title: Estimation of the Number of Compartments Associated With the Apparent Diffusion Coefficient in MRI: The Theoretical and Experimental Investigations.
abstract: OBJECTIVE
  The goal of the present study was to estimate the number of compartments and the mean apparent diffusion coefficient (ADC) value with the use of the DWI signal curve.
  
  
  METHODS
  A useful new mathematic model that includes internal correlation among subcompartments with a distinct number of compartments was proposed. The DWI signal was simulated to estimate the approximate association between the number of subcompartments and the molecular density, with density corresponding to the ratio of the ADC values of the compartments, as determined using the Monte Carlo method.
  
  
  RESULTS
  Various factors, such as energy depletion, temperature, intracellular water accumulation, changes in the tortuosity of the extracellular diffusion paths, and changes in cell membrane permeability, have all been implicated as factors contributing to changes in the ADC of water (ADCw); therefore, one may consider them as pseudocompartments in the new model proposed in this study. The lower the coefficient is, the lower the contribution of the compartment to the net signal will be. The results of the simulation indicate that when the number of compartments increases, the signal will become significantly lower, because the gradient factor (i.e., the b value) will increase. In other words, the signal curve is approximately linear at all b values when the number of compartments in which the tissues have been severely damaged is low; however, when the number of compartments is high, the curve will become constant at high b values, and the perfusion parameters will prevail on the diffusion parameters at low b values. Therefore, normal tissues will be investigated when the number of compartments and the ADC values are high and the b values are low, whereas damaged tissues will be evaluated when the number of compartments and the ADC values are low and the b values are high.
  
  
  CONCLUSIONS
  The present study investigates damaged tissues at high b values for which the effect of eddy currents will also be compensated. These b values will probably be used in functional MRI.
authors.affiliation: 1 Radiation Application Research School, Nuclear Science and Technology Research Institute, Tehran, Iran.
authors.forename: Mansour
authors.initials: M
authors.lastname: Ashoor
authors.affiliation: 2 Department of Medical Physics and Biomedical Engineering, Tehran University of Medical Sciences, PO Box 141556559, Tehran, Iran.
authors.forename: Abdollah
authors.initials: A
authors.lastname: Khorshidi
mesh_terms: D000818:Animals; D038524:Diffusion Magnetic Resonance Imaging; D004195:Disease Models, Animal; D008297:Male; D008962:Models, Theoretical; D009010:Monte Carlo Method; D051381:Rats; D017208:Rats, Wistar; D020521:Stroke / Q000175:diagnosis*
keywords: DWI; Monte Carlo method; apparent diffusion coefficient; compartment; gradient factor