Applications of scaling laws of tree structures

1. A method for diagnosing vascular disease, the method comprising the steps of:

obtaining a vessel image showing a vasculature of a vessel having a vascular disease, the vasculature of the vessel including at least part of a biological tree having a stem and a crown;

identifying at least two measurements from the vessel image, the measurements relating to at least two parameters selected from the group consisting of a vessel volume, a vessel length, a vessel diameter, a flow rate of a stem, and crown resistance;

calculating at least two cumulative measurements corresponding to the selected at least two parameters, the at least two cumulative measurements selected from the group consisting of a volume of the crown corresponding to the vessel volume parameter, a cumulative vessel length of the crown corresponding to the vessel length parameter, a diameter of a most proximal stem corresponding to the vessel diameter parameter, a flow rate of a most proximal stem corresponding to the flow rate of the stem parameter, and a resistance of the biological tree corresponding to the crown resistance parameter;

calculating a relationship between the at least two parameters from the at least two measurements and the at least two cumulative measurements to generate one or more vasculature data points using a processor operably connected to a storage medium having the at least two measurements stored thereon; and

comparing the one or more vasculature data points to data relative to a model vasculature to determine the extent of vascular disease.

2. The method of claim 1 , wherein the vessel image is an image selected from the group consisting of an angiograph, a computed tomography scan, and a magnetic resonance image.

3. The method of claim 1 , wherein the at least two parameters comprise the vessel volume and the vessel length, and wherein the at least two cumulative measurements comprise the volume of the crown and the cumulative vessel length of the crown.

4. The method of claim 3 , wherein the step of calculating a relationship between the at least two parameters is performed using a volume-length relation.

5. The method of claim 3 , wherein the step of calculating a relationship between the at least two parameters is performed using a resistance-length and volume relation.

6. The method of claim 1 , wherein the at least two parameters comprise the vessel diameter and the vessel length, and wherein the at least two cumulative measurements comprise the diameter of the most proximal stem and the cumulative vessel length of the crown.

7. The method of claim 6 , wherein the step of calculating a relationship between the at least two parameters is performed using a diameter-length relation.

8. The method of claim 1 , wherein the at least two parameters comprise the flow rate and the vessel diameter, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the diameter of the most proximal stem.

9. The method of claim 8 , wherein the step of calculating a relationship between the at least two parameters is performed using a flow rate-diameter relation.

10. The method of claim 1 , wherein the at least two parameters comprise the crown resistance, the vessel length, and the vessel volume, and wherein the at least two cumulative measurements comprise the resistance of the biological tree, the cumulative vessel length of the crown, and the volume of the crown.

11. The method of claim 10 , wherein the step of calculating a relationship between the at least two parameters is performed using a resistance-length and volume relation.

12. The method of claim 1 , wherein the at least two parameters comprise the flow rate of the stem and the vessel length, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the cumulative vessel length of the crown.

13. The method of claim 12 , wherein the step of calculating a relationship between the at least two parameters is performed using a flow rate-length relation.

14. The method of claim 1 , wherein the step of comparing the one or more vasculature data points to data relative to a model vasculature is performed by graphically comparing said data points to data relative to a model vasculature to determine the extent of vascular disease by identifying graphical differences between said data points to data relative to a model vasculature.

15. The method of claim 1 , wherein the step of comparing the one or more vasculature data points to data relative to a model vasculature is performed by comparing said data points to data relative to a model vasculature in table form to determine the extent of vascular disease by identifying numerically calculated differences between said data points to data relative to a model vasculature.

16. A method for diagnosing vascular disease in a patient's vascular tree, the method comprising the steps of:

generating a model vascular tree from a minimum energy hypothesis calculation using one or more scaling laws having at least two parameters selected from the group consisting of a vessel volume, a vessel length, a vessel diameter, a flow rate of a stem, and crown resistance, the model vascular tree generated using a processor operably connected to a storage medium having data relating to the one or more scaling laws stored thereon;

calculating a relationship between the at least two parameters from at least two model measurements to generate one or more model vasculature data points within the model vascular tree; and

determining the extent of vascular disease, wherein the patient's vascular tree is obtained using the one or more scaling laws using at least two patient measurements relating to the at least two parameters as applied to a vessel image showing a vasculature of the patient's vessel having a vascular disease, the vasculature of the patient's vessel including at least part of the patient's vascular tree having a stem and a crown, the determining step comprising:

calculating at least two cumulative measurements corresponding to the selected at least two parameters, the at least two cumulative measurements selected from the group consisting of a volume of the crown corresponding to the vessel volume parameter, a cumulative vessel length of the crown corresponding to the vessel length parameter, a diameter of a most proximal stem corresponding to the vessel diameter parameter, a flow rate of a most proximal stem corresponding to the flow rate of the stem parameter, and a resistance of the biological tree corresponding to the crown resistance parameter;

calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements to generate one or more patient vasculature data points; and

comparing the one or more patient vasculature data points to the one or more model vasculature data points to determine the extent of vascular disease.

17. The method of claim 16 , wherein the at least two parameters comprise the vessel volume and the vessel length, and wherein the at least two cumulative measurements comprise the volume of the crown and the cumulative vessel length of the crown.

18. The method of claim 17 , wherein the step of calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a volume-length relation.

19. The method of claim 17 , wherein the step of calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a resistance-length and volume relation.

20. The method of claim 16 , wherein the at least two parameters comprise the vessel diameter and the vessel length, and wherein the at least two cumulative measurements comprise the diameter of the most proximal stem and the cumulative vessel length of the crown.

21. The method of claim 20 , wherein the step of calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a diameter-length relation.

22. The method of claim 16 , wherein the at least two parameters comprise the flow rate and the vessel diameter, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the diameter of the most proximal stem.

23. The method of claim 22 , wherein the step of calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a flow rate-diameter relation.

24. The method of claim 16 , wherein the at least two parameters comprise the crown resistance, the vessel length, and the vessel volume, and wherein the at least two cumulative measurements comprise the resistance of the biological tree, the cumulative vessel length of the crown, and the volume of the crown.

25. The method of claim 24 , wherein the step of calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a resistance-length and volume relation.

26. The method of claim 16 , wherein the at least two parameters comprise the flow rate of the stem and the vessel length, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the cumulative vessel length of the crown.

27. The method of claim 26 , wherein the step of calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a flow rate-length relation.

28. The method of claim 16 , wherein the determining step is performed by graphically comparing the patient's vascular tree with the model vascular tree to determine the extent of vascular disease by identifying graphical differences between the patient's vascular tree with the model vascular tree.

29. The method of claim 16 , wherein the determining step is performed by comparing the patient's vascular tree with the model vascular tree in table form to determine the extent of vascular disease by identifying numerically calculated differences between the patient's vascular tree with the model vascular tree.

30. A system for diagnosing vascular disease, the system comprising:

a computer processor;

a storage medium operably connected to the processor, the storage medium capable of receiving and storing data relative of measurements from a vasculature of a vessel;

wherein the processor is operable to:

obtain a vessel image showing a vasculature of a vessel having a vascular disease, the vasculature of the vessel including at least part of a biological tree having a stem and a crown;

identify at least two measurements from the vessel image, the measurements relating to at least two parameters selected from the group consisting of a vessel volume, a vessel length, a vessel diameter, a flow rate of a stem, and crown resistance;

calculate at least two cumulative measurements corresponding to the selected at least two parameters, the at least two cumulative measurements selected from the group consisting of a volume of the crown corresponding to the vessel volume parameter, a cumulative vessel length of the crown corresponding to the vessel length parameter, a diameter of a most proximal stem corresponding to the vessel diameter parameter, a flow rate of a most proximal stem corresponding to the flow rate of the stem parameter, and a resistance of the biological tree corresponding to the crown resistance parameter;

calculate a relationship between the at least two parameters from the at least two measurements and the at least two cumulative measurements to generate one or more vasculature data points; and

compare the one or more vasculature data points to data relative to a model vasculature to determine the extent of vascular disease, wherein the extent of vascular disease is identified based upon a difference in the one or more vasculature data points in connection with one of the at least two parameters while another of the at least two parameters remains constant.

31. The system of claim 30 , wherein the vessel image is an image selected from the group consisting of an angiograph, a computed tomography scan, and a magnetic resonance image.

32. The system of claim 30 , wherein the at least two parameters comprise the vessel volume and the vessel length, and wherein the at least two cumulative measurements comprise the volume of the crown and the cumulative vessel length of the crown.

33. The system of claim 32 , wherein the calculation of a relationship between the at least two parameters is performed using a volume-length relation.

34. The system of claim 32 , wherein the step of calculating a relationship between the at least two parameters is performed using a resistance-length and volume relation.

35. The system of claim 30 , wherein the at least two parameters comprise the vessel diameter and the vessel length, and wherein the at least two cumulative measurements comprise the diameter of the most proximal stem and the cumulative vessel length of the crown.

36. The system of claim 35 , wherein the calculation of a relationship between the at least two parameters is performed using a diameter-length relation.

37. The system of claim 30 , wherein the at least two parameters comprise the flow rate and the vessel diameter, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the diameter of the most proximal stem.

38. The system of claim 37 , wherein the calculation of a relationship between the at least two parameters is performed using a flow rate-diameter relation.

39. The system of claim 30 , wherein the at least two parameters comprise the crown resistance, the vessel length, and the vessel volume, and wherein the at least two cumulative measurements comprise the resistance of the biological tree, the cumulative vessel length of the crown, and the volume of the crown.

40. The system of claim 39 , wherein the calculation of a relationship between the at least two parameters is performed using a resistance-length and volume relation.

41. The system of claim 30 , wherein the at least two parameters comprise the flow rate of the stem and the vessel length, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the cumulative vessel length of the crown.

42. The system of claim 41 , wherein the calculation of a relationship between the at least two parameters is performed using a flow rate-length relation.

43. The system of claim 30 , wherein the comparison of the one or more vasculature data points to data relative to a model vasculature is performed by graphically comparing said data points to data relative to a model vasculature to determine the extent of vascular disease by identifying graphical differences between said data points to data relative to a model vasculature.

44. The system of claim 30 , wherein the comparison of the one or more vasculature data points to data relative to a model vasculature is performed by comparing said data points to data relative to a model vasculature in table form to determine the extent of vascular disease by identifying numerically calculated differences between said data points to data relative to a model vasculature.

45. The system of claim 30 , further comprising a program stored upon the storage medium, said program operable by the processor upon data relative of measurements from a vasculature of a vessel.

46. The system of claim 30 , wherein the system comprises a user system and a server system, and wherein the user system and the server system are operably connected to one another.

47. A system for diagnosing vascular disease in a patient's vascular tree, the system comprising:

a computer processor; and

a storage medium operably connected to the processor, the storage medium capable of receiving and storing data relative of measurements from a vasculature of a vessel;

wherein the processor is operable to:

generate a model vascular tree from a minimum energy hypothesis calculation using one or more scaling laws having at least two parameters selected from the group consisting of a vessel volume, a vessel length, a vessel diameter, a flow rate of a stem, and crown resistance;

calculate a relationship between the at least two parameters from at least two model measurements to generate one or more model vasculature data points within the model vascular tree; and

determine the extent of vascular disease, wherein the patient's vascular tree is obtained using the one or more scaling laws using at least two patient measurements relating to the at least two parameters as applied to a vessel image showing a vasculature of the patient's vessel having a vascular disease, the vasculature of the patient's vessel including at least part of the patient's vascular tree having a stem and a crown, wherein the extent of vascular disease is identified based upon a difference in one or more vasculature data points in connection with one of the at least two parameters while another of the at least two parameters remains constant, and wherein the extent of the vascular disease is determined by:

calculating at least two cumulative measurements corresponding to the selected at least two parameters, the at least two cumulative measurements selected from the group consisting of a volume of the crown corresponding to the vessel volume parameter, a cumulative vessel length of the crown corresponding to the vessel length parameter, a diameter of a most proximal stem corresponding to the vessel diameter parameter, a flow rate of a most proximal stem corresponding to the flow rate of the stem parameter, and a resistance of the biological tree corresponding to the crown resistance parameter;

calculating a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements to generate one or more patient vasculature data points; and

comparing the one or more patient vasculature data points to the one or more model vasculature data points to determine the extent of vascular disease.

48. The system of claim 47 , wherein the at least two parameters comprise the vessel volume and the vessel length, and wherein the at least two cumulative measurements comprise the volume of the crown and the cumulative vessel length of the crown.

49. The system of claim 48 , wherein the calculation of a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a volume-length relation.

50. The system of claim 48 , wherein the calculation of a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a resistance-length and volume relation.

51. The system of claim 47 , wherein the at least two parameters comprise the vessel diameter and the vessel length, and wherein the at least two cumulative measurements comprise the diameter of the most proximal stem and the cumulative vessel length of the crown.

52. The system of claim 51 , wherein the calculation of a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a diameter-length relation.

53. The system of claim 47 , wherein the at least two parameters comprise the flow rate and the vessel diameter, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the diameter of the most proximal stem.

54. The system of claim 53 , wherein the calculation of a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a flow rate-diameter relation.

55. The system of claim 47 , wherein the at least two parameters comprise the crown resistance, the vessel length, and the vessel volume, and wherein the at least two cumulative measurements comprise the resistance of the biological tree, the cumulative vessel length of the crown, and the volume of the crown.

56. The system of claim 55 , wherein the calculation of a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a resistance-length and volume relation.

57. The system of claim 47 , wherein the at least two parameters comprise the flow rate of the stem and the vessel length, and wherein the at least two cumulative measurements comprise the flow rate of the most proximal stem and the cumulative vessel length of the crown.

58. The system of claim 57 , wherein the calculation of a relationship between the at least two parameters from the at least two patient measurements and the at least two cumulative measurements is performed using a flow rate-length relation.

59. The system of claim 47 , wherein the determination of the extent of vascular disease is performed by graphically comparing the patient's vascular tree with the model vascular tree to determine the extent of vascular disease by identifying graphical differences between the patient's vascular tree with the model vascular tree.

60. The system of claim 47 , wherein the determination of the extent of vascular disease is performed by comparing the patient's vascular tree with the model vascular tree in table form to determine the extent of vascular disease by identifying numerically calculated differences between the patient's vascular tree with the model vascular tree.

61. The system of claim 47 , further comprising a program stored upon the storage medium, said program operable by the processor upon data relative of measurements from a vasculature of a vessel.

62. The system of claim 47 , wherein the system comprises a user system and a server system, and wherein the user system and the server system are operably connected to one another.