Anal canal closure depends on a delicate balance between the tension in the wall of the sphincters, their diameter, and the closure pressure generated by this system, which is governed by Laplace's law. Three muscular structures maintain anal canal closure: the smooth muscle of the internal anal sphincter (IAS), the striated muscle of the external anal sphincter, and the striated puborectal muscle. The IAS plays a key role in maintaining continence, providing 75 percent of the maximum resting pressure.⁶ Whereas this resting pressure is provided by the fatigue resistant internal anal sphincter to guarantee anal closure, the striated external anal sphincter can be volitionally used to generate additional closure pressure (maximum squeeze) during large increases in abdominal pressure, such as during coughing, sneezing, or lifting heavy objects.

The thickness of the IAS is known to increase with advancing age.^7–9 Previous studies have measured IAS thickness by using ultrasound with an endoanal probe or via magnetic resonance imaging (MRI) with a coil. However, measurements performed with an endoanal probe are invasive in that they alter both the diameter and thickness of the sphincter. Sultan et al.¹⁰ illustrated the distortion of the anatomic arrangement of epithelial structures and sphincter muscles by using anal endosonography, thereby demonstrating a new approach using a vaginal ultrasound technique to visualize the sphincter.

Laplace's law describes the relationship between the muscle wall thickness, wall tension, and the squeeze pressure generated within a tubular structure, such as the anal canal. However, to determine these relationships, the radius of the tubular structure must be known. Therefore, measurements without the distortion of the canal by an endoanal probe are needed.

One limitation of the endoanal technique is that by attempting to measure IAS diameter, the probe's diameter rather than the sphincter's diameter has been evaluated. To illustrate the distortion that occurs with endoanal techniques, let us consider the inner diameter of the IAS measured with and without an endoanal apparatus. In our Urogynecologic Clinic, for example, an endoprobe is covered with a 17-mm diameter hard plastic cone. Compared with the undistorted inner diameter of the IAS (mean = 7.8 mm) measured by using MR scans, the cone causes an almost 120 percent increase in the inner diameter of the inner sphincter, with an associated architectural distortion of the sphincter. Therefore, the present study circumvents these artifacts by measuring the undisturbed sphincter diameter, a measurement that is needed to understand the effects of age, such as altered thickness and wall tension, on the delicate anal sphincter complex.

The internal anal sphincter has a cylindrical structure. The tension in its circularly oriented smooth muscle produces a high-pressure zone in the anal canal. Failure of this system to produce high pressure increases the chance that fecal incontinence will occur. The importance of knowing both sphincter thickness and diameter becomes apparent when considering Laplace's law because it relates pressure, thickness, diameter, and stress (“wall tension” per unit area) in hollow organs, such as the heart and vessels^12–14 or the gastrointestinal tract. Although stress is the biomechanically correct term, we will use the word “tone” of the sphincter to denote wall tension to avoid confusion.

The following examples illustrate the importance of considering how these parameters are interrelated. According to Laplace's law (Fig. 4), the inward pressure of the IAS depends on the diameter and thickness as well as the radius and tone (more accurately stress or wall tension). More precisely, the ratio of diameter (or radius) to thickness affects the relationship between tone and pressure. For example, a 25 percent increase in radius (e.g., from 6 mm to 7.5 mm) would result in a 25 percent decrease in internal pressure, assuming constant tone and thickness. However, a 25 percent increase in thickness (e.g., from 4 mm to 5 mm) at the same time would compensate for the increased diameter and result in the original pressure. In our sample size, we reported a 25 percent increase in mean radius and a 33 percent increase in thickness with age. In the next paragraph, we shall explore the functional significance of these results.

In our study, we demonstrated a significant increase of both IAS diameter and thickness in the elderly. We can use Laplace's law to predict the tone of the IAS (smooth muscle tensile stress σ) based on our measurements of IAS thickness and radius, and the extrapolated maximal anal resting pressure from the literature.¹⁵ In our study, we reported a 25 percent difference in mean radius and a 33 percent difference in thickness (Fig. 2). According to Laplace's law, this should result in a small (6 percent) increase in anal canal pressure in the elderly, assuming constant tone. However, this is not consistent with resting anal pressures established in the literature.¹⁵ If we extrapolate values from Ryhammer's data for our two study groups, the mean maximal anal resting pressures would be 100 cm H₂0 in the younger group and 75 cm H₂O in the older group. This represents a 25 percent decrease compared with the 6 percent increase predicted by Laplace's law. The most reasonable explanation is that σ, the tone of the IAS (smooth muscle tensile stress or “wall tension per unit area”), decreases with advancing age. We applied Laplace's law (using our own measurements of radius and thickness, and Ryhammer's data on pressure) and found a significant difference in the sphincter's tone that was 30 percent lower in older females (1.28 ± 0.16 N/mm² vs. 0.9 ± 0.12 N/mm² (mean ± standard deviation); P < 0.001). This is consistent with histologic studies that show increased collagen deposition (sclerosis) and decreased smooth muscle with increasing age.¹⁶

In other words, in trying to explain why a thicker internal anal sphincter is weaker, we need to emphasize changes in all four variables of Laplace's law. Whereas increasing diameter and decreasing tone (wall tension or stress) of the IAS lead to lower anal pressures, thickening of the IAS leads to increased pressures. However, it remains speculative whether an increase in IAS thickness in the elderly is an attempt at compensation, which ultimately fails because of a loss of tone (wall tension).

We could find only one other study¹⁷ in which Laplace's law was used to characterize anal sphincter function. That study focused on diameter, wall tension, and anal closure but assumed constant thickness and did not consider the effect of age as a variable.

One limitation of our study was the possible confounding effect of a significant difference in BMI between the two study groups. However, when we examined data for the whole study population, we were unable to find a significant correlation between BMI and thickness or diameter or the IAS. Because of practical limitations in our study design, we could not provide data on endoanal ultrasound or anal manometry. Therefore, we needed to use published data that described anatomic distortion caused by endoanal imaging techniques¹⁰ as well as reported data on anal manometry¹⁵ to strengthen our findings. At this time, we are recruiting patients for a new study in which MRI, endoanal ultrasound, and anal manometry will all be performed.

This study corroborates earlier findings that IAS thickness increases with age. We have shown for the first time that IAS diameter (undistorted by an endoanal apparatus) also increases with age. By using Laplace's law, we have predicted that internal anal sphincter's tone probably decreases with increasing age. This prediction awaits experimental confirmation. It is known that the maximum anal resting pressure decreases with age, therefore, alterations in thickness and diameter are crucial physiologic implications of age as well. Thus, any pathologic condition may be expected to exacerbate this loss in tonic closure and increase the risk of incontinence.