We show theoretically that the lower lung volume [31] and higher metabolic O2 consumption [32] of preterm compared to term infants predisposes to a rapid onset and progression of desaturation during apnea. Two reports offer support for this view. First, rapid desaturation occurs in infants with low functional residual capacity [15], a finding that may help to explain the more frequent O2 desaturation events during active sleep [33] when functional residual capacity is reduced. Second, frequent desaturation is characteristic of preterm infants with bronchopulmonary dysplasia (BPD) [34] whose O2 consumption is 25% greater [35], and functional residual capacity is 25% less [36], than in preterm

infants without BPD; Equations 11 and 12 predict that such differences increase both immediate and peak Sao2 by ~70%. In addition, hypoventilation and reduced resting PAQ2 in infants with BPD, as inferred from elevated Paco2 [ЗУ], further increase desaturation at apnea onset. Our finding that each rise of 1% in inspired O2 provides ~1 s of delay (right-shift) in the onset of apneic desaturation (Equation 15) may guide the titration of supplemental O2 for the prevention of apneic hypoxemia while minimising the well known side-effects of long-term exposure to hyperoxia.

Our study has implications for the management of infants in clinical care. Metabolic O2 consumption can be elevated after


- Sv02 --1-r -1

Time (s)

8 7 6 5 4 3 2 1 0

n 1 Sai i i i

20 30 Fs (%)

Figure 9. Impact of R-L shunt (Fs) on SaO2. (A) Effect of three levels of Fs, (i) 0%, (ii) 15%, and (iii) 30%, on arterial (SaO2) and mixed venous (SvO2) O2 during apnea. Note that resting R-L shunt fraction has a negligible impact on SaO2 during apnea. (B) Sensitivity of SaO2 to changes in Fs. n ='normal' values; S1, stage 1 slope; S2, stage 2 slope. doi:10.1371/journal.pcbi.1000588.g009

feeding [38], with reduced ambient temperature [39], and via the adminstration of methylxanthines [40]. Despite the success of methylxanthines in reducing the frequency of apnea and

Stage 1 Stage 2


Figure 10. Conceptual framework depicting the temporal sequence of influence of the key cardiorespiratory factors on

Sao2. Note the regions of influence of lung volume (Vl), cardiac output (Qt) and blood volume (Qb), each with respect to metabolic O2 consumption (Vo2). Hemoglobin content (Hb) influences the latter phase of stage 1 as well as stage 2. The impact of reduced VL is limited to stage 1, and blood volume to stage 2. Reduced PAo2 causes a leftward shift in the desaturation trajectory. Note that the point of inflection at the transition between stages reveals the resting SvO2. doi:10.1371/journal.pcbi.1000588.g010

bradycardia, such treatment has surprisingly little impact on hypoxemic episodes [41]; we suggest that the elevated O2 consumption and the absence of bradycardia are likely to increase SaO2 during those apneas that persist despite treatment. The severity of hypoxemic episodes is reduced by switching preterm infants from supine to prone [42], which may increase functional residual capacity [43] and improve diaphragm function, increase tidal volume and increase resting alveolar Po2 [44]. Our finding that low cardiac output leads to increased SaO2 during apnea leads to the suggestion that judicious adjustment of inotropic support in infants with cardiac abnormalities could improve resting mixed-venous saturation and reduce apneic hypoxemia.

Hypoxemic events become less frequent between infancy and childhood, despite an unchanged apnea frequency [28], perhaps as a result of a fall in O2 consumption per body weight. However, before this occurs, infants experience a period of susceptibility to rapid desaturation during apnea as a result of a fall in hemoglobin content and O2 affinity [22] and a rise in O2 consumption [45]. The implications for SIDS are obvious in that these changes coincide with the peak incidence for SIDS at 2-3 months [46]. SIDS also occurs disproportionately in preterm infants [46], who manifest severe anemia [22] and greater O2 consumption. Infants resuscitated from apparent life threatening events have been found to have lower hemoglobin content [47], pointing to a potential role for rapid SaO2 in the progression of such events. It is possible that the rapid development of apneic hypoxemia initiates prolonged hypoxic cardiorespiratory depression that in turn leads to SIDS.


We have provided a mathematical framework for quantifying the relative importance of key cardiorespiratory factors on the rate of arterial O2 desaturation during apnea, with particular relevance to preterm infants. For the first time we have demonstrated that each of the factors examined has a signature influence on the trajectory of desaturation, providing quantitative insight into the causes of rapidly developing hypoxemia during apnea.


Mathematical model

Lung compartment. For the lung, a single homogeneous compartment is assumed based on the model of Grodins et al [48]. Each equation describing changes in the alveolar partial pressure of each gas (G) is based on the conservation of mass (specifically, the pressure-volume product) and is expressed in terms of inspired and expired alveolar ventilation and transfer of gases into the pulmonary capillary:

IP Ag =

V/ iPIg-У ePag-PqY pG

where Pag represents the rate of change of alveolar Po2 , Pco2 , and Pn2 ; Pig represents the inspired alveolar partial pressure of each gas G; P0 is atmospheric pressure converted from STP to BTP (863 mmHg); VpG represents Vp02 and — VpC02, pulmonary gas uptake (STPD) for O2 and CO2 (VpN2 was neglected in this study for simplicity); Vl and VE are inspired and expired alveolar ventilation (BTPS). Accounting for the difference in Ve and VI due to a net pulmonary gas uptake into the pulmonary blood, yields:

V/ E = УI-

-У ptotal

where Pb = barometric pressure (760 mmHg); Pvap = water vapour pressure (47 mmHg); Vptotal is the net pulmonary gas

uptake, Vptotai = VPo2 {VPco2 ■

Since purely obstructive apneas are relatively rare in preterm infants [49], an unobstructed airway was chosen as the standard model in this study. In the current study it was assumed that lung volume did not fall during apnea, as in active sleep [24], when apneic desaturation events are most common [33]. With lung volume constant, conservation of mass requires that passive airflow into the unobstructed airway must occur in response to a net pulmonary gas uptake into the pulmonary blood [11] ■ To account for this effect, we can write:

-У ptotal

Pilot simulations predicted that the volume of gas inflow during apnea is unlikely to exceed physiological deadspace. Thus, during apnea Pig is taken as Pag of the last exhaled breath prior to apnea onset.

For the current study we assumed diffusion equilibrium at the pulmonary capillaries, such that PAg = PcG. Gas uptake is determined from the Fick equation; specifically, pulmonary blood flow (Qp), and the difference between end capillary (CcG) and mixed venous (CvG) content:

У pg=Q p(CcG-Cvg)

Utilising equations for R-L shunt, arterial content of each gas G is determined from its end capillary (CcG) and mixed venous (CvG) content, and pulmonary shunt fraction (Fs):

CaG = (1-Fs)CcG + (Fs)CvG

Fs defines the ratio of pulmonary blood flow to cardiac output, such that Fs = (1 — (Qp)/QT.

Body compartment. Assuming that the PO2 of the venous blood is equilibrated with the tissue P02, the mass-balance equations are:

Q т[CaG(t-Ta)-CVGl-У G Qvg

where CaG(t —Ta) represents the gas content of O2 and CO2 in the arterioles; Ta is arterial transit time; Vg represents Vo2 and — VC02, the metabolic consumption of O2 and production of CO2; QvG represents Qv02 and QvC02 the combined venous/ tissue volumes for O2 and CO2.

Blood O2 stores were partitioned by assigning blood volume (Qb) to arterial (25%) and venous (75%) compartments [50] and they were modelled assuming an entirely unmixed arterial compartment, and an entirely mixed and homogenous venous compartment. The arterial transit time (Ta) is constrained by the arterial volume (Qa) by the relationship Ta = Qa/Qt. The body compartment volume Qv02 is taken as the venous volume. QvC02, the effective venous/tissue volume for CO2 is taken as the same value for Qv02, based on published data (see Methods -Derivation of equations). Physiologically this represents no additional contribution of a specific tissue reservoir for CO2 within the time frame of apnea.

To characterise the O2-dissociation curve we used a modified form of the equation of Severinghaus [51]. We re-expressed the equation with respect to the partial pressure at 50% (P50) and at 90% (P 90) saturation:

Sq2 = 100[k2(Po23+k1Po2)-1+1l-

where ki = (9Ps°3-P9°3)/(P9°-9Ps°) and k2 =Ps°3 +kiPs°. Values for P50 (24.0 mmHg) and P90 (53.6 mmHg), were obtained from the data of Delivoria-Papadopoulos [22] for a 9-10 wk-old preterm infant. O2 content (C02, ml ml21) includes that bound to hemoglobin (Hb, g ml21) and that dissolved in plasma:

CQ2 = 1.36 Hb(SQ2|100) + 0.00003PO2

The relationship between CO2 content (CCO2) and PCO2 was assumed linear:

Cco2 = ßbco2Pco2 +kco2

where ßbCo2 = 0.0048 ml ml"1mmHg"1 and kCo2 =0.364 ml ml-1

as adapted for STPD from Grodins et al. [52].

Simulations were performed using software written in MA-TLAB (The Mathworks; Natick, MA).


A general equation. In an earlier study we developed a general relationship that describes the factors influencing the magnitude of Sao2 at any instant in time during apnea [12]:

S ao2 =

ßbo2PoQ т Yl

(Sao2 -SV02)

where pbO2 is the capacitance co-efficient of blood for O2. To specifically demonstrate the role of gas exchange, it is more useful to represent SaO2 in terms of VpO2. Using Equation 1 for O2 under conditions of apnea (VI,Ve = °), assuming Pa02 =Pao2, and

using SaO2 = ßffiic^PAo2, reveals:

S ao2 =

ßнbo2Pc Vl

V/ PO2

where РиЬо2 (% mmHg"1) is defined as the slope of the O2-dissociation curve, specifically regarding end-capillary Po2 with respect to SO2. It is clear from Equation 11 that SaO2 is directly proportional to the product РиЬо2 x VpO2, which both vary substantially during apneic arterial desaturation. Although Equations 10 and 11 are useful conceptually, values for (SaO2 — SvO2) or VpO2 throughout apnea are unknown, and thus

SaO2 is not simple to predict explicitly.

Special cases. The original framework to understand factors influencing SaO2 was based on the assumption that VpO2 = VO2 [10,23] which does not hold true during apnea [11,12]. However, such an assumption is valid prior to any substantial fall in Sao2, and as therefore useful to explicitly describe SaO2 immediately upon apnea onset (Sa0nset):


SaO2 =

ßнbo2Po Vl

Notably, Equation 12 demonstrates that for any level of VO2 and Vl, SaO^®' is intimately related to PHbO2. Consequently, SaO^®' increases dramatically with reduced resting Pao2 (Figure 11).

Although no simple expression could be written to describe SaO2 explicitly for stage 1, we derived an expression for SaO2 during stage 2 (see Methods - Derivation of equations), given by:

S a^ase 2 = -

1.3б нЬ Qb +


Since the total blood O2 capacity (1.36 Hb Qb) is much greater

than VL/(PHbO2Po), S aOf'2 is determined principally by (1 .36 Hb Qb) with negligible influence coming from lung volume (Vl) and the slope of the O2-dissociation curve (PHbO2), as well as QT. Using the values for the preterm infant in Table 2 and maximum PHbO2 = 2.8% mmHg-1, Equation 13 predicts that SaOage2 = 1.8%s-1. The little remaining VpO2 during stage 2 can be found by combining Equations 11 and 13:

V/ PO2 =


1.3б нЬ Qb+VLAßffl^Po)

Equation 14 predicts that VpO2 = 8.5% of its resting value during stage 2. Notably, VpO2 is increased by reducing Hb and Qb; the greater VpO2 and thus a greater rate of alveolar O2 depletion with reduced blood O2 capacity (1.36 Hb Qb) will increase S aOf2.

How can we reconcile that Equation 13 shows that Vl no longer influences SaO2 during stage 2, when the general equation (Equation 11) implies that reduced Vl will accelerate SaO2 throughout apneic desaturation? Equation 14 reveals that during stage 2, elevated Vl also acts to increase VPo2; thus nearly entirely offsetting the direct influence on Sao2. The same applies for reduced Риь02, which acts to elevate VpO2 and therefore no longer accelerates Sa02 during stage 2.

Derivation of equations

Here we derive the explicit equations used within the current study to encapsulate key relationships pertaining to gas exchange and arterial desaturation during apnea.

Stage 2 arterial O2 desaturation.. This section details the derivation of an explicit equation to predict the rate of both arterial and venous desaturation during the severe desaturation of stage 2, a phase where Vp02 is substantially reduced below V02 and both Sa02 and Sv02 fall at the same rate. Ignoring dissolved plasma O2, consideration of Equation 1 for O2 and assuming Sa02 = Sv02 yields:

S ao2 =

VO2 -1.3б нЬ QT(Sao2(t - Ta) - Svo2 1.3б нЬ Qv

By substituting the following relationships into Equation 15: (SaO2(t-Ta)-SvO2 ) = (SaO2 -S^ + SaO2Ta; Ta = Qa/Qt; Qb = Qa+Qv; VpO2 = 1.36HbQT(SaO2 -SvO2); it can be shown that SaO2 is directly proportional to the difference between VO2 and VPO2, where:

S ao2 =

V O2 V po2 1.3бнь Qb

Combining Equations 11 and 16 yields Equation 13.

Estimation of effective blood volume for CO2. Using the same methodology as described above, the ratio of CvO2 to CvCO2 during stage 2 can be used to estimate the ratio of QbCO2 to QbO2. CvO2 and CvCO2 can be found using:

Figure 11. Relationship between the slope of the oxyhemoglobin dissociation curve and alveolar PO2. Note that reduced alveolar PO2 (PAo2) causes a substantial increase in the slope of the oxy-hemoglobin dissociation curve (PHbO2; see inset) and in SaO2 at apnea onset (SaO™0'; based on Equation 12). doi:10.1371/journa l.pcbi.1000588.g011

C aG = CVg =

where QbO2 and QbCO2 are the effective blood volumes for O2/

CO2; bbCO2 is the capacitance coefficient for CO2. Neglecting pulmonary gas exchange, combining Equation 17 for O2 and CO2 gives:

QbcO; QbO;


Equation 18 permitted the calculation of QvC02 /Qv02 based on published data [53; their Figure 3] where during apnea the rate of rise in CvC02 is very close to the rate of fall in the product of Cvo2 and the respiratory exchange ratio (RER); using — Cvo2 /Cvco2 = 1.29 from their data, and assuming resting RER = 0.8, we find that QbC02/Qb02 = 1.23 or approximately 1. Thus QvC02/Qv02 is assumed to be 1.

Stage 1 hypercapnia. Here we develop a relationship to describe the time-course of alveolar/arterial hypercapnia during stage 1 for CO2. Using Equation 1 for CO2, taking Vi,Ve = 0, gives the relationship PAco2 = P°VpC02 /Vl. Substituting the steady-state Fick equation, VpC02 = PbC02Q T(PaC02 -PvC02), assuming alveolar-arterial equilibrium (Paco2 = Paco2 ), using VpC02 = VC02 under resting conditions, assuming that PvC02 is constant, and solving for PAco2 yields:

Equations 19 and 20 describe the slowing of PAco2 from the initial rate PAco2 = PoVpCO2 /Vl as PAco2 rises towards PvCO2. Specifically, the time constant t = VL/(pbCO2PoQt) demonstrates that high PbCO2 causes a rapid slowing of VpCO2 and hence of Pac02 as the arterial value approaches venous value. Indeed, fitting an exponential curve to the PAco2 trace (Figure 2) during the first 5 s of apnea yielded a rapid time constant of 1.26 s, a value close to that predicted by VL/(pbCO2P0Qt). The corollary is that the low value of pbO2 prevents the slowing of VpO2 as desaturation progresses, giving rise to a rapid PAo2 decline and thus rapid arterial desaturation. Likewise, further reducing pbo2 by lowering hemoglobin content potentiates such effect.

Impact of supplemental O2. The delay (right-shift) in arterial desaturation during apnea with increasing supplemental O2 (APIO2) can be predicted explicitly. Using Equation 1 for O2 under the conditions of apnea, and assuming APi02 =APa02, the delay (At) in arterial desaturation is given by:

APiq2Yl PO/O;


У CQ ььсо2ро<гт „

VCQ; e--(19)


Calculating the rate of rise in Pac02 (Pac02) by taking the derivative gives:

Author Contributions

Conceived and designed the experiments: SAS PJB. Performed the experiments: SAS. Analyzed the data: SAS BAE MRD MHW PJB. Wrote the paper: SAS BAE VJK MRD MHW PJB. Designed and implemented the model: SAS VJK MRD MHW.

P Aco; = PYCQ2 e-^ t Yl


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