A web-based human liver atlas

ABSTRACT The liver is the largest solid organ in the body that can be anatomically divided into segments. We present in this work a web-based subject-specific human liver atlas based on the Couinaud segments simulated from portal venous (PV) perfusion zones, hepatic arterial (HA) and hepatic venous (HV) trees, as well as biliary drainage. The purpose of the atlas is to provide the modelling community with freely accessible 3D hepatic structures for in silico simulations, which are of tremendous value in yielding novel insights in hepatic circulation, drug transport and clearance.


Introduction
As the largest organ in the human body, the liver plays the critical role of biosynthesis, metabolism and clearance.Liver functions rely critically on the three vasculatures in the organ: a dual supply system consisting of a portal venous (PV) and a hepatic arterial (HA) trees, and a draining system of hepatic venous (HV) branches.In a healthy adult about 0.8-1.2L of blood flow through the organ every minute (Eipel et al. 2010).In addition, a biliary system carries bile and metabolism wastes produced by hepatocytes to an extra-hepatic common hepatic duct.After merging with a cystic duct from the gallbladder, the bile fluid is eventually emptied into the second part of the duodenum.
Hepatic resection that involves removal of part of the liver follows the segmental anatomy, which is defined according to the perfusion and draining regions of PV and HV trees, respectively (Couinaud 1999).The variability of segment boundaries should be recognised for each individual patient, because it is this variability that underlies the need for preoperative modelling.For example, the conventional Couinaud classification of segmental anatomy has been redefined by computational techniques, e.g. by solving the transient diffusion equation for portal veins (Selle et al. 2002;Barléon et al. 2018).The liver segments, along with the vascular and biliary structures constitute an atlas that is of tremendous value in pre-surgical planning and liver function modelling.While numerous computational models have been made for the liver, there are few web-based human liver atlases that are accessible freely by the modelling community.One such atlas is presented in the Open Anatomy Project (https://www.openanatomy.org/)wherein hepatic structures are segmented from a computed tomography (CT) image.However, the hepatic vessels were not further digitised into the form of a parametric mesh that facilitates biomechanical simulations.Neither were bile ducts segmented.The principal aim of this work is to present a human liver atlas with biomechanical or physiological simulations in mind.We also introduce useful numeric techniques for simulating liver segments and blood flow, i.e. through applying a combination of tree growing and Laplacian fractal algorithms.

Methods
We have previously constructed a computational pipeline (H.Ho et al. 2020).The pipeline starts from a semi-automatic segmentation technique for digitising large hepatic vessels from medical scanning images.From the image database of 15 subjects who were healthy live liver donor candidates, we chose the CT images of one subject whose large PV, HV and HA vessels as well as bile ducts could be segmented.The CT images were obtained with different scanning protocols, i.e. at venous and arterial enhancing stages for veins and arteries, and with a biliscopin technique for bile ducts, respectively.The digitised vessels and bile ducts are then registered based on the location of the root portal vein, which is visible in all imaging protocols.
Using image segmentation techniques, vessels in the first several generations were digitised.A constructive constraint optimisation (CCO) algorithm was used to further extend the segmented vessels from about six to seven generations to smaller vessels till the twelfth generation.Mathematical and numerical details of the CCO algorithm have been introduced in several literatures, e.g. in Schwen and Preusser (2012), and therefore are not repeated here.In brief, the CCO algorithm assumes the blood uses minimum energy to perfuse a tissue, then the geometric distribution of vessels in the tissue such as the branching angle can be simulated from an optimisation algorithm.An attractive feature of the CCO algorithm is that it uses the Poiseuille law to determine the characteristics of vessels.Therefore, assuming steady flow in veins, the blood flow in the PV and HV trees is solved.In order to emulate the Couinaud segments, we use perfusion zones generated from the second generation of portal veins.This is achieved by solving the Laplacian equation for portal veins, as described in more details in Barléon et al. (2018).
The CCO algorithm and the perfusion solver were implemented in Matlab (MathWorks, USA).An open-source software Cmgui was used to post-processing the 3D liver segments and vasculatures.3D objects shown in a Cmgui window can be exported into human-readable file formats (such as the STL or JSON format).To achieve cross-platform neutrality, we used a JavaScript 3D library Three.js(https://threejs.org/) to render 3D objects in a web browser via WebGL.JSON files, which are the 3D object files used in Three.js,contain three main components: (1) Vertices that hold the coordinates of a point in the surface mesh; (2) Normal that holds a normal vector at each vertex; (3) Faces that define each triangular element on the surface mesh.With such information, a user could re-use the 3D hepatic structures in customised applications.

Results
Figure 1 shows the web-based human liver atlas that was constructed based on the techniques described above.Each CCO algorithm-generated vascular tree contains 8,198 vessels.The user interface (UI) is shown in Figure 1(a).The controls at the left panel allow a user to show/hide a Couinaud segment, the blood vessels (HA, PV and HV trees) and bile ducts within that segment.The right panel is a 3D graphics panel that visualises hepatic structures.The boundaries of liver segments emulated from portal perfusion are shown in different colours (Figure 1b).
In addition to a viewer for the liver atlas, another viewer for blood flow simulation pre-and post-liver surgery is also made available (Figure 1c).The simulation scenario is a left lateral hepatic resection, where the Couinaud segments II and III are removed.After resection, approximately 20% of the blood flow that was originally supplied to the left lobe is re-routed to the remnant lobe.
The liver atlas can be viewed from a weblink (https://hyu754.github.io/patient_id_2.html).The geometric files of all hepatic structures are provided in the supplementary file.

Discussion and conclusion
The human liver atlas presented in this communication represents a synergy of several advanced modelling techniques in vascular tree generation, liver segment and blood flow simulations (Barléon et al. 2018) (H.Ho et al. 2020), as well as vascular and biliary structures digitised and fused from CT images of three different protocols.To our knowledge, this is also the first time that a segment-based liver atlas, with both segment surface and vasculatures included, is presented from a web-based interface.In addition, physiological simulations, i.e. the blood flow in portal veins before and after a virtual left lateral hepatectomy, are also provided.The introduced computational methods, which are presented in just one surgical scenario (hemihepatectomy) in this paper, can well be applied to other scenarios, e.g. a left lateral hepatectomy (Barléon et al. 2018), or resection of only one segment.In a relevant previous work, a web-based rat liver atlas was presented (Ho et al. 2020).However, the human liver atlas presented in this work represents several extra features.Firstly, the vasculatures were extended by the CCO algorithm.Secondly, blood flow was solved for portal veins to simulate a surgical scenario.From a haemodynamic perspective, drastic flow variations occur after a major hepatectomy.Portal hypertension and hyper-perfusion in the remnant liver may cause a Small for Size Syndrome (SFSS) that leads to liver dysfunction (Christ et al. 2017).Haemodynamic factors are an important stimulus for liver regeneration (Christ et al. 2017).These series of events are of great interest to the modelling community.
In silico modelling for the liver calls for collaborations amongst a cluster of academic and healthcare institutions (Kuepfer et al. 2014).However, there are still barriers for data sharing including different data formats, software, and implementation methods of involving institutions.Solutions have been proposed, e.g. by the use of markup languages such as SMBL for curating cellular and molecular kinetic models, as well as using FieldML for defining spatial dimension models (Christie et al. 2009).Web-based, human readable 3D models have the advantage of easy accessibility and readiness to be translated to other file formats for mechanistic simulations.
In conclusion, a first web-based human liver atlas is presented in the work that is the results of the application of several computational and imaging techniques.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Figure 1 .
Figure 1.A web-based liver atlas: (a) the user interface of the atlas.The user interface has a control panel and a 3D viewer for liver atlas and portal flow simulations; (b) each liver segment and its vasculatures can be viewed individually; (c) portal flow simulations pre-and post-left lateral hepatectomy, as shown in the simulation viewer.