title: Predicting endothelial cell loss and long-term corneal graft survival.
abstract: OBJECTIVE
  To evaluate a biexponential decay model for describing the loss of corneal endothelial cells with age as well as the increased loss of cells after cataract surgery and penetrating keratoplasty.
  
  
  METHODS
  Data from previous studies were identified and the sum of two exponentials, d = p. exp(-at) + q. exp(-bt) (where d is cell density at time t, p and q are constants the sum of which is equal to the initial cell density, and a and b are exponential rate constants), fitted to each data set by a nonlinear least-squares algorithm. Goodness of fit was indicated by the residual standard deviation. Half times were calculated from the exponential rate constants.
  
  
  RESULTS
  The model identified in each instance a rapid and a slow component to the cell loss. The half time for the slow component of the loss with age was 224 years, underlining the excess endothelial capacity in normal eyes. After surgery, the rapid component of the cell loss was probably due to surgical trauma and, after penetrating keratoplasty, cell-mediated rejection and other complications. The half times of the slow component were only 26 years after cataract surgery and 21 years after penetrating keratoplasty.
  
  
  CONCLUSIONS
  The loss of endothelial cells followed a biexponential decay and could thus be described by a single equation. The half times of the slow component of the cell loss after surgery were substantially less than for the loss with age, indicating a markedly increased rate of cell loss that persisted for many years after surgery. A mechanism for this accelerated cell loss is suggested that involves a nonspecific, innate response initiated by the breakdown of the blood-ocular barrier. The model was used to calculate endothelial cell loss in the long term after penetrating keratoplasty and to predict when cell density would reach levels that are incompatible with maintenance of transparency and graft function. Thus, a rationale is presented for the setting of minimum donor cell densities by eye banks.
authors.affiliation: Division of Ophthalmology, University of Bristol, Bristol, United Kingdom. w.j.armitage@bristol.ac.uk
authors.forename: W John
authors.initials: WJ
authors.lastname: Armitage
authors.forename: Andrew D
authors.initials: AD
authors.lastname: Dick
authors.forename: William M
authors.initials: WM
authors.lastname: Bourne
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000375:Aging; D002387:Cataract Extraction / Q000009:adverse effects*; D002452:Cell Count; D002648:Child; D002675:Child, Preschool; D004728:Endothelium, Corneal / Q000473:pathology*; D006085:Graft Survival; D006801:Humans; D007223:Infant; D015948:Keratoplasty, Penetrating / Q000009:adverse effects*; D008875:Middle Aged; D008954:Models, Biological; D011183:Postoperative Complications