Integration of inspiratory and expiratory intra-abdominal pressure: a novel concept looking at mean intra-abdominal pressure

Background The intra-abdominal pressure (IAP) is an important clinical parameter that can significantly change during respiration. Currently, IAP is recorded at end-expiration (IAPee), while continuous IAP changes during respiration (ΔIAP) are ignored. Herein, a novel concept of considering continuous IAP changes during respiration is presented. Methods Based on the geometric mean of the IAP waveform (MIAP), a mathematical model was developed for calculating respiratory-integrated MIAP (i.e. MIAPri=IAPee+i⋅ΔIAP), where 'i' is the decimal fraction of the inspiratory time, and where ΔIAP can be calculated as the difference between the IAP at end-inspiration (IAPei) minus IAPee. The effect of various parameters on IAPee and MIAPri was evaluated with a mathematical model and validated afterwards in six mechanically ventilated patients. The MIAP of the patients was also calculated using a CiMON monitor (Pulsion Medical Systems, Munich, Germany). Several other parameters were recorded and used for comparison. Results The human study confirmed the mathematical modelling, showing that MIAPri correlates well with MIAP (R2 = 0.99); MIAPri was significantly higher than IAPee under all conditions that were used to examine the effects of changes in IAPee, the inspiratory/expiratory (I:E) ratio, and ΔIAP (P <0.001). Univariate Pearson regression analysis showed significant correlations between MIAPri and IAPei (R = 0.99), IAPee (R = 0.99), and ΔIAP (R = 0.78) (P <0.001); multivariate regression analysis confirmed that IAPee (mainly affected by the level of positive end-expiratory pressure, PEEP), ΔIAP, and the I:E ratio are independent variables (P <0.001) determining MIAP. According to the results of a regression analysis, MIAP can also be calculated as MIAP=-0.3+IAPee+0.4⋅ΔIAP+0.5⋅IE. Conclusions We believe that the novel concept of MIAP is a better representation of IAP (especially in mechanically ventilated patients) because MIAP takes into account the IAP changes during respiration. The MIAP can be estimated by the MIAPri equation. Since MIAPri is almost always greater than the classic IAP, this may have implications on end-organ function during intra-abdominal hypertension. Further clinical studies are necessary to evaluate the physiological effects of MIAP.


Introduction
The intra-abdominal pressure (IAP) is an important clinical parameter with major prognostic impact [1,2]. An unrecognised pathological increase in IAP eventually leads to intra-abdominal hypertension (IAH) and abdominal compartment syndrome (ACS) [3,4], which result in significant morbidity and mortality [5]. Thus, recognition and reliable measurement of IAP are the first important steps for prevention and management of IAH and ACS in critically ill patients [6].
Assuming no respiratory movement, the IAP would be relatively constant and primarily determined by body posture and anthropomorphy (e.g. body mass index) [3,7].
The IAP may be affected by conditions influencing intraabdominal volume and abdominal compliance (C ab ) [3,8,9]. Further, the complex interaction between intraabdominal volume and C ab during respiration ( Figure 1) may significantly [10] and frequently (12 to 40 changes per minute) change the IAP (Figure 2), with more intense effects during positive-pressure mechanical ventilation or the presence of positive end-expiratory pressure (PEEP) [10][11][12].
According to the current consensus definitions of the World Society of the Abdominal Compartment Syndrome (WSACS), the IAP should be measured at end-expiration (IAP ee ) [13], referred to as the 'classic IAP' throughout the text. However, the IAP ee is only a single component of an ever-changing trend and thus does not incorporate a considerable portion of this IAP trend ( Figure 2). The objectives of this study were to develop and validate a novel IAP measurement concept to consider IAP changes during respiration and to identify independent variables influencing IAP within this novel concept.

Methods
Part A: mathematical model A set of numerous IAP values occurs for a patient during a single respiratory cycle. The central tendency of a set of values can be calculated by the mathematical function of the 'mean'. In determining the mean IAP, the arithmetic mean for IAP ee and the end-inspiratory IAP (IAP ei ) was described previously [14], calculated by dividing the sum of the values by the number of values. However, employing the arithmetic mean for the IAP waveform is mathematically incorrect. Instead, the mean of a waveform can be calculated by the 'geometric mean' function. The geometric mean is calculated by dividing the area under the waveform in a definite interval (i.e. the definite integral of the waveform) by the value of the definite interval [15]. Therefore, the mean IAP (MIAP) for a sample IAP waveform between the times (T 0 ) and (T) in Figure 2 can be calculated as follows: where 'MIAP ri ' is the respiratory-integrated MIAP, 'T−T 0 ' is the time interval for a full respiratory cycle, and 'IAP (t) dt' is the IAP at each time point (t). The result would be a time-weighted mean for the IAP waveform. This is closely analogous with the critically important cardiovascular concept of mean arterial blood pressure [16][17][18], which is the geometric mean of the arterial blood pressure waveform [19,20]. Equation 1 may be simplified as follows (see the addendum) [21]: Abdominal muscle contraction Rib cage action IAP IAV Figure 1 Relationship between intra-abdominal volume (IAV), abdominal wall compliance (C ab ) and intra-abdominal pressure (IAP). The directions of the movement of IAP on the x axis and IAV on the y axis associated with the isolated action of the rib cage inspiratory muscles, abdominal expiratory muscles, and the diaphragm are shown. The direction of the action of the diaphragm depends on the abdominal compliance. Adapted from de Keulenaer et al. [7].
Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18 where 'i' is the decimal fraction of the inspiratory time in a respiratory cycle and can be calculated from the inspiratory/expiratory (I:E) ratio (i = I /(I + E); 0 <i < 1) and ΔIAP = IAP ei − IAP ee . Since IAP ee , i, and ΔIAP can be assumed to be independent, a computerised iteration can be used for a set of values for each parameter to determine their effect on MIAP ri and to compare the MIAP ri with the classic IAP.
The effects of IAP ee on MIAP ri and the classic IAP were examined through a gradual increase of IAP ee from 12 to 25 mmHg, with steps of 1 mmHg (Figure 3). For each IAP ee , a range of possible MIAP ri values was calculated according to Equation 2 with an I:E ratio of 4:1 and an ΔIAP of 8.16 mmHg for the maximum MIAP ri , and an I:E ratio of 1:4 and an ΔIAP of 1 mmHg for the minimum MIAP ri . Because previous studies have shown a correlation between ΔIAP and IAP ee , the ΔIAP was increased 10% for each 1 mmHg increase in the IAP ee .
The effects of the I:E ratio on MIAP ri and the classic IAP were examined by a gradual increase in the I:E ratio from 1:4 to 4:1 with steps of 0.5 ( Figure 4). The amount of IAP ee was held constant (19 mmHg). For each I:E ratio, a range of possible MIAP ri values was calculated with an ΔIAP of 7 mmHg for the maximum MIAP ri and an ΔIAP of 2 mmHg for the minimum MIAP ri .
The effects of ΔIAP on MIAP ri and the classic IAP were examined by a gradual increase in ΔIAP from 1 to 5 mmHg, with steps of 0.5 mmHg ( Figure 5). The amount of IAP ee was held constant (19 mmHg). For each ΔIAP, a range of possible MIAP ri values was calculated with an I:E ratio of 4:1 for the maximum MIAP ri and an I:E ratio of 1:4 for the minimum MIAP ri .
Each of the abovementioned data sets was assumed to be a unique case, and the values shown in Figures 3,4,5 should not be considered as a trend in changes that can be obtained in a single patient.

Part B: human pilot study
In six ICU patients that were mechanically ventilated with Evita XL ventilators (Draeger, Lubeck, Germany), the mean IAP was automatically calculated as the geometrical mean (MIAP) via a balloon-tipped nasogastric tube connected to a CiMON monitor (Pulsion Medical Systems, Munich, Germany). The MIAP ri was also calculated according to Equation 2. Data were collected on respiratory settings, plateau and mean alveolar pressures (P plat , P mean ), PEEP, and dynamic compliance (calculated as the tidal volume (TV) divided by (P plat -PEEP)). The C ab was calculated as TV divided by ΔIAP. The thoraco-abdominal index of transmission (TAI) was calculated as ΔP alv (= P plat − PEEP) divided by ΔIAP, in which P alv is the alveolar pressure.
The effects of IAP ee on MIAP ri were examined by a gradual increase in PEEP from 0 to 15 cmH 2 O, with steps of 5 cmH 2 O during a best-PEEP manoeuvre (20 measurements at each PEEP level in five patients, resulting in 80 measurements). The effects of ΔIAP on MIAP ri were examined by a gradual increase in TV from 250 to 1,000 ml, with steps of 250 ml during a low-flow pressurevolume loop (20 measurements at each TV level in five patients, resulting in 80 measurements). The effects of I:E ratio on MIAP ri were examined by a gradual increase in the I:E ratio from 1:2 to 2:1, with steps of 0.5 during a recruitment manoeuvre (9 measurements at each I:E ratio in one patient, resulting in 45 measurements). Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18 Page 3 of 10   12 13 14 15 16 17 18 19 20 21 22 23 24   Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18 Statistical analysis was performed using SPSS software. Pearson correlation analysis and Bland and Altman analysis were performed. For comparisons between MIAP ri and IAP ee at different levels of IAP ee (PEEP), TV, and I: E ratio, a two-tailed paired Student's t-test was performed. Data are expressed as the mean with the standard deviation (SD), unless specified otherwise. A P value below 0.05 was considered statistically significant. The local EC and IRB approved the study, and informed consent was obtained from next of kin.

Part A: mathematical modelling
According to Equation 2, three major independent parameters determine the MIAP ri : IAP ee , I:E ratio, and ΔIAP. Therefore, for each IAP ee , the MIAP ri depends on two other factors (Figure 3). For IAP ee values between 16 and 20 mmHg, the classic IAP remained below the ACS threshold (dashed line in Figure 3); however, the MIAP ri was able to exceed the ACS threshold. Furthermore, as seen in Figures 4 and 5, the classic IAP was continuously below the ACS threshold, but different ranges of probable MIAP ri values were above the ACS threshold. By changing the I:E ratio, the MIAP ri values changed with dissimilar intensities (e.g. when the I:E ratio decreased from 4:1 to 3.5:1, the intensity of changes in the MIAP ri values was less than that when the I:E ratio decreased from 1.5:1 to 1:1; Figure 4). Furthermore, for a constant IAP ee , higher values for either the I:E ratio or ΔIAP were found to be capable of causing a wider range of possible MIAP ri values (Figures 4 and 5). Mathematically, for all instances in which the ΔIAP was greater than 0 mmHg, the MIAP ri was larger than the classic IAP (see the addendum) [21].

Part B: human pilot study
Six mechanically ventilated patients (three severely burned patients and three surgical ICU patients) were studied. The male-to-female ratio was 2:1. Table 1 summarises the baseline patient demographics.

Regression analysis and Bland and Altman analysis
In total, 205 paired MIAP and MIAP ri measurements were performed with an identical statistical mean of 12.2 ± 3.8 mmHg. Figure 6A shows an excellent correlation between the MIAP and MIAP ri (R 2 = 0.99, P <0.001). Analysis according to Bland and Altman showed a bias and precision of 0 and 0.2 mmHg, respectively, with small limits of agreement ranging from −0.4 to 0.5 mmHg ( Figure 6B). The percentage error was 3.5%.

IAP (mmHg)
Classic IAP MIAPri (Max) MIAPri (Min) Figure 5 Mathematical modelling of IAP measurement for a constant 19 mmHg end-expiratory IAP (IAP ee ) and various ΔIAP. The classic (IAP ee ) and novel (MIAP ri ) methods were used to measure the IAP. The MIAP ri values were calculated for each ΔIAP. A range of possible MIAP ri values for each ΔIAP was calculated according to various I:E ratios. The dashed line represents the ACS threshold.
The classic IAP of patients was below the IAH grade I threshold; however, the MIAP ri significantly exceeded the threshold in several instances (P < 0.001; Figure 7).

Multivariate regression analysis
Analyses showed that the IAP ee (mainly affected by PEEP), ΔIAP, and I:E ratio were independent variables defining the MIAP (Table 2). According to the regression analysis in our sample population, the MIAP can also be calculated from the following simplified formula (P <0.001), in which 'I' and 'E' are elements of the I:E ratio:

Discussion
A novel concept of IAP measurement based on the geometric mean of the IAP waveform was presented. The  Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18 independent parameters determining the IAP in this concept were defined. The human pilot study validated the mathematical modelling with an excellent correlation. A significant difference was observed between the classic IAP and the MIAP ri in our clinical study.
The human study confirmed that MIAP ri is as accurate as an automated geometric MIAP calculation by a CiMON monitor. More importantly, the higher the MIAP or IAP ee , the higher the ΔIAP since ΔIAP acts as an indirect marker of C ab . The ΔIAP is correlated with ΔP alv or is thus inversely correlated with dynamic compliance. As well, the higher the C ab , the lower the TAI. The human study confirmed the predictions of the mathematical modelling in which IAP ee (affected by different PEEP settings), ΔIAP, and I:E ratio were recognised as the major independent determinants of MIAP ri . We also showed that in patients with IAH and under mechanical ventilation, the IAP may be influenced by ventilator settings.
The critical difference between the MIAP ri and the classic IAP near the ACS threshold in our mathematical modelling, as well as the significantly higher MIAP ri than the IAP ee around the IAH threshold in our human study, calls for future studies. The dissimilar intensity in MIAP ri changes under changes in the I:E ratio in Figure 4 may implicate the existence of critical points in the I:E ratio, wherein changing this ratio may cause a more intense change in the MIAP ri . Furthermore, since MIAP ri seems to be almost always larger than the classic IAP, relying only on the classic IAP may place some patients at risk of silent IAH or ACS. Although the aim of the current study was not to address these implications clinically, these findings indicate that further investigations should be performed on respiratory manoeuvres to manage IAH in mechanically ventilated patients (e.g. decreasing the I: E ratio and/or the ΔIAP, or maintaining the I:E ratio in a predefined range).
A limitation of our study was the lack of data to evaluate the physiological difference between the MIAP ri and the classic IAP. However, this study only aimed to prove the concept and to set the stage for further studies. Therefore, we believe that the lack of physiological data does not limit our findings. Nonetheless, further studies on the clinical effects of this concept are necessary before it can be introduced in clinical practice.

Conclusions
A novel concept MIAP ri was presented to consider the IAP changes during respiration and was based on the geometric mean (MIAP) of the IAP waveform. An excellent correlation was observed between the results of the mathematical modelling and those obtained in real patients. Substantial differences were observed between the two IAP methods (the classic IAP measured at end expiration and the novel MIAP). Based on our findings, we believe that the novel concept of MIAP ri may be a better representation for the pressure concealed within the abdominal cavity. Further clinical studies are necessary to reveal the physiological effects of this novel concept.  Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18 Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18 Ahmadi-Noorbakhsh and Malbrain Annals of ?Intensive Care 2012, 2(Suppl 1):S18 http://www.annalsofintensivecare.com/content/2/S1/S18