Current applications of mathematical models of the interstitial cells of Cajal in the gastrointestinal tract.

Abstract

The interstitial cells of Cajal (ICC) form interconnected networks throughout the gastrointestinal (GI) tract. ICC act as the pacemaker cells that initiate the rhythmic bioelectrical slow waves and intermediary between the GI musculature and nerves, both of which are critical to GI motility. Disruptions to the number of ICC and the integrity of ICC networks have been identified as a key pathophysiological mechanism in a number of clinically challenging GI disorders. The current analyses of ICC generally rely on either functional recordings taken directly from excised tissue or morphological analysis based on images of labeled ICC, where the structural-functional relationship is investigated in an associative manner rather than mechanistically. On the other hand, computational physiology has played a significant role in facilitating our understanding of a number of physiological systems in both health and disease, and investigations in the GI field are beginning to incorporate several mathematical models of the ICC. The main aim of this review is to present the major modeling advances in GI electrophysiology, in order to introduce a multi-scale framework for mathematically quantifying the functional consequences of ICC degradation at both cellular and tissue scales. The outcomes will inform future investigators utilizing modeling techniques in their studies.

Graphical abstract:

Mathematical models of the interstitial cells of Cajal in the gastrointestinal tract across multiple spatiotemporal scales.

1. INTRODUCTION

Motility of the gastrointestinal (GI) tract plays an integral role in the digestion of food. A key discovery in GI motility has been the central role played by interstitial cells of Cajal (ICC) in generating bioelectrical slow waves, which coordinate the motility of the GI tract.¹ Sub-classes of ICC can be classified according to their functions and/or locations in the GI tract. In addition, ICC are also known to act as intermediary between the GI tract and nerves.²

Recent clinical evidences have pointed to ICC depletion as a recognized hallmark of gastroparesis, chronic nausea and vomiting, and functional dyspepsia.^3,4 However, challenges arise in interpreting the importance of these associations between ICC integrity and slow waves. It is difficult to investigate directly in live tissues or subjects, partly due to the fixing and staining processes involved in the imaging of ICC.⁵ To circumvent this issue, mathematical models offer an in silico medium in which physiological conditions can be tested, thus presenting an attractive strategy for investigating the relationship between slow waves and ICC network structures.⁶ Simulations can be conducted in concert with experimental studies and have the ability to reproduce the effects of conditions that are applied under experimental conditions. A validated mathematical model can reduce animal usage by refining the parameter space required to test a specific hypothesis before experiments are conducted.

The main aim of this review is to present the major modeling advances in GI electrophysiology, in order to introduce a multi-scale framework for mathematically quantifying the functional consequences of ICC degradation. Basic physiology and pathophysiology of ICC and slow waves are introduced first, followed by mathematical models. The simulation results present quantifiable differences between normal and pathological ICC networks with regard to a number of physiological mechanisms that are critical for the maintenance of GI functions.

2. INTERSTITIAL CELLS OF CAJAL (ICC)

ICC are mesenchymal cells that were first reported by Santiago Ramon y Cajal in 1911.⁷ These specialized pacemaker cells are predominantly distributed throughout the GI tract to aid in the coordination of motility in the GI tract through the generation of slow waves at different frequencies.^8,9 In recent years, ICC have been identified in the vasculature and rhythmically active structures such as the cardiac myocardium, ureteropelvic junction, and urethra.^10–14

ICC are typically identified immunohistochemically through c-kit (CD117), which is a tyrosine kinase protein receptor (encoded by the KIT gene at the W locus).¹⁵ Apart from c-kit, anoctamin 1 (Ano1) is another recently described marker for identifying ICC in the GI tract.¹⁶ Furthermore, electron microscopic images have also been used to identify ICC based on the ultrastructural features of ICC.^17,18 Sections 2.1–2.2 present a list of the different classes of ICC, the major known ion conductance pathways responsible for the generation of slow waves, and diseases that are related to ICC pathology.

2.1. Classes of ICC and pacemaker functions

Several classes of ICC have been identified based on morphology, anatomical locations within the GI tract, ultrastructural features, and function. The organization of the various ICC networks based on location and function is presented in Table 1. In general, ICC in the myenteric plexus (ICC-MP) are located between the longitudinal and circular muscle layers.¹⁹ Intramuscular ICC (ICC-IM) are located within the muscle layers and are associated with nerve varicosities throughout these smooth muscle layers.^19,20 The ICC-MP are the primary pacemaker cells in the stomach and small intestine while ICC-IM provide secondary activation of slow waves.^21,22

Table 1:

The various type of ICC classified by locations and functions.

Type of ICC		Location	Function
ICC-SS		Sub-serosal layer19	Act as a stretch receptor to detect circumferential expansion and swelling of the colon wall. Connect to the ICC-LM and trigger the contraction of the longitudinal muscle.86
ICC-MP		Between longitudinal and circular smooth muscle layers ( region of the myenteric plexus)19	Primary pacemaker cells in the stomach and small intestine.21
ICC-IM	ICC-CM	Intramuscularly in the circular muscle layer19	Regenerate slow waves in the circular muscle87,88	Mediate neural signals from the enteric nervous system,89 and act as secondary pacemaker cells.90
	ICC-LM	Intramuscularly in the longitudinal muscle layer19	Regenerate slow waves in the longitudinal muscle87,88
ICC-DMP		Between circular muscle layers in the small intestine (in the deep muscular plexus) 19	Mediate neural signals from the enteric nervous system.89
ICC-SEP/SM		In the connective tissue septa between circular muscle bundles88	Responsible for generating spontaneous pacemaker activity, similar to the function of ICC-IM.83
ICC-SMP		Between the submucosa and circular muscle in the colon (near the submucous plexus)91	Primary pacemaker cells in the colon92

At the tissue and organ scales, entrainment occurs by phase-locking multiple ICC with different intrinsic frequencies of slow waves to form a sustained propagating wavefront. A key feature of entrainment is the convergence to a single frequency by “pulling” ICC with lower intrinsic frequencies to a higher frequency.²³

The evidence at subcellular scales have pointed to the existence of multiple intracellular sites termed pacemaker units (PMUs), which generate unitary potentials that gives rise to slow wave activity via summation and entrainment of many unitary potential depolarization.^24–26 There are several ion-transport pathways that are integral to a slow wave cycle. The key intracellular ion transport pathways in a PMU include the mitochondria uniporter, the mitochondria Na⁺/Ca²⁺ exchanger, the sacro(endo)plasmic reticulum Ca²⁺ ATPase (SERCA) pump, and the inositol 1,4,5-trisphosphate receptors ( IP₃-R) of the endoplasmic reticulum (ER). The ER and mitochondria Ca²⁺ handling is essential in generating slow waves^24,27–29 and disruptions to any of these key ion-transport pathways would result in the abolishment of slow waves. ^30,31Table 2 provides a summary of the typical roles of ion channels that have been identified in ICC.

Table 2.

Key ICC ion channels and their known functions.

	Ion Channels		Roles
Calcium (Ca2+) Channels	Transient, low voltage-activated T-Type Ca2+ channel		Contribute to the upstroke phase of the slow wave.93,94
	Long-lasting, high-voltage activated L-type Ca2+ channel.		The inward current may contribute to the duration/ amplitude of the slow wave plateau phase.94,95
Sodium (Na+) Channels	Voltage-dependent, mechanosensitive sodium channel, Nav 1.5		Contribute to slow wave upstroke phase.37
Chloride (Cl−) Channels	Anoctamin 1 (ANO1) channel Ca2+ activated Cl− channel		Essential for slow wave generation.61
	High-conductance chloride current (HCCC)		Contribute directly to pacemaking and stabilizing resting membrane potential.96
	Volume-activated Cl− current		Contribute to resting membrane potential and increase excitability during stretch.97
Non-Selective Cation Channels (NSCC)			Generate unitary potentials.26
Potassium (K+) Channels	Ca2+ - activated K+ Channels	Intermediate (IK)	Regulate ICC excitability.98
		Large (BK)	Maintain the resting membrane potential to regulate ICC excitability in response to neurotransmitters and other chemical stimuli.99
	Delayed-rectifier K+ Channel (KV1.1)		Contribute to repolarization.100
	Inward-rectifier K+ Channel (ERG K+ Channels)		Maintain consistent slow wave duration, contributes to slow wave plateau and regulates resting membrane potential.101–103
	Transient outward K+ current		Regulate the slow wave upstroke phase.104

2.2. Clinical Significance of ICC Pathologies

Several GI motility disorders are associated with either deficiency, damage, or remodeling of ICC networks along with a concomitant loss of enteric neurons and/or smooth muscles.³² A reduction of ICC is also observed with age.³³ Presently investigators still debate whether the defects in ICC networks are a mechanistic cause or a consequence of the disease process.³⁴ Table 3 lists a compilation of histopathological and confocal imaging evidences that demonstrates major changes to the ICC network in various GI motility disorders.

Table 3.

Evidence of ICC abnormalities in different GI motility disorders.

GI Motility Disorders	Histopathological Findings
Gastroparesis	Loss of ICCs in the stomach is regarded as a pathological hallmark. 4,105
Slow transit constipation	The volume of ICC significantly decreased in all layers of sigmoid colonic specimens from patients.106 Significantly decreased in the densities of ICC and enteric nerves in all layers of the patients’ sigmoid colon specimens. 107
Chronic Intestinal Pseudo-Obstruction (CIPO)	Decrease or total loss of the numbers of c-kit+ cells. 108,109 Abnormal distribution of the ICCs have also been observed.110,111
Ileus	Ileus may be associated with ICC, myenteric neurons and nNOS immunoreactive neurons deficiency. 112
Intestinal Artesia	The distal and proximal parts of the atretic segments have a significantly lower number of ICCs per field than in the control group.113
Hirschsprung’s Disease (HD)	Reduction of each subtype of ICCs (especially ICC-IM and ICC-SMP) in the aganglionic colon region. 114 Sparse ICC-MP networks in the aganglionic bowel, transitional zone, and ganglionic bowel in HD patients. Reduced density of ICC-IM in the aganglionic bowel, transitional zone, and normogaglionic bowel of HD patients.115–117 Altered ICC distribution in the entire resected bowel of HD patients.115,118
Chronic Unexplained Nausea & Vomiting (CUNV) Syndrome	Fewer ICCs counts per field and with mild ultrastructural abnormalities compared to controls.119

One hypothesis that has been postulated based on intra-operative recordings of slow waves is that slow wave dysrhythmias are associated with degradation of the ICC networks.³⁵ Other than degradation of the integrity of ICC due to the loss of ICC, chemical and mechanical perturbations also have a significant impact on slow wave functions. For example, surgical manipulations often lead to local release of prostaglandins, which are known to have a chronotropic effect on ICC.³⁶ Another hypothesis is that mechano-sensitive sodium channels could also elevate the frequency of slow waves and increase the likelihood of the emergence of an ectopic pacemaker.³⁷ The mutations in these sodium channels are associated with irritable bowel syndrome³⁸ and intestinal pseudo-obstruction.³⁹ Thuneberg et al. also hypothesized that the stretch of GI musculature could exert deformation of ICC and this information was transmitted to smooth muscles via peg-and-socket contacts.⁴⁰

3. MATHEMATICAL CELL MODELS OF ICC

A number of investigators have proposed mathematical models that aimed to replicate ICC functions. The details of the models vary depending on the understanding of ICC physiology at the time and the specific applications of the cell model. In general, ICC models can be classified into either phenomenological or biophysically based models. Phenomenological models consist of a system of differential equations that simulate oscillatory patterns to match the periodicity of slow waves in different regions of the GI tract. Nelsen and Becker proposed one of the earliest models using a chain of coupled Van der Pol relaxation oscillators.⁴¹ Subsequently, Sarna et al. proposed a linear bidirectional network of coupled relaxation oscillators to simulate GI slow waves in the stomach and small intestine.^42,43 Once the role of the coordination of slow waves between ICC and smooth muscle cells (SMC) was established, Aliev et al. proposed an updated oscillator-based model to simulate the pacemaking role of ICC and the dynamics of coupled ICC and muscle layer.⁴⁴ Readers are referred to Further Reading for more detailed descriptions of the applications of those earlier models.

The more recent applications of the coupled-oscillator models have extended to higher dimensions and matched against imaging evidence of intestinal motility under experimental conditions.^45,46 A key mechanism explored in these recent simulation studies was the emergence of pacemaker activities, particularly in the proximal region of the intestine, where the entrainment frequency is generally the highest.⁴⁷ The model was further extended to reproduce the step-wise plateau frequency gradients or “dislocations” of interval slow waves in the intestine.⁴⁶ The dependence of the interval slow waves on neural inputs was also explored through both experimental data and mathematical modeling, both of which showed a smooth gradient of the mouse intestine in the presence of local release of neurotransmitters.⁴⁶ The series of investigations presented a complex and dynamic picture of intestinal slow wave and motility.

A number of biophysically based ICC models have also been proposed recently. These cell models contain parameters that can be directly related to physical quantities that can be measured and/or imposed during experiments. Lees-Green et al. provided a detailed review of the physiological foundations behind a number of previous biophysically based ICC models, predominantly the incorporation of roles of individual ion gating variables in slow wave generation.⁴⁸

One of the earliest biophysically based ICC models based on the more up-to-date understanding of the pacemaking intracellular mechanisms was proposed by Youm et al.⁴⁹ The model contained components that were partially based on cardiac cell models by Luo and Rudy⁵⁰, and Matsuoka et al.⁵¹ Four major ion conductances were included: an inward rectifier K⁺ current (I_K1), L-type Ca²⁺ current (I_Cal), a voltage-dependent and dihydropyridine (DHP)-resistant current (I_VDDR), and an autonomous inward current (I_A1). There are also three ion transporters: a Na⁺/ Ca²⁺ exchange current (I_NaCa), a Na⁺/K⁺ pump current (I_NaK), and plasmalemmal Ca²⁺ pump current (I_PMCA).⁴⁹ The initial triggering event is thought to begin with the Ca²⁺ leak from the sarco-endoplasmic reticulum and the voltage dependent DHP resistant pathway.⁴⁹ The model was driven by an external current and reproduced the experimental slow waves recordings taken from an isolated mouse small intestine, which occurred a rate of approximately 20 cycles per minute (cpm) (Figure 1A).

Figure 1:

Examples of mathematical ICC models encoded using the CellML standard. (A) Youm et al. model.⁴⁹ (B) Corrias and Buist model. ⁵² (C) Lees-Green et al. model. ⁶³ (D) Faville et al. model.⁵⁸ Other than (B), which simulated gastric slow waves, the remaining models simulated intestinal slow waves, which demonstrate a range of frequencies, resting membrane potentials and amplitudes.

Corrias and Buist proposed an ICC model that was principally based on the non-selective cation channels (NSCC) hypothesis, which states that the Ca²⁺-inhibited NSCC current (I_NSCC), contained in the PMU as the primary pacemaker conductance.⁵² The PMUs are represented as a single bulk PMU that takes the aggregate of all PMUs in an ICC, through which the simulated slow wave is generated by summation of nine types of ion conductances in the bulk cytoplasm: The delayed-rectifier K_V1.1 current (I_Kv1.1), the ether-a go-go K⁺ current (I_ERG), a Ca²⁺ activated K⁺ conductance (I_BK), a background K⁺ leak current (I_Kb), the L-type Ca²⁺ current (I_L-type), a voltage dependent DHP resistant current (I_VDDR), the voltage dependent Na⁺ current (I_Na), a Ca²⁺ dependent chloride channel (I_ClCa), and a Ca²⁺ extrusion mechanism (I_Extrussion).⁵² The intracellular Ca²⁺ dynamics in the PMU compartment were formulated using the mitochondria-ER model developed by Fall and Keizer.⁵³ The frequency of slow waves generated by the Corrias and Buist ICC model matches the experimental slow wave recordings of the canine gastric antrum and the guinea pig antral ICC (Figure 1B).²² Furthermore, the ICC model also showed the behavior in terms of termination of slow waves generation and increase in slow wave frequency, that were in agreement with experimental observations under the effects of several different experimental conditions.⁵⁴ Overall, the ICC model presented a reproducible and stable slow wave output and the parameters can be manipulated to enable a predictive investigation to be performed.

Ellingson et al. conducted a study based on an extension of the model developed by Corrias and Buist to investigate the effects of the upregulation of the plasma membrane Ca²⁺ ATPase (PMCA) pump.⁵⁵ A perturbation analysis was performed by increasing the rate constant of the PMCA pump by 180%. The simulations demonstrated that the upregulation of the PMCA pump can reduce the frequency of slow waves until a critical value is reached, after which the cell model becomes quiescent. On the other hand, the downregulation of the PMCA pump appeared to induce a multi-stable phase of slow waves even under normal physiological conditions. The authors further demonstrated that the mitochondrial calcium concentration was critical in the transition between the multi-stable phase and the quiescent phase of slow waves. However, there is an ongoing dispute regarding the nature of the primary pacemaker conductance as there exist other theories that differ from the NSCC hypothesis.⁵⁶ Therefore, alternative ICC models were proposed to address the different pacemaking mechanism theories.

Faville et al. proposed a single PMU model can be built into a whole cell model to simulate intestinal slow waves, as shown in Figure 1D.⁵⁷ Unlike those other previously established biophysically based ICC models, this model establishes that unitary potential depolarizations constitute the basic event for the generation of slow waves. The model was then extended to incorporate multiple PMUs based on the unitary potential theory of ICC pacemaking,⁵⁸ and simulations showed that the model is capable of qualitatively replicating slow waves characteristics. Both versions of the cell model assumed that the IP₃-R mediated Ca²⁺ release from the ER could stimulate a substantial uptake of Ca²⁺ by the mitochondria, resulting in the local Ca²⁺ concentration in the submembrane space to decrease below the resting level.^57,58 Subsequently, this would activate the Ca²⁺-inhibited NSCC and depolarize the membrane.²⁴ However, the intracellular model of Means and Sneyd⁵⁹, which originated from a pacemaker hypothesis proposed by Sanders et al.²⁴ refuted the mechanism of action adopted in both models of Faville et al.^57,58 Theoretically, under normal conditions, the rate of Ca²⁺ uptake by the mitochondria within its physiological range would not have been sufficient to cause the local Ca²⁺ concentration to decrease below the baseline.⁵⁹ An alternative simulated demonstrated that IP₃ agonist may play a role in Ca²⁺ release from the ER and induces subsequent uptake by the mitochondria, and the eventual activation of ER store-operated Ca²⁺ entry determines the frequency of slow waves.⁶⁰

Among the various ion channels that have been identified in an ICC and play crucial roles in modulating slow wave morphology, Ano1 pacemaker channel has been recently identified to be essential for ICC slow waves,⁶¹ and is found to be highly expressed in all classes of ICC in the human and mouse GI tracts.⁶² Based on the role of the Ano1 channel, Lees-Green et al. implemented Ano1 as the pacemaker channel and incorporated store-operated calcium entry as a key component of the Ca²⁺ dynamics, as shown in Figure 1C.⁶³ Specifically, the Cl⁻ equilibrium potential was found to play an important role in modulating the shape of slow waves, thus, highlighting the need for better understanding of Cl⁻ dynamics in ICC which might contribute to improving future ICC models.⁶³

Although biophysically based ICC models are capable of reproducing many important features of slow waves, there are a number of major limiting factors to these mathematical models. Generally, some parameters in the cell models are difficult to measure directly in typical experiments, and therefore the foremost limiting factor is the lack of available experimental data describing dynamics such as transmembrane ion exchange, intracellular ion dynamics, and metabolic pathways,^{49, 57, 58} leading to a lack of suitable specific data to represent the model parameter values. Moreover, a number of model parameter values are approximated based on analogous data from appropriate alternative cell types, while others are assumed and fitted using optimization techniques so as to reproduce important characteristic features from experimental observed slow waves.⁵⁸ In addition, carefully designed experiments that measure the parameter in a stochastic manner would also account for the stochastic variations in the behaviors of slow waves.

4. TISSUE AND NETWORK MODELS OF ICC

In consonance with the International Union of Physiological Sciences (IUPS) Physiome project,⁶⁴ anatomical detailed tissue models of the heart have been successfully constructed to date. Ensuing what has been vastly accomplished in cardiac modeling over the years, similar reconstruction of a virtual GI tissue block with the required anatomical detail through extended tissue-level imaging of the smooth muscle structural heterogeneity and ICC network structures is an active field of research. At present, the major motivation for tissue modeling studies of the GI tract is to assist in the interpretation of the functional consequences of ICC network damage/loss that is known to engender various GI motility disorders.

One major limitation in GI tissue modeling studies is the lack of available large-scale imaging data and registration techniques for studying spatial patterns of ICC depletion. Previous studies utilized confocal images of ICC networks to perform subject-specific simulations of slow wave propagation.^65,66 However, the limited number of images and size of networks impeded the use of the imaged ICC network as an effective data source for tissue models. One way to overcome this limitation is to simulate propagation of slow waves in an ICC network using an automata model approach and explore changes due to ICC loss.^67,68 Gao et al. proposed a more sophisticated ICC network generation algorithm adapted from SNESIM (single normal equation simulation algorithm), which is an established geostatistical algorithm used to build numerical models of oil reservoirs.⁶⁹ Structural features of ICC network were extracted from confocal images and provided to the network generation algorithm to generate large-scale realistic virtual ICC network across a spectrum of ICC degradation, and the slow wave propagation over these networks was simulated.⁷⁰ This methodology seems promising and further modifications can be made to the SNESIM algorithm⁷¹, to capture depletion of finer structural details of ICC networks and subsequently relate the depletions to the changes in slow waves at the tissue level.⁶⁹

Tissue model with anatomical representation of ICC network layers within a three-dimensional in-silico tissue block has proven to be valuable in previous studies such as to investigate the impact of surgical excisions orientation on human gastric slow wave conduction,³⁵ overcoming ethical problems with performing multiple full-thickness biopsies/surgical excisions in humans.⁷² Du et al. investigated the mechanism of human gastric slow wave conduction in a virtual ICC network model that included three bidirectionally-coupled ICC layers based on a voltage-dependent IP₃ ICC model proposed by Imtiaz et al.^35,73 As shown in Figure 2, the top layer of the three-dimensional in-silico tissue block is made up of the ICC-LM layer, in which slow wave preferentially conducts in the longitudinal direction. The middle layer represents the ICC-MP layer in which slow wave conduction is isotropic.²² As for the bottom layer, it represents the ICC-CM layer, in which SW preferentially conducts in the circumferential direction. The coupling between the layers allowed the formation of the longitudinal wavefront at the distal region of the excision.

Figure 2:

(A) A three layered tissue model setup with two intramuscular muscle ICC layers (longitudinal muscle (LM) and circumferential muscle (CM) layers), and a myenteric plexus (PM) layer. (B) The LM and CM layers contain preferential conduction in the longitudinal and circumferential direction, respectively. The MP layer conducts slow waves equally in all directions. (C) Time snapshots of the propagation of slow waves in the model under the normal condition and with a conduction block/excision placed at two different orientations. Slow wave propagation is recovered distal to the excision due to the coupled MP layer to the LM and CM layers.³⁵

Another noteworthy simulation study of the ICC networks was conducted by Gao et al. on the effects of developmental changes in ICC structure and function.⁷⁴ C-kit labeled ICC-MP networks from murine subjects were obtained up to 24 days postnatal. The networks were meshed and embedded with a finite-state model developed by Sathar et al., which relied on a membrane potential threshold-based activation of intracellular Ca²⁺ activity.⁷⁵ Alongside structural metrics, the study highlighted an association between the increase of ICC population and transmission efficiency of slow waves in the early stages of postnatal development, and while the ICC networks underwent further morphological developments, the transmission efficiency maintained at a steady level. It is possible that a similar process in reverse could be applied to ICC degradation under pathological conditions, where the initial degradation of ICC does not cause a major impact on the functions of the GI tract till a critical loss is reached, after which significant dysmotility patterns and symptoms can occur. Another avenue of research is to develop 3D network presentations of ICC over an extended space (up to 860×860×90 µm³) (Figure 3), which can be used to simulate realistic propagation of slow waves across the network.¹²⁰

Figure 3.

Simulation of slow wave activity in a mouse gastric ICC-MP network (862×862×90 μm).¹²⁰ Shown are (A) potential distribution at one time instant and (B) slow wave velocity profile over the network. We thank Professor JM Vanderwinden for providing the ICC network image.

5. CONCLUSIONS AND FUTURE PERSPECTIVES

Current gastrointestinal (GI) electrophysiology and motility studies exhibit a powerful trend toward utilizing mathematical models to effectively investigate structure-function relationships and overcome multi-scale challenges in basic and clinical GI research. Although the development of several sophisticated GI modeling studies across multiple biophysical scales is at a relatively nascent stage, they have already been applied as useful tools to test hypotheses and providing a more “macroscopic” view of the effects of certain ion channelopathies and/or network loss.

The most established modeling method of evaluating ICC pathology is through investigating the effects of channelopathy on the generation of slow waves.⁷⁶ This area is equally supported by a large amount of experimental research data over the past three decades. Another critical investigation is the effects of drugs on slow waves under both normal and pathological conditions. Though ICC models have been successfully used to model the effects of certain agents such as acetylcholine,⁷⁷ more detailed mechanistic models are required at the ion channel and intracellular levels to fully explore the effects of different drugs and neurotransmitters.⁷⁸ In particular, the cell models can act as a conduit through which the role of ICC as an intermediary between slow waves and enteric innervation can be effectively addressed. It is also important to recognize that the multiscale approach of modeling hinges on a robust approach at the cellular scale before tissue scale simulations can be conducted and interpreted in a meaningful manner.

Current techniques to evaluate ICC depletion in histopathological studies generally employ nuclei counts based on histological images, volume computations, and visual grading. The present research interest in quantifying ICC network geometries by developing effective quantitative tools that will enable us to analyse the relationship between GI tissue structure and function. Recent quantitative studies of ICC network geometries have led to the development of a set of numerical metrics, i.e., density, thickness, hole size, contact ratio, connectivity, and anisotropy, for quantifying the structural properties of ICC networks.⁷⁹ These numerical metrics, however, are limited to two-dimensional network analysis, and for more in-depth quantitative studies of ICC network geometries, efforts to adapt and extend the existing, and develop new numerical metrics suitable for quantifying three-dimensional ICC network properties are needed. Ultimately, the investigation is anticipated to give rise to reliable quantitative tools that enable the analysis of the relationship between ICC network structure and function, especially in light of the recent progress in imaging and segmentation of ICC network from full-thickness tissue biopsies to quantify its spatial distribution in health and disease. For example. recently Mah et al. provided some insights into the relationship between ICC-MP network structure and slow waves following their investigation into the reliability of different supervised machine learning approaches in segmenting ICC network from murine confocal tissue blocks.⁸⁰

Validating the tissue model developed poses another major limitation in GI tissue modeling studies since ICC injury is heterogenous and difficult to model. Both ICC loss and injury have been identified in various GI motility disorders, however, present tissue confocal microscopy images available only facilitate modeling of ICC depletion. One way to guide the modeling for ICC damage is to incorporate biophysical ICC models to simulate varying degrees of ICC injury severities analogous to what has been carried out in the cardiac field to model myocardial ischemia.^81,82 Another way of obtaining experimental data for validating the tissue model may be through Ca²⁺⁻ - fluorescence video imaging of ICC network functions.^83,84 Apart from leveraging on in vivo animal models, mathematical modeling represents an attractive and reliable alternative approach to investigate the structure-function relationship within the underlying ICC network.^6,9,65 One hypothesis that can be tested is whether an aging-related loss of ICC and potential compensatory mechanisms can sustain proper slow wave pacemaking in the human stomach and colon.³³ By programmatically altering the expression of ICC in the myenteric plexus, investigators can then impose for disease conditions, i.e., channelopathy, on the cell models to calibrate slow wave abnormalities and aging at different locations along the GI tract.

Finally, given the relatively large physical and temporal scales needed to quantify slow wave propagations at the tissue scale, the computational cost is also a concern. Nevertheless, the scale and efficiency of simulations of biological processes have rapidly increased over the recent years attributed to the increase in high-performance computing power and applications of advanced numerical solution techniques.⁸⁵ Together, the advancements in mathematical modeling and computational techniques will facilitate our understanding of the mechanisms behind ICC channelopathy and loss in GI motility disorders.