SYSTEM FOR ENHANCING INTENSITY MODULATED RADIATION THERAPY, PROGRAM PRODUCT, AND RELATED METHODS

• US 20080049898A1
• Filed: 07/26/2007
• Published: 02/28/2008
• Est. Priority Date: 07/26/2006
• Status: Active Grant

• Current Assignee: Best Medical International Incorporated (TeamBest Group)
• Original Assignee: Nomos Corporation (North American Scientific, Inc.)
• Inventors: Nizin, Paul, Romesberg, Merle, Pino, Ramiro
• Granted Patent: US 7,519,150 B2
• Time in Patent Office: Days
• US Class Current: 378/65
• CPC Class Codes: A61N 5/1031 using a specific method of dose optimization

Abstract

A system to provide enhanced computational efficiency in determining dose in a media of varying density from a high-energy radiation-beam for radiation treatment, program product, and related methods are provided. The system can include a radiation treatment planning computer and radiation treatment planning program product stored in the memory of the radiation treatment planning computer and adapted to enhance optimization of a radiation treatment plan for delivering radiation to a complex medium defining a patient volume. The radiation treatment planning program product provides functions including those for predetermining a delivery machine-dependent representation of radiation dose for a plurality of different electron densities selected over a preselected representative range, predetermining a depth-dependent representation of central axis properties of a pencil beam passing through a complex medium for each of a plurality of pencil beams, and determining with constant time computational complexity radiation dose for each of a plurality of points of interest in a heterogeneous medium having a complex spatial distribution of heterogeneous electron densities by applying the predetermined machine-dependent and depth-dependent representations.

Claims

1. A system for determining dose in heterogeneous media of varying electron density from a therapeutic high-energy radiation-beam for radiation treatment, comprising:

a communication network;

an image gathering device accessible to the communication network to provide an at least two-dimensional image slice of a target volume and an adjacent structure volume in a patient defining a patient volume;

a radiation beam source to deliver radiation to the target volume according to a radiation treatment plan along a plurality of pencil beams;

a radiation treatment planning computer in communication with the image gathering device and having memory and a processor coupled to the memory; and

radiation treatment planning program product stored in the memory of the radiation treatment planning computer and adapted for enhanced optimization of a radiation treatment plan for delivering radiation to the target volume, the radiation treatment planning program product including instructions that when executed by the processor of the radiation treatment planning computer causes the computer to perform the operations of;

receiving a set of photon beam data for a water medium to thereby parameterize a dose model for unit relative electron density,

parameterizing a machine-dependent dose model for unit relative electron density responsive to the set of photon beam data,

determining a machine-dependent primary dose profile for each of a first set of a plurality of electron densities distributed through a preselected range of electron densities responsive to the dose model for unit relative electron density,

determining a machine-dependent scatter dose profile for each of a second set of a plurality of electron densities distributed through a preselected range of electron densities responsive to the dose model for unit relative electron density,

determining patient specific primary dose profile parameters for each of the plurality of pencil beams to be utilized during radiation treatment responsive to the primary dose profiles,

determining patient specific scatter dose profile parameters for each of the plurality of pencil beam to be utilized during radiation treatment,

retrieving the patient specific primary and scatter dose profile parameters separately for each of a plurality of points of interest in a patient volume to compute dose with constant time computational complexity for each pencil-beam to each point of interest as selected a posteriori to profile parameter determination responsive to one of the following;

a value of electron density associated with the respective point of interest and an electron density distribution associated with the respective point of interest, defining a local electron density value for the respective point of interest, to thereby determine total dose at each of the plurality of points of interest, and

producing a map of radiation dose delivered to the patient volume to allow a user to iteratively evaluate the total dose of the patient volume.

2. A system as defined in claim 1,

wherein the operations of determining machine-dependent primary dose profiles for each of the electron densities in the first set of electron densities includes performing the operations of separating a total dose model into a central axis primary and scatter dose models, and performing a two-dimensional convolution of the associated geometric kernel and radiological kernel of the respective electron density with an aperture description of a characteristic pencil beam;

and

wherein the operation of determining a machine-dependent scatter dose profiles for a second set of electron densities distributed through a preselected range of electron densities includes performing the operations of accessing the dose model for unit relative electron density to obtain profile data using a beam field size equal to a product of beam field size by each respective electron density.

3. A system as defined in claim 1,

wherein the operation of determining patient specific primary dose profile parameters for each pencil beam to be utilized during radiation treatment includes the operations of modeling a plurality dose build-up and dose build-down regions;

and

wherein the operation of determining patient specific scatter dose profile parameters for each pencil beam to be utilized during radiation treatment includes determining an effective electron density.

4. A system as defined in claim 1, wherein the radiation treatment planning program product further includes instructions to perform the operations of:

storing two-dimensional primary dose profiles in separate look-up tables for each electron density in the first set of electron densities;

storing three-dimensional scatter dose profiles in separate look-up tables for each electron density in the second set of electron densities; and

storing the primary and scatter dose profile parameters in separate look-up tables for each of the plurality of pencil beams.

5. A system for determining dose in a media of varying electron density from a high-energy radiation-beam for radiation treatment, comprising:

a radiation treatment planning computer having memory and a processor in communication with the memory; and

radiation treatment planning program product stored in the memory of the radiation treatment planning computer and adapted to determine dose for a radiation treatment plan to deliver radiation to a complex medium defining a patient volume, the radiation treatment planning program product including instructions that when executed by the processor of the radiation treatment planning computer causes the computer to perform the operations of;

receiving measured dose data for unit relative electron density,

determining machine-dependent primary dose profiles for each of a first set of a plurality of electron densities distributed through a preselected range of electron densities responsive to the measured dose data for unit relative electron density,

determining machine-dependent scatter dose profiles for each of a second set of a plurality of electron densities distributed through a preselected range of electron densities responsive to the measured dose data for unit relative electron density, and

using the primary and scatter dose profiles to compute dose with constant time computational complexity for each of a plurality of points of interest in the complex medium responsive to one of the following;

a value of electron density associated with the respective point of interest and an electron density distribution associated with the respective point of interest, defining a local electron density value for the respective point of interest, to thereby determine total dose at each of the plurality of points of interest.

6. A system as defined in claim 5, wherein the radiation treatment planning program product further includes instructions to perform the operations of:

determining patient specific primary dose profile parameters for each of a plurality of pencil beams to be utilized during radiation treatment responsive to the primary dose profiles; and

determining patient specific scatter dose profile parameters for each of the plurality of pencil beam to be utilized during radiation treatment.

7. A system as defined in claim 6, wherein the radiation treatment planning program product further includes instructions to perform the operation of retrieving the patient specific primary and scatter dose profile parameters separately for each of the plurality of points of interest in the patient volume responsive to one of the following:

a value of electron density associated with the respective point of interest and an electron density distribution associated with the respective point of interest, defining the local electron density value for the respective point of interest to determine total dose at each of the plurality of points of interest, to thereby produce a three-dimensional map of radiation dose delivered to the patient volume.

8. A system as defined in claim 5, wherein the operation of determining machine-dependent primary dose profiles includes performing for each electron density in the first set of electron densities a two-dimensional radiological kernel integration convolved with geometric penumbra kernel whereby a central axis primary dose implied by the kernel is substantially equivalent to a central axis primary dose in water of a field size substantially equal to a desired field size multiplied by a ratio of electron density of the homogeneous medium to electron density of water.

9. A system as defined in claim 5, wherein the operation of determining a machine-dependent scatter dose profiles for a second set of electron densities distributed through a preselected range of electron densities includes performing for each electron density in the second set of electron densities a modified Clarkson integration whereby central axis dose in the homogeneous medium is derived from the central axis dose of water for a field size equal to the field size of the pencil beam multiplied by a ratio of an electron density of the homogeneous medium to an electron density of water.

10. A system as defined in claim 6,

wherein the operation of determining patient specific primary dose profile parameters for each pencil beam to be utilized during radiation treatment includes using a electron density-dependent kernel and combining linearly current and previous depth-dependent electron densities to determine the primary dose profile parameters around media boundaries;

and

wherein the operation of determining patient specific scatter dose profile parameters for each pencil beam to be utilized during radiation treatment includes performing a modified Clarkson integration for a set of electron densities.

11. A method of determining dose in a media of varying electron density from a high-energy radiation-beam for radiation treatment, the method comprising the steps of:

predetermining a delivery machine-dependent representation of radiation dose for a plurality of different homogeneous media, each having an electron density selected over a preselected representative range;

predetermining a depth-dependent representation of central axis properties of a pencil beam passing through a complex medium having a complex spatial distribution of heterogeneous electron densities for each of a plurality of pencil beams; and

determining with constant time computational complexity, radiation dose for each of a plurality of points of interest in the complex medium, by applying the predetermined machine-dependent and depth-dependent representations.

12. A method as defined in claim 11, wherein the step of predetermining a delivery machine-dependent representation of radiation dose includes the steps of determining an at least two-dimensional primary dose profile for each of the plurality of different electron densities and an at least two-dimensional scatter dose profile for at least a representative portion of the plurality of different electron densities.

13. A method as defined in claim 11, wherein the step of predetermining a depth dependent representation of central axis properties of a pencil beam passing through a complex medium for each of a plurality of pencil beams includes the steps of:

determining a depth-dependent weighted value to form a weight for a primary dose profile for a point at a current electron density at a current depth and a weight for at least one dose profile for a corresponding at least one point at a previous electron density at a previous depth so that when the weighted values are applied to a linear combination of the dose profiles a resulting dose profile provides a value substantially equal to a computed value of central axis primary dose at the current depth when a point of interest applied to the linear combination at the current depth is on the central axis; and

determining an effective electron density to apply to a scatter dose profile that when applied provides a value substantially equal to a computed value of central axis scatter dose at the current depth when a point of interest applied to the scatter dose profile at the current electron density at the current depth is on the central axis.

14. A method as defined in claim 11, wherein the step of determining with constant time computational complexity, radiation dose for each of a plurality of points of interest in the complex medium includes the steps of:

determining for each of the plurality of points of interest at least one of the following;

a value of electron density associated with the point of interest and an electron density distribution associated with the point of interest defining a local electron density value; and

accessing predetermined off-axis properties corresponding to a homogeneous electron density having a value derived from the respective local electron density value associated with each point of interest responsive to the respective local electron density value for each respective one of the plurality of points of interest and a pencil beam intensity for each associated pencil beam directed through each respective one of the plurality of points of interest to thereby determine radiation dose for each of the plurality of points of interest.

15. A method as defined in claim 11,

wherein the step of predetermining a delivery machine-dependent representation of radiation dose includes the step of determining a radiation dose profile for a plurality of media each having a different electron density, the electron densities selected over a representative range;

and

wherein the step of predetermining a depth dependent representation of central axis properties of a pencil beam passing through a complex medium for each of a plurality of pencil beams includes the steps of;

determining for each of the plurality of pencil beams a depth dependent weight factor for each of a plurality of depths along a central axis of the respective pencil beam, each of the plurality of depths for each of the plurality of pencil beams having a determined electron density, each depth dependent weight factor to be applied to at least one function within an least two-dimensional electron density dependent primary dose profile associated with the depth of the respective point and having a value determined so that when a point of interest is selected along the central axis of the respective pencil beam at the respective depth, the associated at least two-dimensional electron density dependent primary dose profile provides a value substantially equal to a convoluted value of central axis primary dose of the current depth when a point of interest applied to the linear combination at the current depth is on the central axis, and

determining an effective electron density to apply to a scatter dose profile that when applied provides a value substantially equal to a convoluted value of central axis scatter dose when a point of interest applied to the scatter dose profile at the current electron density at the current depth is on the central axis.

16. A method as defined in claim 11,

wherein the step of predetermining a delivery machine-dependent representation of radiation dose includes the steps of:

receiving data parameters for a medium having properties substantially similar to that of water,

forming a primary dose profile table for each of the plurality of electron densities responsive to the data parameters, and

forming a scatter dose profile table for at least a representative portion of the plurality of electron densities;

wherein the step of predetermining a depth dependent representation of central axis properties of a pencil beam passing through a complex medium for each of a plurality of pencil beams includes the steps of;

receiving electron density parameters for a patient volume developed from a patient-specific image generating device,

determining current and previous electron density values for each of a plurality of depths along each separate one of a plurality of pencil beams,

determining a separate depth dependent weight w(d) for each of the plurality of depths, and

determining a depth-dependent effective electron density ρ

′

(d) for each of the plurality of depths, to thereby form at least one table of off-axis dose parameters including representations of a plurality of regions of dose build-up and dose build-down; and

wherein the step of determining with constant time computational complexity radiation dose for each of a plurality of points of interest in the complex medium includes the steps of;

determining for each of a plurality of points of interest at least one of the following;

a value of electron density associated with the point of interest and an electron density distribution associated with the point of interest, defining a local electron density value, and

retrieving the stored off-axis dose parameters responsive to the local electron density value for each of the plurality of points of interest.

17. A method as defined in claim 11, wherein the step of predetermining a depth dependent representation of central axis properties of a beam passing through a complex medium for each of a plurality of pencil beams includes the step of modeling a three-dimensional primary dose profile by:

linearly combining two profiles, the first profile at a current electron density and the second profile at a previous electron density to form a model of a three-dimensional primary dose profile; and

setting weighted values of each profile so that the model provides a convoluting value of the central axis primary dose when a point applied to the model at the current depth is on the central axis.

18. A method as defined in claim 11, wherein the method is applied to enable at least one of the following:

inverse planning, forward plan dose calculation, and interactive dose calculation.

19. A method as defined in claim 11, wherein the high-energy radiation-beam includes one of the following:

photons, electrons, neutrons, and protons.

20. A method as defined in claim 11, wherein the step of predetermining a depth dependent representation of central axis properties of a beam passing through a complex medium for each of a plurality of pencil beams includes for each of the plurality of pencil beams the step of modeling a dose profile by determining a differential change to central axis dose traveling into the complex medium along the central axis of the respective pencil beam in proportion to a product of a difference between a current central axis dose and a dose to a homogeneous medium having an electron density at a point of interest and an electron density dependent proportionality constant that depends on the electron density at the point of interest to thereby form representations of a plurality of regions of dose build-up and dose build-down.

21. A method as defined in claim 20,

wherein the step of determining a differential change to central axis dose is applied to at least one of the following:

primary dose and scatter dose; and

wherein the electron density-dependent proportionality constant depends on a ratio of electron density of the medium and an associated proportionality constant applied to a medium having properties substantially similar to that of water.

22. A method of determining central axis dose in a media of varying electron density from a high-energy radiation-beam for radiation treatment, the method comprising the step of modeling a dose profile by performing the steps of:

determining a difference between a current central axis dose and a central axis dose at previous depth traveling into a complex medium along a central axis of a pencil beam in proportion to a product of a difference between the central axis dose at previous depth and an equilibrium dose to a homogeneous medium having an electron density at a point of interest, and an electron density dependent proportionality constant that depends on the electron density at the point of interest; and

determining the sum of the central axis dose at previous depth and the difference between the current central axis dose and the central axis dose at previous depth, to thereby form representations of a plurality of regions of dose build-up and dose build-down.

23. A method as defined in claim 22,

wherein the step of determining a differential change to central axis dose is applied to at least one of the following:

primary dose and scatter dose; and

wherein the electron density-dependent proportionality constant depends on a ratio of electron density of the medium and an associated proportionality constant applied to a medium having properties substantially similar to that of water.

24. A method of determining an off-axis dose profile actions in heterogeneous media of varying electron density from a therapeutic high-energy radiation-beam for radiation treatment, the method comprising the steps of:

receiving a central axis primary dose;

receiving homogeneous medium off-axis primary dose profiles for a plurality of electron densities; and

determining an off-axis primary dose profile for a region of a complex medium having an electron density varying with depth along a central axis of a pencil beam by forming a combination of the homogeneous medium off-axis primary dose profiles weighted by values applied so that the center of the determined off-axis primary dose profile has primary dose equal the received central axis primary dose.

25. A method as defined in claim 24, wherein the step of determining an off-axis primary dose profile includes the step of linearly combining a two-dimensional primary dose profile for a point having a electron density value related to a current depth with a two-dimensional primary dose profile for the point having a electron density value related to that of the previous depth to form an off-axis dose profile for the complex medium.

26. A method of determining an off-axis dose profile in heterogeneous media of varying electron density from a therapeutic high-energy radiation-beam for radiation treatment, the method comprising the steps of:

receiving a central axis scatter dose;

receiving homogeneous medium off-axis scatter dose profiles for a plurality of electron densities; and

determining an off-axis scatter dose profile for a region of a complex medium having an electron density varying with depth along a central axis of a pencil beam from off-axis properties of a homogeneous medium corresponding to an effective electron density selected so that central axis scatter dose of the determined homogeneous medium off-axis scatter dose profile matches the received central axis scatter dose of the complex medium.

27. A method as defined in claim 26, wherein the step of determining an off-axis scatter dose profile includes the step of determining an effective electron density to apply to the off-axis scatter dose profile that when applied provides a value substantially equal to a convoluted value of the central axis scatter dose of the complex medium when a point of interest applied to the off-axis scatter dose profile at the current electron density at the current depth is on the central axis.

28. A method of determining dose in heterogeneous media of varying electron density from a therapeutic high-energy radiation-beam for radiation treatment, the method comprising the step of:

determining an off-axis dose profile for a pencil beam to a point of interest of a complex medium having an electron density distribution varying laterally at a depth of interest associated with the point of interest by using an off-axis dose profile of the pencil beam at a depth and an off-axis position of interest corresponding to the electron density distribution substantially equal to that of a local electron density distribution near the point of interest.

29. A method as defined in claim 28, wherein the modeled electron density distribution is a single electron density value.

30. A method of determining dose in heterogeneous media of varying electron density from a therapeutic high-energy radiation-beam for radiation treatment, the method comprising the step of:

determining for a preselected size pencil beam, a central axis primary dose in a homogeneous medium of arbitrary electron density from a central axis primary dose model for water equivalent medium of an equivalent effective field size by resealing a dose normalization factor and a linear attenuation and longitudinal buildup coefficients as a function of the arbitrary electron density.

31. A method as defined in claim 30, wherein the step of determining central axis primary dose includes the step of modifying a two-dimensional radiological kernel representing electron transport so that a central axis dose implied by the kernel is substantially equivalent to a central axis dose in water of a pencil beam field size substantially equal to a desired field size multiplied by a ratio of electron density of the homogeneous medium to electron density of water by employing a representation of a dose normalization factor expressed as a linear combination of exponential functions that model lateral electron transport whose longitudinal buildup coefficients scale linearly with electron density.

32. A method of determining dose in heterogeneous media of varying electron density from a therapeutic high-energy radiation-beam for radiation treatment, the method comprising the steps of:

receiving a central axis scatter dose model representing central axis scatter dose as a function of field size and depth for water equivalent medium;

determining a central axis scatter dose model representing central axis scatter dose as a function of field size and depth for a homogeneous medium of arbitrary electron density using an equivalent effective field size responsive to the received scatter dose model; and

determining at least one scatter volume for a homogeneous medium of arbitrary electron density by performing a modified Clarkson integration utilizing the determined central axis scatter dose model of the homogeneous medium of arbitrary electron density in the integration to derive the scatter volume.

33. A method as defined in claim 32,

wherein the equivalent field size is equal to the field size in the homogeneous medium of arbitrary electron density multiplied by a ratio of an electron density of the homogeneous medium to an electron density of water;

and

wherein the step of determining central axis scatter dose model for the water equivalent medium includes the step of applying a linear fit of a measured total central axis dose as a function of a distance variable, to separate the central axis scatter dose from a central axis primary dose.

34. A computer readable medium that is readable by a computer, the computer readable medium comprising a set of instructions that, when executed by the computer, cause the computer to perform the following operations:

predetermining a delivery machine-dependent representation of radiation dose for a plurality of different electron densities selected over a preselected representative range;

predetermining for each of a plurality of pencil beams, a depth-dependent representation of central axis properties of a pencil beam passing through a complex medium having a complex spatial distribution of heterogeneous electron densities; and

determining with constant time computational complexity, radiation dose for each of a plurality of points of interest in the complex medium by applying the predetermined machine-dependent and depth-dependent representations.

35. A computer readable medium as defined in claim 34, wherein the operation of predetermining a delivery machine-dependent representation of radiation dose includes the operations of determining an at least two-dimensional primary dose profile for each of the plurality of different electron densities and an at least two-dimensional scatter dose profile for at least a representative portion of the plurality of different electron densities.

36. A computer readable medium as defined in claim 34, wherein the operation of predetermining for each of a plurality of pencil beams a depth dependent representation of central axis properties of a pencil beam passing through a complex medium includes the operations of:

determining a depth-dependent weighted value to form a weight for a primary dose profile for a point at a current electron density at a current depth and a weight for at least one dose profile for a corresponding at least one point at a previous electron density at a previous depth so that when the weighted values are applied to a linear combination of the dose profiles a resulting dose profile provides a value substantially equal to a convoluted value of central axis primary dose at the current depth when a point of interest applied to the linear combination at the current depth is on the central axis; and

determining an effective electron density to apply to a scatter dose profile that when applied provides a value substantially equal to a convoluted value of central axis scatter dose at the current depth when a point of interest applied to the scatter dose profile at the current electron density at the current depth is on the central axis.

37. A computer readable medium as defined in claim 34, wherein the operation of determining with constant time computational complexity, radiation dose for each of a plurality of points of interest in a complex medium includes the operations of:

determining for each of a plurality of points of interest at least one of the following;

a value of electron density associated with the point of interest and an electron density distribution associated with the point of interest defining a local electron density value; and

accessing predetermined off-axis properties corresponding to a homogeneous electron density having a value derived from the respective local electron density value associated with each point of interest responsive to the respective local electron density value for each respective one of the plurality of points of interest and a pencil beam intensity for each associated pencil beam directed through each respective one of the plurality of points of interest to thereby determine radiation dose for each of the plurality of points of interest.

38. A computer readable medium as defined in claim 34,

wherein the operation of predetermining a delivery machine-dependent representation of radiation dose includes the operation of determining a radiation dose profile for a plurality of media each having a different electron density, the electron densities selected over a representative range;

and

wherein the operation of predetermining for each of a plurality of pencil beams, a depth dependent representation of central axis properties of a pencil beam passing through a complex medium for each of a plurality of pencil beams includes the operations of;

determining for each of the plurality of pencil beams a depth dependent weight factor for each of a plurality of depths along a central axis of the respective pencil beam, each of the plurality of depths for each of the plurality of pencil beams having a determined electron density, each depth dependent weight factor to be applied to at least one function within an least two-dimensional electron density dependent primary dose profile associated with the depth of the respective point and having a value determined so that when a point of interest is selected along the central axis of the respective pencil beam at the respective depth, the associated at least two-dimensional electron density dependent primary dose profile provides a value substantially equal to a convoluted value of central axis primary dose of the current depth when a point of interest applied to the linear combination at the current depth is on the central axis, and

determining an effective electron density to apply to a scatter dose profile that when applied provides a value substantially equal to a convoluted value of central axis scatter dose when a point of interest applied to the scatter dose profile at the current electron density at the current depth is on the central axis.

39. A computer readable medium as defined in claim 34,

wherein the operation of predetermining a delivery machine-dependent representation of radiation dose includes the operations of:

receiving data parameters for a medium having properties substantially similar to that of water,

forming a primary dose profile table for each of the plurality of electron densities responsive to the data parameters, and

forming a scatter dose profile table for at least a representative portion of the plurality of electron densities;

wherein the operation of predetermining for each of a plurality of pencil beams, a depth dependent representation of central axis properties of a pencil beam passing through a complex medium includes the operations of;

receiving electron density parameters for a patient volume developed from a patient-specific image generating device,

determining current and previous electron density values for each of a plurality of depths along each separate one of a plurality of pencil beams,

determining a separate depth dependent weight w(d) for each of the plurality of depths, and

determining a depth-dependent effective electron density ρ

′

(d) for each of the plurality of depths, to thereby form at least one table of off-axis dose parameters including representations of a plurality of regions of dose build-up and dose build-down; and

wherein the operation of determining with constant time computational complexity, radiation dose for each of a plurality of points of interest in the complex medium includes the operations of;

determining for each of a plurality of points of interest at least one of the following;

a value of electron density associated with the point of interest and an electron density distribution associated with the point of interest, defining a local electron density value, and

retrieving the stored off-axis dose parameters responsive to the local electron density value for each of the plurality of points of interest.

40. A computer readable medium as defined in claim 34, wherein the operation of predetermining for each of a plurality of pencil beams, a depth dependent representation of central axis properties of a beam passing through a complex medium includes the operation of modeling a three-dimensional primary dose profile by:

linearly combining two dose profiles, the first dose profile at a current electron density and the second dose profile at a previous electron density to form a model of a three-dimensional primary dose profile; and

setting weighted values of each dose profile so that the model provides a convoluting value of the central axis primary dose when a point applied to the model at the current depth is on the central axis.

41. A computer readable medium as defined in claim 34, wherein the operation of predetermining for each of a plurality of pencil beams, a depth dependent representation of central axis properties of a beam passing through a complex medium includes for each of the plurality of pencil beams the operation of modeling a dose profile by determining a differential change to central axis dose traveling into the complex medium along the central axis of the respective pencil beam in proportion to a product of a difference between a current central axis dose and a dose to a homogeneous medium having an electron density at a point of interest and a electron density dependent proportionality constant that depends on the electron density at the point of interest to thereby form representations of a plurality of regions of dose build-up and dose build-down.

42. A computer readable medium as defined in claim 41,

wherein the operation of determining a differential change to central axis dose is applied to at least one of the following:

primary dose and scatter dose; and

wherein the electron density-dependent proportionality constant depends on a ratio of electron density of the medium and an associated proportionality constant applied to a medium having properties substantially similar to that of water.

43. A computer readable medium as defined in claim 34, wherein the operation of predetermining for each of a plurality of pencil beams, a depth dependent representation of central axis properties of a beam passing through a complex medium for each of a plurality of pencil beams includes for each of the plurality of pencil beams the operations of:

receiving a central axis primary dose;

receiving homogeneous medium off-axis primary dose profiles for a plurality of electron densities; and

determining an off-axis primary dose profile for a region of a complex medium having an electron density varying with depth along a central axis of a pencil beam by forming a linear combination of the homogeneous medium off-axis primary dose profiles weighted by values applied so that the center of the determined off-axis primary dose profile has primary dose substantially equal to the received central axis primary dose.

44. A computer readable medium as defined in claim 43, wherein the operation of determining an off-axis primary dose profile includes the operation of linearly combining a two-dimensional primary dose profile for a point of interest having a electron density value related to a current depth with a two-dimensional primary dose profile for the point of interest having a electron density value related to that of the previous depth to form an off-axis dose profile for the complex medium.

45. A computer readable medium as defined in claim 34, wherein the operation of predetermining for each of a plurality of pencil beams, a depth dependent representation of central axis properties of a beam passing through a complex medium for each of a plurality of pencil beams includes for each of the plurality of pencil beams the operations of:

receiving a central axis scatter dose;

receiving homogeneous medium off-axis scatter dose profiles for a plurality of electron densities; and

determining an off-axis scatter dose profile for a region of a complex medium having an electron density varying with depth along a central axis of a pencil beam from off axis properties of a homogeneous medium having an effective electron density selected so that central axis scatter dose of the determined homogeneous medium off-axis profile substantially matches the received central axis scatter dose of the complex medium.

46. A computer readable medium as defined in claim 45, wherein the operation of determining an off-axis scatter dose profile includes the operation of determining an effective electron density to apply to the off-axis scatter dose profile that when applied provides a value substantially equal to a convoluted value of the central axis scatter dose for a complex medium when a point of interest applied to the off-axis scatter dose profile at the current electron density at the current depth is on the central axis.

47. A computer readable medium that is readable by a computer, the computer readable medium comprising a set of instructions that, when executed by the computer, cause the computer to perform the operation of:

determining an off-axis dose profile for a pencil beam to a point of interest of a complex medium having an electron density distribution varying laterally at a depth of interest associated with the point of interest by using an off-axis dose profile for a homogeneous medium of the pencil beam at the depth of interest corresponding to the electron density distribution substantially equal to that of a local electron density distribution near the point of interest.

48. A computer readable medium as defined in claim 47, wherein the modeled electron density distribution is a single electron density value.

49. A computer readable medium as defined in claim 47, wherein the instructions further include those to perform the operation of determining central axis primary dose for a pencil beam having a field size in a homogeneous medium from a central axis primary dose model for water equivalent medium of an equivalent effective field size.

50. A computer readable medium as defined in claim 49, wherein the operation of determining central axis primary dose includes the operation of modifying a two-dimensional radiological kernel representing electron transport so that a central axis dose implied by the kernel is substantially equivalent to a central axis dose in water of a pencil beam field size substantially equal to a desired field size multiplied by a ratio of electron density of the homogeneous medium to electron density of water.

51. A computer readable medium as defined in claim 47, wherein the instructions further include those to perform the operation of determining central axis scatter dose for a pencil beam having a field size in a homogeneous medium from a central axis scatter dose model for water equivalent medium of an equivalent effective field size.

52. A computer readable medium as defined in claim 51, wherein the operation of determining central axis scatter dose includes the operation of performing a modified Clarkson integration whereby central axis dose in the homogeneous medium is derived from the central axis dose of water for a field size equal to the field size of the pencil beam multiplied by a ratio of an electron density of the homogeneous medium to an electron density of water.