Since the concept of AC was proposed in 2014, AC has gradually become an important advancement and research direction in the field of IAH and ACS[8–9]. 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, 15]. 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[7–8, 16]. 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, 17–19].
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 findings. The earliest description of the invasive measurement method of AWT was published in a study of abdominal surgery. Bertram et al. [11, 19] 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 kP and 3.5 kP. By controlling the incision tension below 1.5 kP, 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 [9, 20–21]. In 2008, Ramshorst et al.  first 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.  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.  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 fit nonlinear regression, the effect will be very poor. Considering the complexity of the abdominal wall structure and the possible nonlinear relationship between AWT and IVP, we used a polynomial regression method to analyze the correlation between AWT and IVP. We divided the IVP into 5 different pressure areas, performed clustering to obtain the cluster centers, and then used polynomial regression and a quadratic function for fitting. The fitting 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. In 2008, Mulier et al. [7, 9] studied the relationship between intra-abdominal pressure and inflation 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 flatten 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 . Therefore, our research results can better reflect 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. compared the correlation between intra-abdominal pressure and intravesical pressure in patients undergoing laparoscopic cholecystectomy under general anesthesia and found that IVP and IAP have a linear correlation, where the correlation is good when < 12 mmHg and the correlation is relatively poor when > 12 mmHg. In addition, in some clinical situations, such as pelvic fractures, pelvic hematomas, peritoneal adhesions, and neurogenic bladder, the intravesical pressure cannot be measured[26–27]. In the two situations above, the patient's AWT can be measured, and the results of IAP can be calculated using our polynomial regression model to accurately assess IAP, which has potential clinical application value.
Our study found that patients with abdominal hypertension had higher 28-day and 90-day mortality. 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.  analyzed the relationship between the first day of admission and new emergence during hospitalization and the relationship between average IAH and poor prognosis. Studies have shown that IAH on the first day of admission is related to organ dysfunction during ICU hospitalization. The average IAP during hospitalization is not an independent risk factor for death, and newly appearing IAH during hospitalization is 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. 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[30–32]. ACS is defined as IAP > 20 mmHg with newly emerging organ dysfunction[1, 3, 33–34]. 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, 32, 35]. AWT can reflect 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 fitting curve, AWT 2.73–2.97 N/mm is at the peak of the fitting 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 verified in future experiments. We also hope to quantitatively measure AWT to further understand the structural characteristics of the abdominal wall and provide specific reference materials for the diagnosis and treatment of celiac disease.
Conclusion: There was a curve correlation between AWT and IVP in critically ill patients. The polynomial regression model helped us understand the relationship between AWT and IVP. High AWT in critically ill patients indicates poor prognosis.
Limitations: This study enrolled a small number of patients and required large-sample, multicenter clinical trials and related clinical studies of AWT under different physiological or disease states.