Skip to main content

Advertisement

SpringerLink
Log in

Euclidean and fractal geometry of microvascular networks in normal and neoplastic pituitary tissue

  • Review
  • Published:
Neurosurgical Review Aims and scope Submit manuscript

Abstract

In geometrical terms, tumour vascularity is an exemplary anatomical system that irregularly fills a three-dimensional Euclidean space. This physical characteristic and the highly variable shapes of the vessels lead to considerable spatial and temporal heterogeneity in the delivery of oxygen, nutrients and drugs, and the removal of metabolites. Although these biological characteristics are well known, quantitative analyses of newly formed vessels in two-dimensional histological sections still fail to view their architecture as a non-Euclidean geometrical entity, thus leading to errors in visual interpretation and discordant results from different laboratories concerning the same tumour. We here review the literature concerning microvessel density estimates (a Euclidean-based approach quantifying vascularity in normal and neoplastic pituitary tissues) and compare the results. We also discuss the limitations of Euclidean quantitative analyses of vascularity and the helpfulness of a fractal geometry-based approach as a better means of quantifying normal and neoplastic pituitary microvasculature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Albeda SM, Muller WA, Buck CA, Newman PJ (1991) Molecular and cellular properties of PECAM (endoCAM/CD31): a novel vascular cell–cell adhesion molecule. J Cell Biol 14:1059–1068

    Article  Google Scholar 

  2. Anderson JC, Babb AL, Hlastala MP (2005) A fractal analysis of the radial distribution of bronchial capillaries around large airways. J Appl Physiol 98:850–855

    Article  PubMed  Google Scholar 

  3. Baish JW, Jain RK (1998) Cancer, angiogenesis and fractals. Nat Med 4:984

    Article  PubMed  CAS  Google Scholar 

  4. Baish JW, Jain RK (2000) Fractals and cancer. Cancer Res 60:3683–3688

    PubMed  CAS  Google Scholar 

  5. Baish JW, Gazit Y, Berk DA, Nozue M, Baxter LT, Jain RK (1996) Role of tumor vascular architecture in nutrient and drug delivery: an invasion percolation-based network model. Microvasc Res 51:327–346

    Article  PubMed  CAS  Google Scholar 

  6. Barbareschi M, Weidner N, Gasparini G, Morelli L, Forti S, Eccher C, Fina P, Caffo O, Leonardi E, Mauri F, Bevilacqua P, Palma PD (1995) Microvessel density quantification in breast carcinomas. Appl Immunohistochem 3:75–84

    Google Scholar 

  7. Bassingthwaighte JB, Liebovitch LS, West BJ (1994) Fractal physiology. Oxford University Press, New York

    Google Scholar 

  8. Beard DA, Bassingthwaighte JB (2000) The fractal nature of myocardial blood flow emerges from a whole-organ model of arterial network. J Vasc Res 37:282–296

    Article  PubMed  CAS  Google Scholar 

  9. Bochner BH, Cote RJ, Weidner N, Groshen S, Chen SC, Skinner DG, Nichols PW (1995) Angiogenesis in bladder cancer: relationship between microvessel density and tumor prognosis. J Natl Cancer Inst 87:1603–1612

    Article  PubMed  CAS  Google Scholar 

  10. Bruner E, Mantini S, Perna A, Maffei C, Manzi G (2005) Fractal dimension of the middle meningeal vessels: variation and evolution in Homo erectus, Neanderthals, and modern humans. Eur J Morphol 42:217–224

    Article  PubMed  Google Scholar 

  11. Carmeliet P (2003) Angiogenesis in health and disease. Nat Med 9:653–660

    Article  PubMed  CAS  Google Scholar 

  12. Cross SS (1997) Fractals in pathology. J Pathol 182:1–8

    Article  PubMed  CAS  Google Scholar 

  13. Cross SS, Start RD, Silcocks PB, Bull AD, Cotton DW, Underwood JC (1993) Quantitation of the renal arterial tree by fractal analysis. J Pathol 170:479–484

    Article  PubMed  CAS  Google Scholar 

  14. De Felice C, Latini G, Bianciardi G, Parrini S, Fadda GM, Marini M, Laurini RN, Kopotic RJ (2003) Abnormal vascular network complexity: a new phenotypic marker in hereditary non-polyposis colorectal cancer syndrome. Gut 52:1764–1767

    Article  PubMed  Google Scholar 

  15. Dey P (2005) Basic principles and applications of fractal geometry in pathology: a review. Anal Quant Cytol Histol 27:284–290

    PubMed  Google Scholar 

  16. Di Ieva A (2007) Fractal Geometry of the pituitary microvascular network [in Italian]. Dissertation, University of Brescia, Brescia, Italy, October

  17. Di Ieva A, Grizzi F, Ceva-Grimaldi G, Russo C, Gaetani P, Aimar E, Levi D, Pisano P, Tancioni F, Nicola G, Tschabitscher M, Dioguardi N, Rodriguez y Baena R (2007) Fractal dimension as a quantitator of the microvasculature of normal and adenomatous pituitary tissue. J Anat 211:673–680

    Article  PubMed  Google Scholar 

  18. Erroi A, Bassetti M, Spada A, Giannattasio G (1986) Microvasculature of human micro- and macroprolactinomas. A morphological study. Neuroendocrinology 43:159–165

    Article  PubMed  CAS  Google Scholar 

  19. Folkman J (1972) Anti-angiogenesis: new concept for therapy of solid tumours. Ann Surg 175:409–416

    Article  PubMed  CAS  Google Scholar 

  20. Folkman J (1990) What is the evidence that tumours are angiogenesis dependent. J Natl Cancet Inst 82:4–6

    Article  CAS  Google Scholar 

  21. Fox SB, Leek RD, Weekes MP, Whitehouse RM, Gatter KC, Harris AL (1995) Quantification and prognostic value of breast cancer angiogenesis: comparison of microvessel density, Chalkley count, and computer image analysis. J Pathol 177:275–283

    Article  PubMed  CAS  Google Scholar 

  22. Frank RE, Saclarides TJ, Leurgans S, Speziale NJ, Drab EA, Rubin DB (1995) Tumor angiogenesis as a predictor of recurrence and survival in patients with node-negative colon cancer. Ann Surg 222:695–699

    Article  PubMed  CAS  Google Scholar 

  23. Gasparini G, Weidner N, Bevilacqua P, Maluta S, Dalla Palma PD, Caffo O, Barbareschi M, Boracchi P, Marubini E, Pozza F (1994) Tumor microvessel density, p53 expression, tumor size and peritumoral lymphatic vessel invasion are relevant prognostic markers in node-negative breast carcinoma. J Clin Oncol 12:454–466

    PubMed  CAS  Google Scholar 

  24. Goldberger AL, West BJ (1987) Fractals in physiology and medicine. Yale J Biol Med 60:421–435

    PubMed  CAS  Google Scholar 

  25. Grizzi F (2007) The architectural vascular complexity: is it a helpful histopathological biomarker? In: Swenson LI (ed) Progress in tumor marker research. Nova Science, Hauppauge

    Google Scholar 

  26. Grizzi F, Chiriva-Internati M (2005) The complexity of anatomical systems. Theor Biol Med Model 19:2–26

    Google Scholar 

  27. Grizzi F, Colombo P, Barbieri B, Franceschini B, Roncalli M, Chiriva-Internati M, Muzzio PC, Dioguardi N (2001) Correspondence re: E. Sabo et al., microscopic analysis and significance of vascular architectural complexity in renal cell carcinoma. Clin Cancer Res 7:533–537

    Google Scholar 

  28. Grizzi F, Russo C, Colombo P, Franceschini B, Frezza EE, Cobos E, Chiriva-Internati M (2005) Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension. BMC Cancer 8:5–14

    Google Scholar 

  29. Grizzi F, Colombo P, Taverna G, Chiriva-Internati M, Cobos E, Graziotti P, Muzzio PC, Dioguardi N (2007) The geometry of human vascular system: is it an obstacle for quantifying anti-angiogenic therapies. Appl Immunohistochem Mol Morphol 15:134–139

    Article  PubMed  Google Scholar 

  30. Guidolin D, Vacca A, Nussdorfer GG, Ribatti D (2004) A new image analysis method based on topological and fractal parameters to evaluate the angiostatic activity of docetaxel by using the Matrigel assay in vitro. Microvasc Res 67:117–124

    Article  PubMed  CAS  Google Scholar 

  31. Hastings HM, Sugihara G (1993) Fractals. A user’s guide for the natural sciences. Oxford Science, Oxford

    Google Scholar 

  32. Heymans O, Blacher S, Brouers F, Pierard GE (1999) Fractal quantification of the microvasculature heterogeneity in cutaneous melanoma. Dermatology 198:212–217

    Article  PubMed  CAS  Google Scholar 

  33. Hlatky L, Hahnfeldt P, Folkman J (2002) Clinical application of antiangiogenic therapy: microvessel density, what it does and doesn’t tell us. J Natl Cancer Inst 19:883–893

    Google Scholar 

  34. Itoh J, Serizawa A, Kawai K, Ishii Y, Teramoto A, Osamura RY (2003) Vascular networks and endothelial cells in the RAT experimental pituitary glands and in the human pituitary adenomas. Microsc Res Tech 60:231–235

    Article  PubMed  Google Scholar 

  35. Jugenburg M, Kovacs K, Stefaneanu L, Scheithauer BW (1995) Vasculature in nontumorous hypophyses, pituitary adenomas and carcinomas: a quantitative morphologic study. Endocr Pathol 67:115–124

    Article  Google Scholar 

  36. Kirchner LM, Schmidt SP, Gruber BS (1996) Quantitation of angiogenesis in the chick chorioallantoic membrane model using fractal analysis. Microvasc Res 51:2–14

    Article  PubMed  CAS  Google Scholar 

  37. Landini G, Misson GP, Murray PI (1993) Fractal analysis of the normal human retinal fluorescein angiogram. Curr Eye Res 12:23–27

    Article  PubMed  CAS  Google Scholar 

  38. Landini G, Murray PI, Misson GP (1995) Local connected fractal dimensions and lacunarity analyses of 60 degrees fluorescein angiograms. Invest Ophthalmol Vis Sci 36:2749–2755

    PubMed  CAS  Google Scholar 

  39. Latini G, Bianciardi G, Parrini S, Laurini RN, De Felice C (2006) Abnormal oral vascular network pattern geometry: a new clinical sign of down syndrome. J Pediatr 148:132–137

    Article  PubMed  Google Scholar 

  40. Losa GA, Nonnenmacher TF (1996) Self-similarity and fractal irregularity in pathologic tissues. Mod Pathol 9:174–182

    PubMed  CAS  Google Scholar 

  41. Losa GA, Merlini D, Nonnemacher TF, Weibel ER (1998) Fractals in biology and medicine, vol. II. Birhkäuser, Basel

    Google Scholar 

  42. Losa G, Merlini D, Nonnemacher TF, Weibel ER (2002) Fractals in biology and medicine, vol. III. Birhkäuser, Basel

    Google Scholar 

  43. Losa G, Merlini D, Nonnemacher TF, Weibel ER (2005) Fractals in biology and medicine, vol. IV. Birhkäuser, Basel

    Google Scholar 

  44. Maeda K, Chung YS, Takatsuka S, Ogawa Y, Sawada T, Yamashita Y, Onoda N, Kato Y, Nitta A, Arimoto Y (1995) Tumor angiogenesis as a predictor of recurrence in gastric carcinoma. J Clin Oncol 13:477–481

    PubMed  CAS  Google Scholar 

  45. Mandelbrot BB (1982) The fractal geometry of nature. Freeman, New York

    Google Scholar 

  46. Masters BR (2004) Fractal analysis of the vascular tree in the human retina. Annu Rev Biomed Eng 6:427–452

    Article  PubMed  CAS  Google Scholar 

  47. Mukai K, Rosai J, Burgdorf WHC (1980) Localisation of factor VIII-related antigen in vascular endothelial cell using an immuno-peroxidase method. Am J Surg Pathol 4:273–276

    Article  PubMed  CAS  Google Scholar 

  48. Niveiro M, Aranda I, Peiro G, Alenda C, Pico A (2005) Immunohistochemical analysis of tumor angiogenic factors in human pituitary adenoma. Hum Pathol 36:1090–1095

    Article  PubMed  CAS  Google Scholar 

  49. Nonnemacher TF, Losa GA, Merlini D, Weibel ER (1994) Fractals in biology and medicine, vol. I. Birhkäuser, Basel

    Google Scholar 

  50. Oczeretko E, Juczewska M, Kasacka I (2001) Fractal geometric analysis of lung cancer angiogenic patterns. Folia Histochem Cytobiol 39(Suppl 2):75–76

    PubMed  Google Scholar 

  51. Pan LX, Chen ZP, Liu SL, Zhao JH (2005) Magnetic resonance imaging and biological markers in pituitary adenomas with invasion of the cavernous sinus space. J Neurooncol 74:71–76

    Article  PubMed  Google Scholar 

  52. Parsons-Wingerter P, Lwai B, Yang MC, Elliott KE, Milaninia A, Redlitz A, Clark JI, Sage EH (1998) A novel assay of angiogenesis in the quail chorioallantoic membrane: stimulation by bFGF and inhibition by angiostatin according to fractal dimension and grid intersection. Microvasc Res 55:201–214

    Article  PubMed  CAS  Google Scholar 

  53. Pawlikowski M, Pisarek H, Jaranowska M (1997) Immunocytochemical investigations on the vascularization of pituitary adenomas. Endocr Pathol 8:189–193

    Article  PubMed  Google Scholar 

  54. Phillips JD (2005) Entropy analysis of multiple scale causality and qualitative causal shifts in spatial systems. Prof Geogr 57:83–93

    Google Scholar 

  55. Sabo E, Boltenko A, Sova Y, Stein A, Kleinhaus S, Resnick MB (2001) Microscopic analysis and significance of vascular architectural complexity in renal cell carcinoma. Clin Cancer Res 7:533–537

    PubMed  CAS  Google Scholar 

  56. Schecter J (1972) Ultrastructural changes in the capillary bed of human pituitary tumours. Am J Pathol 67:109–126

    Google Scholar 

  57. Stefaneanu L, Kovacs K, Scheithauer BW, Kontogeorgos G, Riehle DL, Sebo TJ, Murray D, Vidal S, Tran A, Buchfelder M, Fahlbusch R (2000) Effect of dopamine agonists on lactotroph adenomas of the human pituitary. Endocr Pathol 11:341–352

    Article  PubMed  CAS  Google Scholar 

  58. Steinmeier R, Fahlbusch R, Powers AD, Dotterl A, Buchfelder M (1991) Pituitary microcirculation: physiological aspects and clinical implications. A laser-Doppler flow study during transsphenoidal adenomectomy. Neurosurgery 29:47–54

    Article  PubMed  CAS  Google Scholar 

  59. Tiboldi T, Nemessanyi Z, Csernay I, Kovacs K (1967) Effect of estrogen on pituitary blood flow in rats. Endocrinol Exp 1:73–77

    Google Scholar 

  60. Tsafnat N, Tsafnat G, Lambert TD (2004) A three-dimensional fractal model of tumour vasculature. Conf Proc IEEE Eng Med Biol Soc 1:683–686

    PubMed  Google Scholar 

  61. Turner HE, Nagy Z, Gatter KC, Margaret ME, Harris AL, Wass JAH (2000) Angiogenesis in pituitary adenomas and the normal pituitary gland. J Clin Endocrinol Metab 85:1159–1162

    Article  PubMed  CAS  Google Scholar 

  62. Turner HE, Nagy Z, Gatter KC, Esiri MM, Wass JA, Harris AL (2000) Proliferation, bcl-2 expression and angiogenesis in pituitary adenomas: relationship to tumour behaviour. Br J Cancer 82:1441–1445

    PubMed  CAS  Google Scholar 

  63. Turner HE, Nagy Z, Gatter KC, Esiri MM, Harris AL, Wass JA (2000) Angiogenesis in pituitary adenomas—relationship to endocrine function, treatment and outcome. J Endocrinol 165:475–481

    Article  PubMed  CAS  Google Scholar 

  64. Vermeulen PB, Gasparini G, Fox SB, Colpaert C, Marson LP, Gion M, Belien JA, de Waal RM, Van Marck E, Magnani E, Weidner N, Harris AL, Dirix LY (2002) Second international consensus on the methodology and criteria of evaluation of angiogenesis quantification in solid human tumours. Eur J Cancer 38:1564–1579

    Article  PubMed  CAS  Google Scholar 

  65. Viacava P, Gasperi M, Acerbi G, Manetti L, Cecconi E, Bonadio AG, Naccarato AG, Acerbi F, Parenti G, Lupi I, Genovesi M, Martino E (2003) Microvascular density and vascular endothelial growth factor expression in normal pituitary tissue adenomas. J Endocrinol Invest 26:23–28

    PubMed  CAS  Google Scholar 

  66. Vico PG, Kyriacos S, Heymans O, Louryan S, Cartilier L (1998) Dynamic study of the extraembryonic vascular network of the chick embryo by fractal analysis. J Theor Biol 195:525–532

    Article  PubMed  CAS  Google Scholar 

  67. Vidal S, Scheithauer BW, Kovacs K (2000) Vascularity in nontumorous human pituitaries and incidental microadenomas: a morphometric study. Endocr Pathol 11:215–227

    Article  PubMed  Google Scholar 

  68. Vidal S, Kovacs K, Horvath E, Scheithauer BW, Kuroki T, Lloyd RV (2001) Microvessel density in pituitary adenomas and carcinomas. Virchows Arch 438:595–602

    Article  PubMed  CAS  Google Scholar 

  69. Vidal S, Horvath E, Kovacs K, Lloyd RV, Scheithauer BW (2003) Microvascular structural entropy: a novel approach to assess angiogenesis in pituitary tumors. Endocr Pathol 14:239–247

    Article  PubMed  Google Scholar 

  70. Weidner N (1996) Intratumoral vascularity as a prognostic factor in cancers of the urogenital tract. Eur J Cancer 32A:2506–2512

    Article  PubMed  CAS  Google Scholar 

  71. Weidner N, Semple JP, Welch WR, Folkman J (1991) Tumor angiogenesis and metastasis: correlation in invasive breast carcinoma. N Engl J Med 324:1–8

    Article  PubMed  CAS  Google Scholar 

  72. Weidner N, Folkman J, Pozza F, Bevilacqua P, Allred EN, Moore DH, Meli S, Gasparini G (1992) Tumour angiogenesis: a new significant and independent prognostic indicator in early stage breast carcinoma. J Natl Cancer Inst 84:1875–1887

    Article  PubMed  CAS  Google Scholar 

  73. West GB, Brown JH, Enquist BJ (1999) The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284:1677–1679

    Article  PubMed  CAS  Google Scholar 

  74. Witt M, Klessen CH (1987) Galactose and fucose binding sites in anterior pituitary cells of the rat: detection by means of biotinylated lectins. Folia Histochem Cytobiol 25:115–118

    PubMed  CAS  Google Scholar 

  75. Zamir M (2001) Fractal dimensions and multifractility in vascular branching. J Theor Biol. 212:183–190

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Neurosurgery, Istituto Clinico Humanitas IRCCS, Via Manzoni 56, 20089, Rozzano, Milan, Italy

    Antonio Di Ieva, Paolo Gaetani & Riccardo Rodriguez y Baena

  2. Laboratories of Quantitative Medicine, Istituto Clinico Humanitas IRCCS, Rozzano, Milan, Italy

    Fabio Grizzi

  3. Department of Endocrinological and Medical Sciences and Center of Excellence for Biomedical Research, San Martino Hospital, Genoa, Italy

    Umberto Goglia

  4. Center of Anatomy and Cell Biology, Medical University of Vienna, Vienna, Austria

    Manfred Tschabitscher

  5. Department of Neurosurgery, University of Brescia, Brescia, Italy

    Pietro Mortini

Authors
  1. Antonio Di Ieva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabio Grizzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Gaetani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Umberto Goglia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Manfred Tschabitscher
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Pietro Mortini
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Riccardo Rodriguez y Baena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Di Ieva.

Additional information

Comments

Michael Buchfelder, Erlangen, Germany

Whether pituitary adenomas are more or less vascularised than normal pituitary tissue is still a matter of considerable debate. It is surprising that 25 years after the recognition of different contrast media kinetics in enhanced computerised tomography images that allowed differentiation of normal and abnormal tissues and a huge body of medical literature devoted to this topic, still the findings could hardly be less contradictory and inconclusive. A better understanding of this problem, however, would have major clinical implications. It was suggested that vascular disturbances that arise from deformation and dislocation of the normal pituitary body are one of the major pathophysiological basics of pituitary insufficiency in tumours, cysts and malformations (e.g. “empty sella”) of the pituitary gland. Furthermore, neovascularisation is a currently promising therapeutic target in tumours otherwise difficult to treat. Moreover, the effects of drugs, particularly in prolactinomas and acromegaly, on tumour size and proliferation during medical therapy could be exerted on the basis of vascular changes. Thus, ongoing studies of vasculature in neoplastic and non-neoplastic tissues and their evolution following different treatments are crucial in pituitary tumours. In my eyes, there is still one major problem that needs to be improved. The wording used by different authors varies considerably. How can the vascular patterns be compared in different categories of adenomas if the categories are not clearly defined. Silent secretors, particularly in respect to gonadotropins and hormonal fragments, should not be classified as hormone-secreting tumours, despite the immunohistological presence of luteinizing hormone or FSH, or other products. The authors have to be congratulated for their discussion of obviously conflicting data. However, their own approach, namely the quantification of microvessel density and the utilisation of fractal geometry still need to be correlated to perfusion measurements, before clinical implications and applications can be considered.

Alessandro Ducati, Torino, Italy

This is an erudite paper that discusses in details the concept of fractal geometry applied to the study of pituitary adenoma pathology. It is well written and documented. The literature has been perused even with too many details. The main point of the work is that a two-dimensional description of the vessel net (that emerges from the lecture of traditional histological slices) is perhaps adequate to explain the structure of normal pituitary but not that of pituitary tumours.

Therefore, it is necessary to use more complex models and different instruments of analysis. The fractal geometry may provide such an instrument, hopefully. Actually, as the authors honestly recognise, many more and more complex studies are required before these new concepts are validated in clinical practice and may have a significant impact on the management of patients. At this point of the story, this is a promising starting point, at least because it can give a justification for the conflicting reports of the literature concerning the relationships between microvasculature of the tumour and clinical behaviour.

Luciano Mastronardi, Roma, Italy

This is an interesting article on Euclidean and fractal geometry of microvascular network in pituitary tissue, both in normal and in neoplastic situations. They maintain that classical Euclidean-based approach for quantifying vascularity in normal and neoplastic pituitary tissues cannot explain their irregular architecture, especially in normal pituitary gland and in secreting pituitary adenomas, in which irregular branches are shorter and smaller in diameter. On this basis, the authors try to evaluate the MVD with a fractal-geometry-based approach as a better means of quantifying normal and neoplastic pituitary microvasculature. The fractal model resulted to being more accurate in evaluating the MVD of normal pituitary tissue and of pituitary adenomas, with contribution in validating the efficacy of anti-angiogenic treatment and as a tool for stratifying patients in the available therapeutic trials.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Di Ieva, A., Grizzi, F., Gaetani, P. et al. Euclidean and fractal geometry of microvascular networks in normal and neoplastic pituitary tissue. Neurosurg Rev 31, 271–281 (2008). https://doi.org/10.1007/s10143-008-0127-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10143-008-0127-7

Keywords

Search

Navigation