title: A statistical model for multidimensional irreversible electroporation cell death in tissue.
abstract: BACKGROUND
  Irreversible electroporation (IRE) is a minimally invasive tissue ablation technique which utilizes electric pulses delivered by electrodes to a targeted area of tissue to produce high amplitude electric fields, thus inducing irreversible damage to the cell membrane lipid bilayer. An important application of this technique is for cancer tissue ablation. Mathematical modelling is considered important in IRE treatment planning. In the past, IRE mathematical modelling used a deterministic single value for the amplitude of the electric field required for causing cell death. However, tissue, particularly cancerous tissue, is comprised of a population of different cells of different sizes and orientations, which in conventional IRE are exposed to complex electric fields; therefore, using a deterministic single value is overly simplistic.
  
  
  METHODS
  We introduce and describe a new methodology for evaluating IRE induced cell death in tissue. Our approach employs a statistical Peleg-Fermi model to correlate probability of cell death in heterogeneous tissue to the parameters of electroporation pulses such as the number of pulses, electric field amplitude and pulse length. For treatment planning, the Peleg-Fermi model is combined with a numerical solution of the multidimensional electric field equation cast in a dimensionless form. This is the first time in which this concept is used for evaluating IRE cell death in multidimensional situations.
  
  
  RESULTS
  We illustrate the methodology using data reported in literature for prostate cancer cell death by IRE. We show how to fit this data to a Fermi function in order to calculate the critical statistic parameters. To illustrate the use of the methodology, we simulated 2-D irreversible electroporation protocols and produced 2-D maps of the statistical distribution of cell death in the treated region. These plots were compared to plots produced using a deterministic model of cell death by IRE and the differences were noted.
  
  
  CONCLUSIONS
  In this work we introduce a new methodology for evaluation of tissue ablation by IRE using statistical models of cell death. We believe that the use of a statistical model rather than a deterministic model for IRE cell death will improve the accuracy of treatment planning for cancer treatment with IRE.
authors.affiliation: Center for Bioengineering in the Service of Humanity and Society, School of Computer Science and Engineering, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel.
authors.forename: Alex
authors.initials: A
authors.lastname: Golberg
authors.forename: Boris
authors.initials: B
authors.lastname: Rubinsky
mesh_terms: D017209:Apoptosis / Q000502:physiology* / Q000528:radiation effects*; D002458:Cell Fractionation / Q000379:methods; D002462:Cell Membrane / Q000502:physiology* / Q000528:radiation effects*; D003198:Computer Simulation; D004574:Electromagnetic Fields; D018274:Electroporation / Q000379:methods*; D008954:Models, Biological; D015233:Models, Statistical