Physiological response prediction system
A system for modeling the evolution of a system overtime using an advection-based process is provided. The system continuously evolves a probability density function (“PDF”) for a characteristic of a characteristic of the state of the system and its time-varying parameters. The PDF is evolved based on advection by solving an advection partial differential equation that is based on a system model of the system. The system model has time-varying parameters for modeling the characteristic of the state of the system. The system uses the continuously evolving PDF to make predictions about the characteristic of the state of the system.
1. A method performed by a computer system for simulating a biological system, the method comprising:
accessing a definition of a model of the biological system, the definition specifying components of the model and connections between outputs and inputs of the components, each component having output component code for calculating output of the component, the components including a cell aging component for modeling aging of cells of the biological system using a differential equation that is implemented by a differential equation component code of the cell aging component;
establishing identifiers for parameters, states, the inputs, and the outputs of the components of the model;
generating implementation code that:
includes a differential equation function based on the differential equation component code of the cell aging component;
calculates outputs of the components as specified by the output component codes of the components; and
sets inputs of the cell aging component based on outputs of connected components to which the inputs are connected including transitively setting an input of a connected component to the output of a component to which it is connected; and
simulating, using the implementation code, behavior of the biological system from a current simulation time to a next simulation time, wherein the simulating comprises invoking a differential equation solver to solve the differential equation as represented by the differential equation component code; wherein:
the cell aging component comprises a state that includes a current cell age distribution for the current simulation time and one or more of a first probability density function (PDF) for a cell birth rate, a second PDF for a cell reduction rate, or a third PDF for a cell aging rate; and
the invoked differential equation solver generates a next cell age distribution for the next simulation time using one or more values sampled from the one or more of the first PDF for the cell birth rate, the second PDF for the cell reduction rate, or the third PDF for the cell aging rate.
2. The method of claim 1 , wherein:
the implementation code is in a programming language: and
the simulating further comprises compiling the implementation code into executable code.
3. The method of claim 2 ,
wherein the simulating further comprises executing the executable code to calculate inputs of the cell aging component.
4. A non-transitory computer-readable storage medium including instructions that, when executed by one or more processors of a computing apparatus, cause the computing apparatus to:
access a definition of a model of a biological system, the definition specifying components of the model and connections between outputs and inputs of the components, each component having output component code for calculating output of the component, the components including a cell aging component for modeling aging of cells of the biological system using a differential equation that is implemented by a differential equation component code of the cell aging component;
establish identifiers for parameters, states, the inputs, and the outputs of the components of the model;
generate implementation code that:
includes a differential equation function based on the differential equation component code of the cell age component;
calculates outputs of the components as specified by the output component codes of the components; and
sets inputs of the cell age component based on outputs of connected components to which the inputs are connected including transitively setting an input of a connected component to the output of a component to which it is connected; and
simulate, using the implementation code, behavior of the biological system from a current simulation time to a next simulation time, wherein the simulating comprises invoking a differential equation solver to solve the differential equation as represented by the differential equation component code; wherein:
the cell aging component comprises a state that includes a current cell age distribution for the current simulation time and one or more of a first probability density function (PDF) for a cell birth rate, a second PDF for a cell reduction rate, or a third PDF for a cell aging rate; and
the invoked differential equation solver generates a next cell age distribution for the next simulation time using one or more values sampled from the one or more of the first PDF for the cell birth rate, the second PDF for the cell reduction rate, or the third PDF for the cell aging rate.
5. The non-transitory computer-readable storage medium of claim 4 , wherein the implementation code is in a programming language, and wherein the simulating further comprises compiling the implementation code into executable code.
6. The non-transitory computer-readable storage medium of claim 5 , wherein
the simulating further comprises executing the executable code to calculate inputs of the cell aging component.
7. A computing apparatus comprising:
one or more processors; and
a memory storing instructions that, when executed by the one or more processors, configure the computing apparatus to:
access a definition of a model of a biological system, the definition specifying components of the model and connections between outputs and inputs of the components, each component having output component code for calculating output of the component, the components including a cell aging component for modeling aging of cells of the biological system using a differential equation that is implemented by a differential equation component code of the cell aging component;
establish identifiers for parameters, states, the inputs, and the outputs of the components of the model;
generate implementation code that:
includes a differential equation function based on the differential equation component code of the cell age component;
calculates outputs of the components as specified by the output component codes of the components; and
sets inputs of the cell age component based on outputs of connected components to which the inputs are connected including transitively setting an input of a connected component to the output of a component to which it is connected; and
simulate, using the implementation code, behavior of the biological system from a current simulation time to a next simulation time, wherein the simulating comprises invoking a differential equation solver to solve the differential equation as represented by the differential equation component code; wherein:
the cell age component comprises a state that includes a current cell age distribution for the current simulation time and one or more of a first probability density function (PDF) for a cell birth rate, a second PDF for a cell reduction rate, or a third PDF for a cell aging rate; and
the invoked differential equation solver generates a next cell age distribution for the next simulation time using one or more values sampled from the one or more of the first PDF for the cell birth rate, the second PDF for the cell reduction rate, or the third PDF for the cell age rate.
8. The computing apparatus of claim 7 , wherein the implementation code is in a programming language, and wherein the simulating further comprises compiling the implementation code into executable code.
9. The computing apparatus of claim 7 , wherein the simulating further comprises executing the executable code to calculate inputs of the cell aging component.