A modeling tool for multilevel physiological systems

Physiological Hierarchy
  Markup Language (PHML)


Physiological Hierarchy Markup Language (PHML) can explicitly describe the multilevel hierarchical structures of the physiological functions in mathematical models. PHML fully took over the specifications of insilicoML (ISML) in 2011. The specifications of ISML can be found at

In PHML, each of the elements constructing a model is called a
module, and the structural and functional relationships among the modules are defined by edges.
Each module is quantitatively characterized by several dynamical variables, constants, time-dependent parameters and morphology data, which are defined as
physical quantities in PHML. The definition of the dynamics or functions of physical quantities is explicitly described by mathematical equations, which are written as MathML in PHML.

There are two types of edges in PHML. One is a
functional edge and the other is a structural edge. The definition of the functional relationship between two modules is represented by a functional edge linking an out-port of a module to an in-port of another module, which carries the value of a physical quantity associated with the out-port in the former module to the other module. The module receives the value at the in-port from another module and stores the value in the physical quantity assigned to the in-port. Then the module can utilize the value coming from outside in equations defined in the module. Logical structures among modules are defined by structural edges. A logical structure represents the ontology-like relationship among modules such as "has a" relationship. In terms of physiology, it corresponds to "constitute" (many cardiomyocyte constitute a heart), "include" (a cell membrane includes organelles) and so on.

Groups of modules can be defined as a module by using structural edges. Through this recursive definition of the modules, the hierarchical structure of the physiological functions can be implemented in a model.