Biliary Tract and Gallbladder Biomechanical Modelling with Physiological and Clinical Elements

Wenguang Li

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000372656
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Gallstone and other diseases of the biliary tract affect more than around 20% of the adult population. The complications of gallstones, acute pancreatitis and obstructive jaundice, can be lethal.

This is the first book to systematically treat biliary tract and gallbladder modelling with physiological and clinical information in a biomechanical context. The book provides readers with detailed biomechanical modelling procedures for the biliary tract and gallbladder based on physiological information, clinical observations and experimental data and with the results properly interpreted in terms of clinical diagnosis and with biomechanical mechanisms for biliary diseases.

The text can be used as a reference book for university undergraduates, postgraduates and professional researchers in applied mathematics, biomechanics, biomechanical engineering and biomedical engineering, as well as related surgeons.

chapter 1

Physiology of the Human Biliary System

The Human Biliary System

The human biliary system consists of the gallbladder (GB), cystic duct (CD) and common duct and sphincter of Oddi (Figure 1.1). The common duct includes both the common bile duct (CBD) and common hepatic duct (CHD). The GB is a thin-walled, pear-shaped sac and generally measures 7–10 cm in length and ~3 cm in width as well as 2.7-mm-thick wall (Oluseyi 2018). This muscular sac is located in a fossa in the posterior of the liver’s right lobe. The GB is divided into three regions: (1) the fundus, (2) the body and (3) the neck. Its average storage capacity is about 20–30 ml (Dodds et al. 1989), depending on sex and age; for healthy men, mean GB volume is 18.7 ± 0.3 (Palasciano et al. 1992) and 33.3 ± 20.5 ml (Caroli-Bosc et al. 1999); for healthy women, 17 ± 0.3 (Palasciano et al. 1992), 27.1 ± 16.9 (Caroli-Bosc et al. 1999). At ages less than 50 years, the average GB volume is 25.6 ± 16.2 ml, otherwise 31.8 ± 19.6 ml (Caroli-Bosc et al. 1999).

The CD, about 3.5 cm long and 3 mm wide (Dodds et al. 1989), merges with the CHD. The mucosa of the proximal CD is arranged into 3–7 crescentic mucous membrane folds known as the spiral valves of Heister. For CDs without gallstones, their mean diameter is 2.63 ± 0.67 mm (Castelain et al. 1993). For men with healthy CDs, the CD lengths are 24.3 ± 9.0, 26.9 ± 5.5 and 29.1 ± 4.6 mm in age groups such as 10–20, 21–40 and 41–60 years, respectively, while for women, the lengths are 24.8 ± 7.6, 28.0 ± 3.6 and 29.1 ± 6.2 mm in the same age groups (Nahar et al. 2011). Interestingly, the mean CD diameters of men are 1.47 ± 0.50, 2.07 ± 0.56 and 2.73 ± 0.59 mm, but the mean diameters of women are 1.70 ± 0.34, 2.20 ± 0.64 and 2.95 ± 0.60 mm in the same age groups, respectively (Nahar et al. 2011).

Figure 1.1 A view of the human biliary system (illustration after Schatz 2020).

Figure 1.2 Histograms of CD length versus number of CDs: (a) the data from Lichtenstein and Ivy (1937) and (b) the data from Brewer (1899).

Two histograms of CD length are illustrated in Figure 1.2 based on observation data made by Lichtenstein and Ivy (1937) as well as Brewer (1899). Mostly, CD length is in a range of 20–40 mm.

The common duct is about 10–15 cm long and 5–15 mm wide, in which the CHD is ~4 cm long (Dodds et al. 1989). The CBD penetrates the wall of the duodenum to meet pancreatic duct at the duodenal ampulla. Early measurements illustrated normal CBD outer diameter was in a range of 4–17 mm with a mean of 8.85 mm (Ferris and Vibert 1959), and a slightly late examination indicated the CBD outer diameter was in a range of 4–12 mm with a mean of 7.39 mm and the CBD wall thickness varied from 0.8 to 1.5 mm with an average of 1.1 mm (Mahour et al. 1967). A histogram of CDB length versus the number of CBDs observed is illustrated in Figure 1.3.

Figure 1.3 Histogram of CBD length versus number of CBDs (the data in figure is from Brewer 1899).

For normal CBDs, their mean inner diameters are 4.1 ± 1.2 (Parulekar 1979), 6.2 ± 2.3 (Kaim et al. 1998) and 4.11 ± 1.54 mm (Vinay et al. 2013). For healthy adults, the mean CBD diameter and length are 5.25 ± 1.28 and 72.02 ± 11.56 mm, respectively; specially for males, the diameter and length are 5.34 ± 1.46 and 73.90 ± 11.55 mm, respectively, while for females they are 5.10 ± 0.90 and 68.96 ± 11.00 mm (Blidaru et al. 2010). Mostly, CBD mean diameter can be correlated to age, when CBDs are in either healthy or diseased conditions (Adibi and Givechian 2006; Benjaminov et al. 2013; Chen et al. 2012; Lal et al. 2014; Perret et al. 2000; Nalaini et al. 2017; Peng et al. 2015; Senturk et al. 2012; Wu et al. 1984; Bachar et al. 2003). For example, $d_{\text{CBD}}$ = 0.0185 × age + 2.42, age ∈ [60, 95] (Perret et al. 2000); $d_{\text{CBD}}$ = 0.055 × age + 2.12, age ∈ [30, 80] (Nalaini et al. 2017); $d_{\text{CBD}}$ = 0.033 × age + 2.624, age ∈ [5, 87] (Peng et al. 2015); $d_{\text{CBD}}$ = 0.06 × age + 2.72, age ∈ [2, 80] (Wu et al. 1984); $d_{\text{CBD}}$ = 0.0262 × age + 2.19, age ∈ [19, 90] (Ahmed 2017). However, two series of CBD measurements confirm mean CBD diameter have no correlation with age (Horrow et al. 2001; Karamanos et al. 2017).

Very recent work showed mean healthy CBD diameter is $d_{\text{CHD}}$ = 3.64 ± 0.93 mm for the Ethiopian group, and the diameter exhibits a nearly linear trend with age but is not statistically significant between male and female (Worku et al. 2020).

In childhood, the CBD diameter is also dependent on children aged between 1 and 14 years with mean values of 2–4.9 mm (Witcombe and Cremin 1978).

For CHDs, their mean diameter is also related linearly with age such as $d_{\text{CHD}}$ = 0.044 × age + 3.93, age ∈ [2, 80] (Takahashi et al. 1985).

The Function of Bile

Bile is synthesised in the liver and excreted into the lumen of the duodenum when a fatty meal or any other sort of meal is consumed, or even water is drunk. Bile consists mostly of water with minor amount of ions, bilirubin (a pigment derived from haemoglobin), cholesterol and an assortment of lipids – the bile salts. The water and ions assist in the dilution and buffering of acids in chyme as it enters the small intestine. The large and water-soluble drops, containing a variety of lipids, are created by mechanical processing in the stomach. The enzymes from the pancreas are not lipid-soluble; consequently, they only interact with lipids at the surface of the lipid drop. Bile salts break the large lipid drops apart. The tiny droplets, with coating of bile salts, increase the surface area available for enzymatic attack. Furthermore, the layer coated by bile salts allows the interaction between the lipids and enzymes to be easier. After lipid digestion has been completed, bile salts promote the absorption of lipids by the intestinal epithelium. More than 90% of the bile salts are themselves reabsorbed primarily in the ileum as lipid digestion is finished. The reabsorbed bile salts enter the hepatic portal circulation and are collected and recycled by the liver (Martini 2001).

Physiology of the GB

The GB has two major functions: (1) bile storage and (2) bile modification. Although liver cells produce around 1 litre of bile each day, the sphincter of Oddi remains closed until chyme enters the duodenum. In this case, bile cannot flow along the CBD; it has to enter the CD for storage within the expandable GB. This kind of bile movement is named as refilling. When bile stays in the GB, much of the water in bile is absorbed, and bile salts and other components become increasingly concentrated. Consequently, the composition of bile gradually changes. Although bile is secreted continuously, bile release into the duodenum occurs only under the stimulation of cholecystokinin (CCK). In the absence of CCK, the sphincter of Oddi is closed and bile produced by the liver reaches the GB through both the CHD and the CD. When chyme enters the duodenum, CCK is released, but the amount secreted highly depends on the amount of lipids contained in chyme. CCK relaxes the sphincter of Oddi and stimulates contractions in the walls of the GB. These contractions push bile into the duodenum (small intestine) (Martini 2001). This process is called emptying.

Recently, a different view on GB function emerges (Turumin et al. 2013). The view is based on the fact that the bile is emptied from the GB in 5–20 min after the food arrives at the gut, while the gastric chyme moves into the duodenum from the gut in 1–3 h later, suggesting the bile may be insignificant for food digestion. The bile may stimulate intestinal peristalsis and promote the intestine to clean the gastric chyme. The role of the GB is to protect the liver, gut mucosa and colon from hepatotoxic and hydrophobic bile acids, and regulate the serum lipid level.

Clinical Physiology of the System

Gallstones and...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Dedication
• Contents
• Preface
• Nomenclature
• Chapter 1 ◾ Physiology of the Human Biliary System
• Chapter 2 ◾ 1D Models of Newtonian Bile Flow in the Biliary Tract
• Chapter 3 ◾ 1D Models of Non-Newtonian Bile Flow in the Biliary Tract
• Chapter 4 ◾ 1D Dimensionless FSI and 3D FSI of CD
• Chapter 5 ◾ Biomechanical Model for GB Pain
• Chapter 6 ◾ Passive and Active Stresses in the GB Wall
• Chapter 7 ◾ Cross Bridges of GB Smooth Muscle Contraction
• Chapter 8 ◾ Quasi-Nonlinear Analysis of the Anisotropic GB Wall
• Chapter 9 ◾ Fully Nonlinear Analysis of the GB Wall
• Chapter 10 ◾ Heterogeneous Biomechanical Behaviour of the GB Wall
• Chapter 11 ◾ Modelling the Viscoelastic Pressure-Volume Curve of the GB
• Chapter 12 ◾ Constitutive Law of GB Walls with Damage Effects
• Chapter 13 ◾ GB 3D Models from Ultrasound Images
• Chapter 14 ◾ Fluid Mechanics of Bile Flow in Biliary Drainage Catheters
• Appendix A Statistical Analysis of GB Pain Prediction
• Appendix B Glossary of THE Biliary System
• Index