Management of constipation in Parkinson’s disease by Bernoulli's principle

Yoshiharu Uno, MD, PhD – Doctor, Researcher and Author
Yoshiharu Uno has more than 30 years of experience in healthcare and research for academia. Currently a freelance doctor working in two clinics and two hospitals in Kobe and Kakogawa, Japan, he also is Editor-in-Chief of Office Uno Column and the author of books focusing on low-FODMAP diets for chronic constipation and IBS.

Introduction
As a gastroenterologist, I read with interest the study by Knudsen et al. in the Journal of Parkinson’s Disease, which clarified the relationship between the colonic transit time and colonic volume in Parkinson's disease (PD) [1]. Due to the fact that calibre and velocity are variables of flow dynamics, I was particularly interested in the correlation between extent of intestinal dilation and colon transit time—that is, how much the intestine is distended and how long it takes for food to travel through the digestive system. Given that constipation is a common non-motor symptom of PD, I did some further analysis.

Method
I measured the colon diameter using the CT image presented by Knudsen et al. in their article. The middle vertebral body width of L5 was set to 5 cm, and the distance of the intestinal tract was calculated by subtracting a line at the center of the intestinal tract. In the colon of PD patients, dolichocolon, as well as a tendency for wide-width was observed, compared to the colon of healthy controls (HC). Since 1,500 mL of water per day flows into the large intestine, the volume flow rate was set to 0.02 cm3 s-1 (1728 mL per day), the fluid density was 1 g cm-3, and each height was set to the length of the colon. Based on Bernoulli's principle, which states that increased speed of a fluid is directly linked to a drop in pressure, I calculated velocity [2].

Bernoulli’s principle:  1/2  v2+ P/ρ + gh = Constant
where:
P
: pressure
v: velocity of the fluid
ρ: density
g: gravity acceleration
h: height

Equation of continuity:  Q = Av
where:
Q: flow volume
A: cross-sectional area 
v: velocity of the fluid

As a result, the theoretical transit times from the caecum to the descending colon in healthy controls, Parkinson’s patients, and Parkinson’s patients with severely increased volume were 10.6 hours, 24.7 hours, and 38.5 hours, respectively. These results were consistent with those of Knudsen et al., showing that the total colon transit time was two days in healthy controls and 3.8 days in people with PD.

The takeaway
Constipation in people with PD can be explained by the theory of flow dynamics, and if the inflow volume to the caecum is doubled in a typical Parkinson’s case, the transit time may be reduced to that of a healthy person. In addition, in the typical Parkinson’s case, if the volume of inflow into the caecum doubles (0.04 cm3 s-1), it can be theoretically reduce the transport time to that of someone without the disease (12.6 hours). From the above, it is possible that treatment to increase the volume of water flowing into the caecum could be effective for constipation in PD patients. However, in the case of megacolon, with a high colonic compliance [3], increasing the flow rate may merely dilate the intestinal lumen, and may not result in an effective velocity. Therefore, administration of laxatives should also be used in consideration of colonic compliance in Parkinson’s disease.

The sigmoid colon and rectum could not be measured, due to image overlap, but it should be noted that to calculate the intestinal tract more accurately, it is necessary to adjust its length in 3-D.

References
[1] Knudsen K, Fedorova TD, Bekker AC, Iversen P, Østergaard K, Krogh K, & Borghammer P (2017) Objective colonic dysfunction is far more prevalent than subjective constipation in Parkinson's disease: A colon transit and Volume study. J Parkinsons Dis, 7, 359-367.
[2] Uno Y (2017) Management of Colon Stents Based on Bernoulli's Principle. Indan J Gastroenterol [in press].
[3] O'Dwyer RH, Acosta A, Camilleri M, Burton D, Busciglio I, & Bharucha AE (2015) Clinical features and colonic motor disturbances in chronic megacolon in adults. Dig Dis Sci, 60, 2398-2407.