Polynomial Regression Model Analysis of Abdominal Wall Tension and Intra-abdominal Pressure in Critically ill Patients


 BackgroundAbdominal wall tension (AWT) plays an important role in the pathogenesis of abdominal compliance (AC). This study uses a polynomial regression model to analyze the correlation between intra-vesical pressure(IVP) and AWT in critically ill patients and provides new ideas for the diagnosis and treatment of critically ill patients with intra-abdominal hypertension（IAH）.MethodsA retrospective analysis was conducted in critically ill patients who met the inclusion criteria and were admitted to the Department of intensive care unit of Daping Hospital of Army Medical University from March 14, 2019, to May 23, 2020. According to the IVP on the first day of ICU admission and death within 28 days, the patients were divided into the IAH group (IVP ≥12 mmHg), the non-IAH group, the survival group and the nonsurvival group. The demographic and clinical data, prognostic indicators, AWT and IVP on days 1-7 after entering the ICU, IAH risk factors, and 28-day death risk factors were collected.ResultsA total of 100 patients were enrolled, with an average age of 45.59±11.4 years. There were 55 males (55%), 30 patients from departments of internal medicine (30%), 43 patients from surgery departments (43%), and 27 trauma patients (27%). In the IAH group, there were 50 patients (29 males, 58%), with an average age of 45.28±12.27 years; there were 50 patients (26 males, 52%) in the non-IAH group, with an average age of 45.90±10.58 years. The IVP on the 1st day and the average IVP within 7 days of the IAH group was 18.99（17.52，20.77）mmHg and 19.43（16.87，22.25）mmHg, respectively, which was higher than that of the non-IAH group [ 6.14（3.48，8.70）mmHg, 6.66（2.74，9.08）mmHg], p＜0.001. The AWT on the 1st day and the average AWT within 7 days of the IAH group was 2.89±0.32 N/mm and 2.82±0.46 N/mm, respectively, which was higher than that of the non-IAH group [(2.45±0.29)N/mm,(2.43±0.39)N/mm],p＜0.001.The polynomial regression models showed that the average AWT and IVP on the 1st day and within 7 days were AWTday1 = -2.450×10-3IVP2+9.695×10-2 IVP+2.046，r=0.667（p＜0.0001），and AWTmean = -2.293×10-3IVP2+9.273×10-2 IVP+2.081, respectively. The logistic regression analysis showed that AWTday1 of 2.73-2.97 N/mm increased the patient's 28-day mortality risk (OR: 6.834; 95%: 1.105-42.266, p=0.010).ConclusionsThere is a nonlinear correlation between AWT and IVP in critically ill patients, and a high AWT may indicate poor prognosis.

Since the establishment of the World Society of the Abdominal Compartment Syndrome (WSACS) in 2004, the occurrence, in uence, treatment and prevention of IAH and abdominal compartment syndrome (ACS) have been widely considered and recognized by medical personnel [3][4][5][6].
Based on previous knowledge, in 2014, Malbrain et al. further proposed the de nition of abdominal compliance (AC), which is considered an important parameter for neglected critically ill patients [7]. Abdominal wall tension (AWT) plays a decisive role in AC due to the anatomical structure of the abdomen.
With the technological innovation of open abdomen (OA) and the understanding of abdominal wall anatomy, the assessment of AWT is particularly important to helping us understand the relationship between abdominal volume (AV), intra-abdominal pressure(IAP)and AC [8,9].
In the United States, there are approximately 350,000 hernia repair surgeries each year, making them one of the most common surgical procedures. Various tension-free hernia repairs and abdominal wall separation techniques may have risks of postoperative pain, infection and recurrence [4,[10][11][12]. Important factors that cause these problems include IAH, basic characteristics of the abdominal wall and changes in tension caused by surgery. Therefore, the quantitative measurement of AWT is particularly important [4,11]. AWT not only can re ect the pressure of the abdominal cavity but also is related to intra-abdominal diseases such as peritonitis [13,14]. Considering the complexity of the abdominal wall structure and its possible nonlinear relationship with intra-vesical pressure(IVP), we improved the linear regression model and used a new mechanism to t the data. We hope that our research will help us improve our understanding of the functional characteristics of the abdominal wall and provide new ideas to help diagnose and treat AWTrelated diseases.

AWT working principle
Power supply: The AWT measuring equipment has a power charging function and uses electromagnetic compatibility and other related designs to supply power to the sensors and MCU.
Pressure measurement: The high-precision resistance strain pressure sensor is located at the front end of the spring self-resetting displacement sensor. The front end of the high-precision resistance strain pressure sensor is forced to obtain a smaller signal voltage, which is ampli ed by the instrument ampli er module AD623 and processed by the MCU after obtaining the accurate pressure value. The measuring range is 0-100 N, and the accuracy is 0.1% FS.
Displacement measurement: According to the displacement change of the spring self-resetting displacement sensor, the voltage value is obtained. After ltering and data processing, a high-precision displacement distance is obtained. The linear accuracy is 0.03% FS, and the stroke is 100 mm.
Data information processing module: The STM32 single-chip microcomputer samples 100 values in 1s with a sampling interval of 0.01s, and the collected sensor data are processed through data to obtain accurate values.
Data storage module: The pressure value, displacement value, and calculated muscle tension data are recorded and stored in the U disk in real time, and the le is in ".csv" format.

AWT measurement method and result analysis
Patients were in a quiet state and placed in supine position, and coverings such as abdominal clothing and accessories were removed. For mechanically ventilated patients, the ventilator parameters (PEEP = 0 mmHg) were adjusted. Nine points on the abdominal wall were selected as the measurement points. After turning on the device switch, the AWT measuring device was placed vertically and gently on the surface of the abdominal wall measuring point, and the displacement sensor was pressed at the end of the patient's expiration to the maximum displacement distance (100 mm). The device recorded the measured data at a frequency of 100 Hz, and the same method was applied to press each point repeatedly approximately 20 times with a rate of 2-3 s each time. The measurement was completed after turning off the device.
MATLAB 2018a mathematical software from MathWorks, USA, was used for data analysis. The AWT data of each measurement point are presented as a pressure/displacement ratio curve, where the X-axis is time and the Y-axis is the pressure/displacement ratio. Three curves with uniform and stable waveforms were selected, the average value of the maximum Y values of the three curves was used as the nal AWT result of each measurement point, and the average value of 9 points on the abdominal wall was used as the total AWT value. Figure 2 shows the location of 9 points on the abdominal wall.

Measurement method of IVP
The IVP measurement method was applied based on the standard method developed by the WSACS 2013 guidelines [4]. Malbrain's modi ed sterile IVP measuring device was used to connect to the patient's urinary tube. Patients were lying at and relaxed, and the parameters of the ventilator were adjusted (PEEP = 0 mmHg). After emptying the urine bag, 20ml of normal saline was injected. The 0 scale of the measuring device was the midline level under the axilla of the patient. The end-of-tide reading value was taken as the measurement result and converted into mmHg. Measurements were conducted twice, and the average value was taken as the nal result.

Research process
All of the included patients were divided into an IAH group and a non-IAH group according to their IVP value on the rst day after entering the ICU. IAH was de ned as IVP ≥ 12 mmHg [4]. Death within 28 days was used to de ne non-survival versus survival (Fig. 3).
The basic data and clinical data (age, number of male patients, reason for admission, height and body mass index, APACHE II score, SOFA score, trauma patient ISS score, serum procalcitonin, C-reactive protein, lactic acid, sepsis diagnosis on the rst day in ICU), IVP and AWT at 7 days after admission, IAH risk factors (risk factors related to decreased abdominal wall tension, increased intestinal cavity content, increased abdominal cavity content, or capillary leakage or uid resuscitation), 28-day death risk factors (age 65 years, sepsis, laparotomy, intestinal obstruction, PH 7.2, coagulation disorder, blood transfusion 10u/day, injury control surgery, and IAH), and prognosis (death within 28 days, ICU and total length of hospital stay) were collected.

Establishment of polynomial regression model of AWT and IVP
IVP was divided into 5 pressure ranges according to an interval of 5 mmHg, and clustering was performed to obtain the cluster center. Polynomial regression and quadratic functions were used for tting. MATLAB 2018a mathematical software from MathWorks, USA, was used for data analysis.

Statistical analysis
Normally distributed measurement data were described using the mean and standard deviation (mean ± std), differences between groups were compared by a T test, nonnormally distributed measurement data were described by the median (25,75), and comparisons between groups were performed using a rank-sum test.
The measurement data described the utilization rate (%), the difference between groups was compared using a chi-squared test, and the linear statistical relationship between AWT and IVP was analyzed by Spearman's    (Table 3 and Fig. 4).    (Table 6).

Discussion
Since the concept of AC was proposed in 2014, AC has gradually become an important advancement and research direction in the eld of IAH and ACS [8,9,16]. In 2015, WSACS further revised its name to the Abdominal Compartment Society (www.wsacs.org) with the purpose of ensuring that doctors and researchers fully understand the integrity of the abdominal cavity, the relationship among the organs in the cavity, the functional state between multiple cavities, and the pathophysiological process of disease occurrence and development [2,16,17]. The abdominal wall occupies most of the soft border of the abdominal cavity and plays a major role in AC. Therefore, the assessment of AWT is even more important for AC [8,9,18]. In addition, with the vigorous development of abdominal surgery, technical updates, and a broader understanding of abdominal wall anatomy and physiology in recent years, there is also an urgent need for technology that can evaluate AWT [4,[19][20][21].
Through the measurement of AWT in critically ill patients and an epidemiological indicator analysis in patients with abdominal hypertension, we found that patients with abdominal hypertension have higher AWT, and there is a nonlinear correlation between AWT and IVP. Our research obtained similar results in AWT measurement compared with previous studies, and there were also some new ndings. The earliest description of the invasive measurement method of AWT was published in a study of abdominal surgery.
Bertram et al. [11,20] used a tensiometer to perform AWT measurements on abdominal wall incisions, compared the operative complications such as the recurrence rate of incisional hernia in the measurement group and the nonmeasurement group, and found that the incision tension level was between 1.5 kPa and 3.5 kPa. By controlling the incision tension below 1.5 kPa, the incisional hernia recurrence rate could be reduced from 44-22%, and the patch usage rate was reduced from 6-2%. A correct understanding of AWT can help surgeons perform surgical operations better and reduce surgical complications. In 2013, WSACS also focused on the important role of AWT in AC and described the method of calculating AWT based on La Place's law [7,[21][22][23]. In 2008, Ramshorst et al. [24] rst performed AWT measurements in two cadavers. In the preliminary experiment, a linear regression equation was used to analyze the correlation between AWT and IAP, and a good association was found at the 7 measurement points of the abdominal wall. In 2011, Ramshorst et al. [25] conducted AWT measurement experiments on cadavers and healthy volunteers and found that AWT and IAP were linearly correlated, with the highest correlation in the upper abdomen. In 2015, Chen et al. [14] conducted AWT measurements on critically ill patients and found that the AWT index was between 0.5 and 3.5 N/mm, and AWT and IVP were linearly correlated with good correlation. At the same time, the author also found that breathing, body position and body mass index (BMI) may affect AWT.
A commonly used method for data correlation analyses in medical research is the linear regression equation.
The limitation of linear regression is that it can only be applied to data with linear relationships. However, in clinical practice, many data have nonlinear relationships. Although linear regression can also be used to t nonlinear regression, the effect will be very poor [26]. Considering the complexity of the abdominal wall structure and the possible nonlinear relationship between AWT and IAP, we used a polynomial regression method to analyze the correlation between AWT and IAP. We divided the IAP into 5 different pressure areas, performed clustering to obtain the cluster centers, and then used polynomial regression and a quadratic function for tting. The tting function showed that the area where the IVP is below 15 mmHg is close to a linear correlation, and the area above 15 mmHg is similar to a horizontal parabolic relationship. We speculate that this result is related to abdominal compliance. AWT plays a major role in AC, and the characteristics of AWT at different pressure stages also play a decisive role in AC [27]. In 2008, Mulier et al. [7,9] studied the relationship between intra-abdominal pressure and in ation volume under laparoscopic pneumoperitoneum and used a digital model to calculate the relationship between intra-abdominal pressure and volume. The study found that the relationship between IAV and IAP is not linear. It can be divided into three stages: shaping, stretching and pressurizing. The slope of these three stages is a curve that starts to atten and increases rapidly in the later stage. This performance can be understood as the difference in the elasticity of the abdominal wall at different pressure stages. When a certain critical value is reached, the elasticity no longer increases, which may lead to a rapid increase in abdominal pressure by a slight volume change [17].
Therefore, our research results can better re ect the true changes in the elasticity of the abdominal wall at different pressure levels. The current conventional method for measuring intra-abdominal pressure is measuring the transvesical pressure. In 2018, Abdulla et al. [28] compared the correlation between IAP and IVP in patients undergoing laparoscopic cholecystectomy under general anesthesia and found that IVP and IAP have a linear correlation, where the correlation is good when IAP 12 mmHg and the correlation is relatively poor when IAP 12 mmHg. In addition, in some clinical situations, such as pelvic fractures, pelvic hematomas, peritoneal adhesions, and neurogenic bladder, the intra-vesical pressure cannot be measured [28,29]. In those situations above, the patient's AWT can be measured, and the results of IVP can be calculated using our polynomial regression model to accurately assess IVP, which has potential clinical application value.
Our study found that patients with abdominal hypertension had higher 28-day. The regression analysis showed that the APACHE II score increased the 28-day mortality, which is similar to previous research results.
In 2005, a multicenter epidemiological study conducted by Malbrin et al. [30] analyzed the relationship between the rst day of admission and new emergence during hospitalization and the relationship between average IAH and poor prognosis. Studies have shown that IAH on the rst day of admission is related to organ dysfunction during ICU hospitalization. The average IAP during hospitalization is an independent risk factor for death, and newly appearing IAH during hospitalization is also a risk factor for death. The results of the 2019 IROI study also showed that new IAH during hospitalization can increase 28-day and 90-day mortality, and the APACHE II score on day 1 is an independent risk factor for death [31]. According to a large number of animal and clinical studies in the past, abdominal hypertension directly or indirectly affects the abdominal cavity or organs outside the abdominal cavity, causing multiple organ dysfunction, which is the direct cause of hospital death [32][33][34]. ACS is de ned as IAP 20 mmHg with newly emerging organ dysfunction [1,3,35,36]. The more important effect of IAH is the dynamic changes in IAP caused by IAV.
Therefore, the WSACS has introduced the concept of AC in recent years, emphasizing the role of compliance in the diagnosis and treatment of IAH [1,2,7,8]. We adopted a noninvasive, portable and simple AWT measurement method that has potential value in the early diagnosis and treatment of emerging IAHs.
Our research also found that an AWT of 2.73-2.97 N/mm is a risk factor for death for the following reasons: palpation is a traditional examination for the detection of abdominal diseases. Patients with abdominal hypertension and peritonitis can experience an increase in AWT, but routine examinations are only preliminary judgments and cannot quantitatively and qualitatively diagnose AWT [13,36,37]. AWT can re ect not only the degree of stretch but also the condition of abdominal cavity infection. The PCT index in the abdominal hypertension group was higher, which may have led to a higher rate of abdominal infection in patients with high AWT and therefore a higher mortality rate. Second, according to the previous AWT tting curve, AWT 2.73-2.97 N/mm is at the peak of the tting curve, which is the stage of the highest elastic tension of the abdominal wall; thus, we speculate that at this stage of AWT, the abdominal pressure may be at the point of the cutoff value and that the internal organs of the abdominal cavity are most severely damaged by pressure. This speculation needs to be veri ed in future experiments. We also hope to quantitatively measure AWT to further understand the structural characteristics of the abdominal wall and provide speci c reference materials for the diagnosis and treatment of abdominal disease.  Research owchart