A New Approach in Anaorectal physiology using the Flow equation as a mathematical Model.

1. HOW THE ANAL
SPHINCTER WORKS?
A NEW MATHEMATICAL APPROACH
BY
Prof .Dr. Ahmed Farag.MD.
Faculty of Medicine – Cairo University

2. Maintenance of continence appears
to be a complex phenomenon
achieved by the combination of
Anatomic and physiologic factors,
the relative contribution of each
being unclear.
(Sangwan and Coller Surg.Clin North Am
1994)

3. Faecal Incontinence May be multi-
factorial due to altered stool
consistency, increased rate of
delivery of contents to the
rectum, abnormal rectal capacity
and compliance, decreased AR
sensations and pelvic floor or
anal sphincter dysfunction
(Jorge and Wekner Dis Colon Rectum 1993)

4. Using traditional research
methodology, the reported data
had been described as being
disseminated research data by
some authors and by the others
as being adding to the confusion
experienced in the world of Anal
Incontinence.
(Varma et al Dis colon Rectum 1999 – editors comment)

5.  The role of Anismus detected on
defecation proctography in idiopathic
constipation was doubted by some
authors due to the high incidence of this
condition in their normal controls.
Schouten WR, Briel JW, Auwerda JJ, Van Dam JH, Gosslink MJ, Giani
AZ, Hop WC: Anismus: fact or fiction? Dis Colon Rectum 1997 Sep
40:1033-41.

6.  In addition very little is known about
what symptoms or defecographic
findings should be considered as an
indication for surgery in patients
suffering from large Rectocele (> 2m )
and impaired rectal emptying.
Karlbom U, Graf W, Nillson S, Pahlman L: Does Surgical repair
of a Rectocele improve rectal emptying? Dis Colo Rectum
1996 Nov 39:1296-1302.

7. The lack of answers to the question
on how the anal sphincter works
is mainly due to the fact that, the
AR segment is functionally highly
integrated and should be studied
using an integrated approach.
(Farag A. Dis Colon Rectum 2000 – Letter)

8. The flow equation had been used
successfully previously in
medicine in order to understand
and study:
1. Urodynamics.
2. Hemodynamics.

9. Recently the flow equation had been
applied for the integration of Anorectal
physiology trying to understand how
the anal sphincter works, Which
should be our information highway for
the investigation and treatment of
patients suffering from A.I. and other
functional A.R. disorders.
Farag A. Eur Surg. Res. 1998
Farag A. Dis Colon Rectum 2000 – Letter.
www.integratedcoloproctology.com

10. Definition of A.I.
Abnormal (involuntary) flow of gas
or stools during rest or during
squeeze (voluntary or reflex).

11. Types of A.I.
1. Passive. (Engel et al 1995)
2. Urgency. (Engel et al 1995)
3. Stress. (Swash 1990)

12.  Similarly Constipation can be defined
as:
A low flow rate of the stools or gases
during defecation per unit time.

13. The Flow Equation
intrarectal Pressure
Flow (A.I.) = -----------------------------------------
Anal canal Resistance

14. The Resistance Equation
128 x Dynamic Viscosity x A.C. Length
A.C. Resistance =
------------------------------------------------
3.14 x (A.C. Diameter )4

15. A.C.L.
A.C.D.

16. Structure – Function relationship
Rest Sq. (X8) Strain (/88)

17. Primary Mechanical
Factors
3.14 x (A.C.
Diameter )4
Flow (A.I.)= intrarectal Pressure X
----------------------------
128 x D.V. x
A.C. Length
Dynamic Viscosity of Air:Water:Barium sulphate paste =
1 : 38 : 68

18. Controversies in A.I.
3.14 x (A.C.
Diameter )4
Flow (A.I.)= intrarectal Pressure X
----------------------------
128 x D.V. x
A.C. Length
1. Anal Canal
Pressure?
2. Anorectal Angle?
3. Perineal Descent?
4. Frequency of A.I.?

21. Longitudinal
muscle
Internal A.
sphincter
External A.
sphincter
Puborectalis
muscle
A.C. Length •It forms a
supportive
framework for
the IAS and
EAS during
rest and
squeeze.
• It decreases
the A.C length
during
defecation
Maintains
A.C.L. during
rest (++)
Maintains ACL
during rest (+)
and during
Squeeze (+)
Maintains ACL
during rest (+
+) and during
squeeze (++)
and relaxes to
decrease ACL
during
defecation (+
+)
A.C. Diameter •Forms a
supportive
framework for
the IAS and
EAS during
rest and
squeeze.
•Opens the
A.C. during
defecation
Maintains
A.C.D. during
rest (++) and
relaxes to
increase ACD
during
defecation (+
+)
Maintains
ACD during
rest (+),
decreases
ACD during
squeeze (++)
and relaxes to
increase ACD
during
defecation (+
Maintains
ACD during
rest (+) and
during
squeeze (+)
and relaxes to
increase ACD
during
defecation (+)

22. Sensory & Reflex
Factors
Flow (A.I.) = intrarectal Pressure / Anal canal
Resistance
Sensory Reflexes

23. THE HYBRID LAW IN
COLOPROCTOLOGY
Since two thirds of continent individuals
still have normal anal pressures as
seen on manometry, and two thirds of
patients with AI have low anal
pressures, can the anal canal
pressure show itself in the flow equation?

24. THE HYBRID LAW IN
COLOPROCTOLOGY
 As was suggested by many authors, the
anal canal pressure measured is the
resistance of the anal canal to
distension by the measuring probes and
is proportionate to the probe diameter.
Keighley MRB. Constipation in: Keighley MRB, Williams(eds). Surgery
of the Anus Rectum and Colon. London, Saunders 1993; 609 – 938.

25.  According to the law of Laplace:
Distending Pressure (p) X Radius
(R)
Wall Tension (T) = –––––––––––––––––––––––––––––––
Anal Canal Wall Thickness (δ)

26. Accordingly:
R (Inside) = Tδ/Anal Canal P
& Since the ACD = 2R

27. THE HYBRID LAW IN
COLOPROCTOLOGY
3.15 (Tδ) 4
Flow = IR ––––––––––––––––
8 X DV (ACP) 4

29.  The Flow Calculator.

30. Flow Index
(Anal Incontinence)
< 0.1 - 1 cc/Sec. <
Fluid Stools
Soft Stools
Gas
Fluid stools
Soft Stools
Normal Soiling Incontinent

31. Passive A.I.
(Mechanical Factors)
IRP (rest)
Flow (A.I.)= -------------------------------------
A.C. Resistance (rest)

32. Passive A.I.
(Sensory Deficit)
Flow (A.I.)= ------------------------------
Sensory
Factors

33. Passive A.I.
(Reflex Factors)
Flow (A.I.)= ------------------------
Reflex
Deficit

34. Stress A.I.
(Mechanical Factors)
IRP (cough)
Flow (A.I.)= -------------------------------------
A.C. Resistance (sq.)

35. Stress A.I.
(Reflex Factors)
IRP (cough)
Flow (A.I.)= -----------------------------------------
A.C. Resistance (Rest)

36. Urgency A.I.
(Mechanical Factors)
IRP (urgency)
Flow (A.I.) = -------------------------------------
A.C. resistance (sq.)

37. Urgency A.I.
(Sensory and reflex Factors)
IRP (urgency)
Flow (A.I.)= --------------------------------------
A.C. Resistance (Strain.)

38. Knowing how the Anal
Sphincter Works Will
help us in:

39. 1. The relative contribution of factors
responsible for A.I. if they coexist
The relative contribution of sensory or
reflex factors
=
Flow after correction – Flow before correction

40. Zone 1: Normal
defecation
Zone II, III&IV:
Obstructed Def.
II: for soft well
formed stools.
III: for fluid
stools.
IV: For Gas.
Defecation norm gram

42. Grade I: Normal or False A.I.(N).
Grade II: Gas Incontinence. (G.I
Grade III: Fluid Stool Soiling(FSS
Grade IV: Soft Stool Soiling. (SSS
Grade V: Fluid Stool Incont. (FSI
Grade VI: Soft Stool Incont. (SSI

43.  The mathematic scoring, diagrammatic
scoring showed statistically significant
correlation with clinical severity scoring
at the level of 0.01.

44.  Mathematic scoring could diagnose
fecal incontinence irrespective to its
severity in 59/63 patients (93.65%) and
could accurately match the clinical
severity in 39/63 patients (61.9%) using
6 points severity scoring and grading
system.
Farag A. III rd International Congress on Pelvic Floor
Surgery 2001

45.  Mathematic scoring could diagnose
fecal incontinence irrespective to its
severity in 59/63 patients (93.65%) and
could accurately match the clinical
severity in 39/63 patients (61.9%) using
6 points severity scoring and grading
system.
Farag A. III rd International Congress on Pelvic Floor
Surgery 2001

46.  The overall correlation between clinical
scores, functional scores using flow
equation (=0.732) and functional scores
using continence normogram (=0.668)
had revealed statistical significance at
0.01 level using Pearson’s correlation.

47.  Similarly correlation between
mathematical scoring using the flow
equation and diagrammatic scoring
using the continence normogram
(=0.841) revealed statistical significance
at 0.01 level using the same statistical
analysis.

48. 2. Patient selection for treatment.
Flow (A.I.)= ------------------------
S

49. 2. Patient selection for treatment.
It helps to select patients for direct
sphincter repair of their sphincter
defects seen on imaging by correlation
between the anatomically lost sphincter
length & decreased A.C. resistance to
flow

50.  Anal sphincter repairs should not be offered
to the patients with normal anal canal
resistance where:

51. The minimum AC dimensions during rest were
set as ACL = 3.0 cm and ACD = 0.8 (AC
resistance = 5639.6 and tolerating IRP up to
42 mmHg).

52. and the minimum AC resistance during squeeze
was taken as ACL = 3.5 cm and ACD = 0.6
cm ( AC resistance = 20794.7), tolerating IRP
up to 155 cm) as calculated from the flow
calculator..

53. Results
O = successful
cases.
x = Failures.
Rectocele Group

54. How the A. Sphincter Works
Can also Help in:
 Predicting outcome.
 Operator independent assessment of
treatment.
 Assessment of different treatment
modalities if used simultaneously.
 Planning for New treatment
modalities.

55. Diseases of the colon and Rectum
Volume Number
42 Cozox R crvM 4
APRIL 1999
CENTENNIAL ARTICLES IN COLON AND RECTAL
SURGERY
One Hundred Years of Rectal
Prolapse Surgery
Robert D. Madoff, M.D., Anders Mellgren, M.D., Ph.D.
From the Division of Colon and Rectal Surgery, University of
Minnesota, Minneapolis, Minnesota

56. One may reasonably expect that the coming century
will provide further incremental gains in our
understanding of the pathophysiology of prolapse
and its related disorders as laboratory investigation
continues to be performed. However, one cannot
discount the notion that an entirely novel and, one
might hope, unifying concept may emerge that radically
alters our understanding of the disease.

57.  Could It be the Flow equation and the
Hybrid Law in Coloproctology the
answer to the visionary question of
Robert Madoff and his co-workers?

58. Knowledge Is Power
Thank You
www.integratedcoloproctology.com