title: Local and Global Function Model of the Liver.
abstract: OBJECTIVE
  To develop a local and global function model in the liver based on regional and organ function measurements to support individualized adaptive radiation therapy (RT).
  
  
  METHODS
  A local and global model for liver function was developed to include both functional volume and the effect of functional variation of subunits. Adopting the assumption of parallel architecture in the liver, the global function was composed of a sum of local function probabilities of subunits, varying between 0 and 1. The model was fit to 59 datasets of liver regional and organ function measures from 23 patients obtained before, during, and 1 month after RT. The local function probabilities of subunits were modeled by a sigmoid function in relating to MRI-derived portal venous perfusion values. The global function was fitted to a logarithm of an indocyanine green retention rate at 15 minutes (an overall liver function measure). Cross-validation was performed by leave-m-out tests. The model was further evaluated by fitting to the data divided according to whether the patients had hepatocellular carcinoma (HCC) or not.
  
  
  RESULTS
  The liver function model showed that (1) a perfusion value of 68.6 mL/(100 g · min) yielded a local function probability of 0.5; (2) the probability reached 0.9 at a perfusion value of 98 mL/(100 g · min); and (3) at a probability of 0.03 [corresponding perfusion of 38 mL/(100 g · min)] or lower, the contribution to global function was lost. Cross-validations showed that the model parameters were stable. The model fitted to the data from the patients with HCC indicated that the same amount of portal venous perfusion was translated into less local function probability than in the patients with non-HCC tumors.
  
  
  CONCLUSIONS
  The developed liver function model could provide a means to better assess individual and regional dose-responses of hepatic functions, and provide guidance for individualized treatment planning of RT.
authors.affiliation: Department of Radiation Oncology, University of Michigan, Ann Arbor, Michigan. Electronic address: hesheng@umich.edu.
authors.forename: Hesheng
authors.initials: H
authors.lastname: Wang
authors.affiliation: Department of Radiation Oncology, University of Michigan, Ann Arbor, Michigan.
authors.forename: Mary
authors.initials: M
authors.lastname: Feng
authors.affiliation: Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, New York.
authors.forename: Andrew
authors.initials: A
authors.lastname: Jackson
authors.affiliation: Department of Radiation Oncology, University of Michigan, Ann Arbor, Michigan.
authors.forename: Randall K
authors.initials: RK
authors.lastname: Ten Haken
authors.affiliation: Department of Radiation Oncology, University of Michigan, Ann Arbor, Michigan.
authors.forename: Theodore S
authors.initials: TS
authors.lastname: Lawrence
authors.affiliation: Department of Radiation Oncology, University of Michigan, Ann Arbor, Michigan; Department of Radiology, University of Michigan, Ann Arbor, Michigan; Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan.
authors.forename: Yue
authors.initials: Y
authors.lastname: Cao
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D006528:Carcinoma, Hepatocellular / Q000098:blood supply / Q000378:metabolism / Q000503:physiopathology* / Q000532:radiotherapy; D003287:Contrast Media / Q000493:pharmacokinetics; D004307:Dose-Response Relationship, Radiation; D005260:Female; D006801:Humans; D007208:Indocyanine Green / Q000493:pharmacokinetics; D008099:Liver / Q000098:blood supply / Q000378:metabolism / Q000503:physiopathology* / Q000528:radiation effects*; D008113:Liver Neoplasms / Q000098:blood supply / Q000378:metabolism / Q000503:physiopathology* / Q000532:radiotherapy; D008279:Magnetic Resonance Imaging; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D011169:Portal Vein / Q000502:physiology; D011336:Probability; D011446:Prospective Studies; D011832:Radiation Injuries / Q000517:prevention & control; D016634:Radiosurgery; D020266:Radiotherapy, Conformal; D013997:Time Factors
chemical_list: D003287:Contrast Media; D007208:Indocyanine Green