Flow simulations of rectal evacuation: towards a quantitative evaluation from video defaecography

Abstract

Mechanistic understanding of anorectal (patho)physiology is missing to improve the medical care of patients suffering from defaecation disorders. Our objective is to show that complex fluid dynamics modelling of video defaecography may open new perspectives in the diagnosis of defaecation disorders. Based on standard X-ray video defaecographies, we developed a bi-dimensional patient-specific simulation of the expulsion of soft materials, the faeces, by the rectum. The model quantified velocity, pressure and stress fields during the defaecation of a neostool with soft stool-like rheology for patients showing normal and pathological defaecatory function. In normal defaecation, the proximal-distal pressure gradient resulted from both the anorectal junction which formed a converging channel and the anal canal. The flow of the neostool through these anatomical parts was dominated by its shear-thinning viscous properties, rather than its yield stress. Consequently, the evacuation flow rate was significantly affected by variations in pressure applied by the rectum, and much less by the geometry of the anorectal junction. Lastly, we simulated impaired defaecations in the absence of obvious obstructive phenomena. Comparison with normal defaecation allowed us to discuss critical elements which should lead to effective medical management.

Keywords: biofluid; biomechanics; rheology.

Figure 1.

X-ray defaecography and image processing. (a) Sagittal view of the rectum filled with standardized radio-opaque neostool. White dots show the segmentation of the rectum. (b) Flow curve of the neostool (circles) fitted by the Herschel–Bulkley constitutive model for yield stress and shear-thinning fluids (plain line), from [21]. At low shear rate, the shear stress tends towards the yield stress. At high shear rate, the shear stress increases and the apparent viscosity decreases. (c) Raw profiles of the rectum after segmentation and interpolation for different time steps (time increasing from blue to red, patient N3). (d) Same profiles after smoothing. (e) Comparison of the area bounded by the raw boundaries (circles) and the smoothed boundaries (plain line) as a function of time t.

Figure 2.

Simulations of normal rectal evacuations through the open anal canal. (a) Evolution of the boundaries of the rectum during the evacuation of the neostool for six patients showing a normal rectal function. The colour code shows the magnitude of the WNS. (b) Example of mean outlet velocity of the neostool through the anal canal V_a (plain lines, left axis) and diameter of the anal canal D_a (dashed lines, right axis) as a function of time (patient N5). (c) The evacuation force F (plain lines, left axis) and its angle with the y axis (dashed lines, right axis) as a function of time for patient N5. (d) Spatio-temporal map of the pressure variation along the length of a mid-line going from the anal canal (0 cm) to the proximal end at time 0 (black line in N5 in a).

Figure 3.

Instantaneous (a) flow fields, (b) pressure fields and (c) viscous stress fields of 6 normal evacuations when the outlet velocity V_a was maximal.

Figure 4.

Simulations of pathologic defaecations showing abnormally slow evacuation. (a) Evolution of the boundaries of the rectum during the evacuation of the neostool for two patients. The colour code shows the magnitude of the WNS. (b) Mean outlet velocity of the neostool through the anal canal V_a (plain lines, left axis) and diameter of the anal canal D_a (dashed lines, right axis) as a function of time. (c) The evacuation force F (plain lines, left axis) and its angle with the y-axis (dashed lines, right axis) as a function of time. (d) Spatio-temporal map of the pressure variation along the length of mid-lines going from the anal canal (0 cm) to the proximal end (black lines in a).

Figure 5.

Flow fields (a), pressure fields (b) and viscous stress fields (c) of two pathologic evacuations when the mean outlet velocity of the neostool through the anal canal V_a was maximal. White colour in (c) corresponds to regions where the viscous stress is lower than the yield stress of the neostool.

Figure 6.

Outlet velocity of the neostool through the anal canal V_a as a function of the force exerted by the rectum wall F for 6 normal (N1–N6, plain circles) and 2 pathologic (crosses and squares, P1–P2) evacuations. Dashed line is V_a ∼ F^2.4.