Fig 1.
Schematic representation of the multi-scale liver architecture.
The human liver is divided grossly into four parts or lobes. The four lobes are the right lobe, the left lobe, the caudate lobe, and the quadrate lobe. Seen from the front the liver is divided into two lobes: the right lobe and the left lobe. It is further divided in eight functionally independent segments based in the the Couinaud classification of liver anatomy. At the microscopic (histological) scale, the liver is organized in repetitive functional units called liver lobules, which take the shape of polygonal prisms (typically hexagonal in cross section). Each lobule is mainly constituted by hepatocytes and it is centered on a branch of the hepatic vein called the central vein which is interconnected with the interlobular portal triads: the hepatic artery (red), the portal vein (blue), bile duct (green).
Fig 2.
Blue box represents the start of the program. Red box represent the diffusion processes. Green box and orange box describe the cell mechanics and cycling processes respectively. Finally, yellow boxes represent the data saving process. After initializing the microenvironment, the cells, and the current simulation time t = 0, our model tracks (internally) tmech (the next time at which cell mechanics methods are run), tcycle (the next time at which cell processes are run), and tsave (the simulation data output time), with output frequency Δtsave. % represents the modulo operation.
Fig 3.
Liver blood vessels architecture.
(a) Schematic representation of the hepatic lobules. They consist of plates of hepatocytes, and sinusoids radiating from a central vein interconnected with the interlobular portal triads: the hepatic artery (red), the portal vein (blue), and the common bile duct (green). (b) computational model of the liver parenchyma in which we can observe the blood vessel architecture. (c) Heat map of the oxygen diffusion in the liver microenvironment. Blue dotted lines were drawn just as a guide to the eye.
Fig 4.
(a) Growth factor concentration in the liver microenvironment after a 30% PH (blue line) and a 70% PH (orange line), and the response it will cause in the hepatocytes. (b) and (c) Heat map of the growth factor concentration after 30% PH and a 70% PH respectively. The concentration is greater in the 70% PH.
Fig 5.
(a) Qualitative representation of the liver regeneration process after a 30% PH. (b) Fold-increase in the liver size. Observational data is shown in gray and represents the weight of the liver measured by Miyaoka et. al [44, 45]. Simulated data is shown in red and represents the liver volume. (c) Quantification of the hepatocytes area during liver regeneration.
Fig 6.
(a) Qualitative representation of the liver regeneration process after a 70% PH. (b) Fold-increase in the liver size. Observational data is shown in gray and represents the weight of the liver measured by Miyaoka et. al [44, 45]. Simulated data is shown in red and represents the liver volume. (c) Quantification of the hepatocytes area during liver regeneration. (d) Quantification of the hepatocytes volume during liver regeneration. (e) Fold-increase in the number of hepatocytes during liver regeneration.
Fig 7.
(a) Schematic representation of blood vessels regeneration after a 70% PH. Left panels show an upper view while right panels show a side view. Blood vessels regenerate by keeping the hepatic lobules structure. (b) Quantification of the blood vessels regeneration by counting the Dirichlet nodes added during the regeneration process. It shows a significant increase during the first 3 days until it finally reaches a plateau. Shaded region represent the standard deviation of 40 simulations.
Fig 8.
Predictions of a 50% PH compared to the outcomes of 30% and 70% PH.
(a) Fold-increase in the liver volume after 30% (violet), 50% (orange) and 70% (green) PH. Black dots represent the time at which the volume increase reaches a plateau and the red dotted line is a polynomial fitting. (b) Percentage of hepatocytes that proliferates during liver regeneration. Black dots represent the time at which the proliferation increase reaches a plateau. Inset: Proliferation percentage in terms of the PH. The red dotted line represents a polynomial fitting. Shaded regions represent the standard deviations of 40 simulations.
Fig 9.
Qualitative representation of the liver regeneration with HCC recurrence, 30 days after the PH. Hepatocytes are represented by transparent pink cells to have a better view of the blood vessels (red tubes) and the tumor (blue cells) growth. (a) The slowest tumor growth happens when the residual tumor clone was seeded in the center of the liver surface. (b) The fastest tumor growth happens when the residual tumor clone was seeded in the periphery of the liver.
Fig 10.
(a) Schematic representation of the recurrence of a hepatocellular carcinoma after a 70% PH. Hepatocytes are represented by transparent pink cells to have a better view of the blood vessels (red tubes) and the tumor (blue cells) growth (b) Fold-increase in liver regeneration and hepatocellular carcinoma recurrence. (c) Time based volume estimation of the hepatocellular carcinoma by using simulation data (blue line) to adjust a Gompertz model growth curve (blue dotted line). Red dotted line represents the earliest recurrence reported in clinical observations and the red point along with the green dotted line,represents the minimum volume that the tumor must reach to be detected (5 mm) by imaging diagnose.
Fig 11.
Relative change of the tumor final size, based on the variation of the parameters that feed our model. The blue line represents the mean tumor size, the yellow shaded region represents the standard deviation of the mean value based on the stochasticity of the model. Red bars and blue bars represent the mean value of the tumor growth when the parameter original value is increased and decreased by 10% respectively and the error bars represent the standard deviation. The three parameters most likely to make an impact on the tumor growth are: the hepatocyte oxygen uptake constant, cancer cells cycle duration and cancer cells oxygen uptake constant.