  In many biological processes heterogeneity within cell populations is an
important issue. In this work we consider populations where the behavior of
every single cell can be described by a system of ordinary differential
equations. Heterogeneity among individual cells is accounted for by differences
in parameter values and initial conditions. Hereby, parameter values and
initial conditions are subject to a distribution function which is part of the
model specification. Based on the single cell model and the considered
parameter distribution, a partial differential equation model describing the
distribution of cells in the state and in the output space is derived.
  For the estimation of the parameter distribution within the model, we
consider experimental data as obtained from flow cytometric analysis. From
these noise-corrupted data a density-based statistical data model is derived.
Using this data model the parameter distribution within the cell population is
computed using convex optimization techniques.
  To evaluate the proposed method, a model for the caspase activation cascade
is considered. It is shown that for known noise properties the unknown
parameter distributions in this model are well estimated by the proposed
method.
