Calculation of esophageal variceal wall tension by direct sonographic and manometric measurements

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Background: LaPlace’s law determines the wall tension of a tubular system by measuring the radius (r), wall thickness (w), and pressure gradient of a tubular structure: wall tension = pressure gradient × r/w. In theory, the determination of wall tension could provide the most accurate method of predicting the likelihood of esophageal variceal rupture. Using high-resolution endoluminal sonography, we measured the variceal wall thickness and radius. Using direct needle puncture, we measured the intravariceal pressure in three patients. We then calculated the wall tension by the LaPlace equation for each of seven varices. Methods: A 20 MHz ultrasonographic transducer was used to image esophageal varices. Outer and inner variceal wall circumferences were measured at a cross section of each varix. The radius and wall thickness of each varix were then calculated. Pressure measurements were obtained in the esophageal lumen and variceal lumen by direct needle puncture of the varices. The pressure gradient was then calculated (esophageal lumen – variceal lumen). Results: The wall tension of the varices from three patients was determined. There was a linear relation (r = 0.88) between the wall tension and pressure gradient. Conclusions: This is a novel technique by which esophageal variceal wall tension can be directly measured. Such information may be useful in the future treatment of patients with portal hypertension by which risk stratification may be determined and pharmacologic response to therapy may be measured.