Mathematical circulatory system model

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a first set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a second set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function;
• a third set of instructions for solving one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a fourth set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments;
• a fifth set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a sixth set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments, wherein said smooth muscle contraction parameter is represented according to the following equation:
• {dot over (V)}=C·({dot over (P)}({dot over (φ)}+{dot over (P)}*))
• wherein {dot over (V)} is a time derivative of a volume of said one of said plurality of compartments, {dot over (P)} is a time derivative of the pressure inside said one of said plurality of compartments, {dot over (φ)} is a time derivative of said smooth muscle contraction parameter, {dot over (P)}* is a time derivative of the pressure outside of said one of said plurality of compartments, and C is an active compliance defined according to the following equation:
• C
• =
• rV
• Max
• ⁢
• ⅇ
• -
• r
• ⁡
• (
• P
• -
• (
• ϕ
• +
• P
• *
• )
• )
• (
• 1
• +
• ⅇ
• -
• r
• ⁡
• (
• P
• -
• (
• ϕ
• +
• P
• *
• )
• )
• )
• 2
• wherein r>0, VMax is a maximum volume of said one of said plurality of compartments, P is the pressure inside said one of said plurality of compartments, P* is the pressure outside said one of said plurality of compartments, and φ is said smooth muscle contraction parameter.

A method of modeling a pressure and volume relationship in a compliant vessel using a programmed computer, the method comprising:

• defining a first parameter as a change in pressure within the vessel using the computer, said change in pressure being due to a contraction of smooth muscles of a wall of the vessel;
• defining a second parameter as an active compliance for the vessel using the computer, said active compliance varying with internal pressure, external pressure, and said first parameter, wherein said second parameter is defined according to the following equation:
• 𝒞
• =
• r
• ⁢
• ⁢
• V
• Max
• ⁢
• ⅇ
• -
• r
• ⁡
• (
• P
• -
• (
• ϕ
• +
• P
• *
• )
• )
• (
• 1
• +
• ⅇ
• -
• r
• ⁢
• (
• P
• -
• (
• ϕ
• +
• P
• *
• )
• )
• )
• 2
• wherein C is said second parameter, r>0, VMax is a maximum volume of said vessel, P is the pressure inside said vessel, P* is the pressure outside said vessel, and φ is said first parameter;
• and
• relating, using the computer, said first parameter and said second parameter via a differential equation, wherein said relating step comprises relating said first parameter and said second parameter according to the following equation:
• {dot over (V)}=C·({dot over (P)}−({dot over (φ)}={dot over (P)}*))
• wherein {dot over (V)} is a time derivative of a volume of said vessel, {dot over (P)} is a time derivative of the pressure inside said vessel, {dot over (φ)} is a time derivative of said first parameter, {dot over (P)}* is a time derivative of the pressure outside of said vessel, and C is said second parameter.

A non-transitory computer readable storage medium containing computer executable instructions implementing a method of modeling a pressure and volume relationship in a compliant vessel, the instructions comprising:

• a first set of instructions for defining a first parameter as a change in pressure within the vessel, said change in pressure being due to a contraction of smooth muscles of a wall of the vessel;
• a second set of instructions for defining a second parameter as an active compliance for the vessel, said active compliance varying with internal pressure, external pressure, and said first parameter, wherein said second set of instructions comprises a set of instructions for defining said second parameter according to the following equation:
• 𝒞
• =
• r
• ⁢
• ⁢
• V
• Max
• ⁢
• ⅇ
• -
• r
• ⁡
• (
• P
• -
• (
• ϕ
• +
• P
• *
• )
• )
• (
• 1
• +
• ⅇ
• -
• r
• ⁢
• (
• P
• -
• (
• ϕ
• +
• P
• *
• )
• )
• )
• 2
• wherein C is said second parameter, r>0, VMax is a maximum volume of said vessel, P is the pressure inside said vessel, P* is the pressure outside said vessel, and φ is said first parameter;
• and
• a third set of instructions for relating said first parameter and said second parameter via a differential equation, wherein said third set of instructions comprises a set of instructions for relating said first parameter and said second parameter according to the following equation:
• {dot over (V)}=C·({dot over (P)}−({dot over (φ)}+{dot over (P)}*))
• wherein {dot over (V)} is a time derivative of a volume of said vessel, {dot over (P)} is a time derivative of the pressure inside said vessel, {dot over (φ)} is a time derivative of said first parameter, {dot over (P)}* is a time derivative of the pressure outside of said vessel, and C is said second parameter.

A method of modeling a circulatory system using a programmed computer, the method comprising:

• providing a circulatory system model in the computer, the model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure in a portion of the circulatory system;
• using a logistic function in the computer to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, said using a logistic function including using a logistic function to represent a cerebral blood flow parameter according to the following logistic function:
• Q1=Linc(PAV− PAV,0.15,1.0001,0)· Q1
• wherein Q1 is said cerebral blood flow parameter, PAV is a pressure difference PA−PV, wherein PA is said time-dependent pressure function for said arterial compartment and PV is said time-dependent pressure function for said venous compartment, PAV is a mean systemic indicative pressure, Q1 is a mean cerebral blood flow, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc;
• dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein said dividing step divides said circulatory system into a set of compartments comprising of an arterial compartment and a venous compartment, and a heart pump;
• assigning, using the computer, one of said one or more time-dependent pressure functions to each of said plurality of compartments;
• using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments;
• and
• solving, using the computer, one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic.

A method of modeling a circulatory system using a programmed computer, the method comprising:

• providing a circulatory system model in the computer, the model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure in a portion of the circulatory system;
• using a logistic function in the computer to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, said using a logistic function including using a logistic function to represent an output versus pressure parameter, said output versus pressure parameter representing an effect of venous pressure on cardiac uptake according to the following logistic function:
• OVP(PV)=Linc(PV− PV,0.5,2.5,0)
• wherein OVP is said output versus pressure parameter, PV is said time-dependent pressure function for said venous compartment, PV is the mean systemic venous pressure, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc;
• dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein said dividing step divides said circulatory system into a set of compartments comprising of an arterial compartment and a venous compartment, and a heart pump;
• assigning, using the computer, one of said one or more time-dependent pressure functions to each of said plurality of compartments;
• using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments;
• and
• solving, using the computer, one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic.

A method of modeling a circulatory system using a programmed computer, the method comprising:

• providing a circulatory system model in the computer, the model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure in a portion of the circulatory system;
• using a logistic function in the computer to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, wherein said regulatory mechanism parameter represents an autonomic nervous system effect on cardiac output according to the following equation:
• ANSo=Ldec(PA− PA,0.1,2,0)
• wherein ANSO is said regulatory mechanism parameter representing said autonomic nervous system effect on cardiac output, PA is said time-dependent pressure function for said arterial compartment, PA is an initial mean arterial pressure, and Ldec is a decreasing logistic function represented by the following equation:
• L
• dec
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• -
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and Ldec<max;
• dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein said dividing step divides said circulatory system into a set of compartments comprising of an arterial compartment and a venous compartment, and a heart pump;
• assigning, using the computer, one of said one or more time-dependent pressure functions to each of said plurality of compartments;
• using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments;
• and
• solving, using the computer, one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic.

A method of modeling a circulatory system using a programmed computer, the method comprising:

• providing a circulatory system model in the computer, the model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure in a portion of the circulatory system;
• using a logistic function in the computer to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, wherein said regulatory mechanism parameter represents an autonomic nervous system effect on non-cerebral blood flow according to the following equation:
• ANSz=Linc(PA− PA,0.3,1.1,0.7)
• wherein ANSz is said regulatory mechanism parameter representing said autonomic nervous system effect on non-cerebral blood flow, PA is said time-dependent pressure function for said arterial compartment, PA is an initial mean arterial pressure, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc;
• dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein said dividing step divides said circulatory system into a set of compartments comprising of an arterial compartment and a venous compartment, and a heart pump;
• assigning, using the computer, one of said one or more time-dependent pressure functions to each of said plurality of compartments;
• using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments;
• and
• solving, using the computer, one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic.

A method of modeling a circulatory system using a programmed computer, the method comprising:

• providing a circulatory system model in the computer, the model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure in a portion of the circulatory system;
• using a logistic function in the computer to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, wherein said regulatory mechanism parameter represents a central nervous system effect on cardiac output according to the following equation:
• CNSo=Ldec(Q1− Q1,0.01,5,0.9)
• wherein Q1 is cerebral blood flow, Q1 is mean cerebral blood flow, and Ldec is a decreasing logistic function represented by the following equation:
• L
• dec
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• -
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and Ldec<max;
• dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein said dividing step divides said circulatory system into a set of compartments comprising of an arterial compartment and a venous compartment, and a heart pump;
• assigning, using the computer, one of said one or more time-dependent pressure functions to each of said plurality of compartments;
• using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments;
• and
• solving, using the computer, one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic.

A method of modeling a circulatory system using a programmed computer, the method comprising:

• providing a circulatory system model in the computer, the model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure in a portion of the circulatory system;
• using a logistic function in the computer to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, wherein said regulatory mechanism parameter represents a central nervous system effects on non-cerebral blood flow according to the following equation:
• CNSz=Linc(Q1− Q1,0.01,1.01,0.1)
• wherein Q1 is cerebral blood flow, Q1 is mean cerebral blood flow, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc;
• dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein said dividing step divides said circulatory system into a set of compartments comprising of an arterial compartment and a venous compartment, and a heart pump;
• assigning, using the computer, one of said one or more time-dependent pressure functions to each of said plurality of compartments;
• using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments;
• and
• solving, using the computer, one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic.

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function;
• a set of instructions for using a logistic function to represent a cerebral blood flow parameter according to the following logistic function:
• Q1=Linc(PAV PAV,0.15,1.0001,0)· Q1
• wherein Q1 is said cerebral blood flow parameter, PAV is a pressure difference PA−PV, wherein PA is said time-dependent pressure function for said arterial compartment and PV is said time-dependent pressure function for said venous compartment, PAV is a mean systemic indicative pressure, Q1 is a mean cerebral blood flow, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc a set of instructions for solving one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein the plurality of compartments includes an arterial compartment and a venous compartment;
• a set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments.

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function;
• a set of instructions for using a logistic function to represent an output versus pressure parameter that represents an effect of venous pressure on cardiac uptake wherein the representing the output versus pressure parameter includes the following logistic function:
• OVP(PV)=Linc(PV− PV,0.5,2.5,0)
• wherein OVP is said output versus pressure parameter, PV is said time-dependent pressure function for said venous compartment, PV is the mean systemic venous pressure, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc a set of instructions for solving one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein the plurality of compartments includes an arterial compartment and a venous compartment;
• a set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments.

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, said regulatory mechanism parameter representing an autonomic nervous system effect on cardiac output according to the following equation:
• ANSo=Ldec(PA− PA,0.1,2,0)
• wherein ANSo is said regulatory mechanism parameter representing said autonomic nervous system effect on cardiac output, PA is said time-dependent pressure function for said arterial compartment, PA is an initial mean arterial pressure, and Ldec is a decreasing logistic function represented by the following equation:
• L
• dec
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• -
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and Ldec<max;
• a set of instructions for solving one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein the plurality of compartments includes an arterial compartment and a venous compartment;
• a set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments.

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, said regulatory mechanism parameter representing an autonomic nervous system effect on non-cerebral blood flow according to the following equation:
• ANSz=Linc(PA− PA,0.3,1.1,0.7)
• wherein ANSz is said regulatory mechanism parameter representing said autonomic nervous system effect on non-cerebral blood flow, PA is said time-dependent pressure function for said arterial compartment, PA is an initial mean arterial pressure, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc.
• a set of instructions for solving one or more equations for said one or more time-Dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein the plurality of compartments includes an arterial compartment and a venous compartment;
• a set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments.

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, said regulatory mechanism parameter representing an a central nervous system effects on cardiac output according to the following equation:
• CNSo=Ldec(Q1− Q1,0.01,5,0.9)
• wherein Q1 is cerebral blood flow, Q1 is mean cerebral blood flow, and Ldec is a decreasing logistic function represented by the following equation:
• L
• dec
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• -
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and Ldec<max;
• a set of instructions for solving one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein the plurality of compartments includes an arterial compartment and a venous compartment;
• a set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartments.

A non-transitory computer readable medium containing computer executable instructions implementing a method of modeling a circulatory system, the instructions comprising:

• a set of instructions for providing a circulatory system model including one or more time-dependent pressure functions, each of said one or more time-dependent pressure functions representing a pressure of a portion of the circulatory system;
• a set of instructions for using a logistic function to represent a regulatory mechanism parameter, said regulatory mechanism parameter representing a regulatory mechanism having an impact on circulatory system function, said regulatory mechanism parameter representing an a central nervous system effects on non-cerebral blood flow according to the following equation:
• CNSz=Linc(Q1− Q1,0.01,1.01,0.1)
• wherein Q1 is cerebral blood flow, Q1 is mean cerebral blood flow, and Linc is an increasing logistic function represented by the following equation:
• L
• inc
• ⁡
• (
• x
• ,
• r
• ,
• max
• ,
• min
• )
• =
• max
• +
• min
• -
• max
• 1
• +
• 1
• -
• min
• max
• -
• 1
• ⁢
• e
• rx
• wherein max is a maximum value for x, min is a minimum value for x, r>0, −∞<x<∞, and min<Linc;
• a set of instructions for solving one or more equations for said one or more time-dependent pressure functions and said logistic function to determine a circulatory system dynamic;
• a set of instructions for dividing the circulatory system into a plurality of compartments and a heart pump, said plurality of compartments representing a portion of the circulatory system, said heart pump interacting with at least one of said plurality of compartments, wherein the plurality of compartments includes an arterial compartment and a venous compartment;
• a set of instructions for assigning a time-dependent pressure function to each of said plurality of compartments;
• and
• a set of instructions for using a smooth muscle contraction parameter, said smooth muscle contraction parameter representing an autonomic nervous system effect on smooth muscle contraction in a wall of one of said plurality of compartment.