Stereotactic Brain Microanatomy: Mathematical Principles and Applications

Ioannis N. Mavridis
C.N.S. Alliance Research Group, Athens, Greece

Series: Neuroanatomy Research at the Leading Edge
BISAC: MED057000

Clear

$160.00

eBook

Digitally watermarked, DRM-free.
Immediate eBook download after purchase.

Product price
Additional options total:
Order total:

Quantity:

Details

Imagine the use of mathematical formulas for brain targeting in neurosurgery. Research results of the 21st century have brought about the beginning of stereotactic anatomy evolution into stereotactic microanatomy, which is primarily based on applied mathematics. The purpose of this book is to present the mathematical principles and applications of stereotactic brain microanatomy in a concise and comprehensive manner. The robust mathematical principles of stereotactic microanatomy of the human brain are explained in detail, as well as its main clinically significant applications to modern stereotactic and functional neurosurgery. Stereotactic space of the human brain is defined in terms of its appropriate mathematical basis, where the principles of analytic geometry are strictly followed. Rigid adherence to these principles can further enable the safe application of mathematical formulas to the processing and use of stereotactic microanatomy data in clinical practice. Additionally, the concept of stereotactically standard brain areas is thoroughly explained, thus opening new horizons for the application of stereotactic microanatomy to highly accurate brain targeting, which is mainly useful for minimally invasive neurosurgical procedures, such as deep brain stimulation. Stereotactic microanatomy aims to guide stereotactic neurosurgical interventions in the best possible way, providing a solid mathematical basis for a safe and respective evolution of stereotactic neurosurgery into stereotactic microneurosurgery. (Imprint: Nova Biomedical)

List of Figures

Preface

Abbreviations

Introduction

Chapter 1. Origin of Stereotactic Space

Chapter 2. Axes of Stereotactic Space

Chapter 3. Planes in Stereotactic Space

Chapter 4. Points in Stereotactic Space

Chapter 5. Other Coordinate Systems

Chapter 6. The Concept of Stereotactically Standard Areas

Chapter 7. The Example of Mavridis' Area

Conclusions

References

Appendices

About the Author

Index

European Mathematical Society - Vicente Munoz, Universidad Complutense de Madrid, Spain

Surgical and Radiologic Anatomy - Efstratios-Stylianos Pyrgelis, 1st Department of Neurology, University of Athens School of Medicine, ‘Eginition’ Hospital, Athens, Greece

Introduction

[1] Mavridis IN. Mavridis’ area of the human brain: mathematically analysed anatomy assists stereotactic neurosurgery. OA Anat. 2014; 2(2): 11.
[2] Hamming RW (ed) Methods of Mathematics Applied to Calculus, Probability and Statistics. Dover Books on Mathematics. Mineola: Dover Publications, 2004, pp. 3, 6.
[3] Xie Z, Duan X, Ouyang Z, Zhang P. Quantitative Analysis of the Interdisciplinarity of Applied Mathematics. PLoS ONE 2015; 10(9): e0137424.
[4] Logan JD (ed) Applied Mathematics, 4th ed. New Jersey: John Wiley & Sons, 2013, pp. 2.
[5] Higham NJ. What is Applied Mathematics? In: Higham NJ (ed) The Princeton Companion to Applied Mathematics. New Jersey: Princeton University Press, 2015, pp. 1, 3, 8.
[6] Mavridis IN. Mavridis’ Area of the Human Brain: Mathematics Applied to Anatomy Offers Microsurgical Accuracy in Stereotactic Neurosurgery. In: Baswell AR (ed) Advances in Mathematics Research. Volume 22. Advances in Mathematics Research. New York: Nova-Nova Science Publishers, 2017 (at press).
[7] Hocken RJ and Pereira PH (eds) Coordinate Measuring Machines and Systems, 2nd ed. Manufacturing Engineering and Materials Processing. Boca Raton: CRC Press-Taylor & Francis Group 2012, pp. 1, 2.
[8] Eisenhart LP (ed) Coordinate Geometry. Dover Books on Mathematics. Mineola: Dover Publications, 2005, pp. ix, 8, 62, 279, 292.
[9] McCrea WH (ed) Analytical Geometry of Three Dimensions, 2nd ed. Dover Books on Mathematics. Mineola: Dover Publications, 2006, pp. 2, 4.
[10] Gelfand IM, Glagoleva EG, Kirillov AA (eds) The Method of Coordinates. Dover Books on Mathematics. Mineola: Dover Publications, 2011, pp. 3, 41, 42.
[11] Sickle JV (ed) Basic GIS Coordinates, 2nd ed. Boca Raton: CRC Press-Taylor & Francis Group, 2010, pp. 2.
[12] Higham NJ. The Language of Applied Mathematics. In: Higham NJ (ed) The Princeton Companion to Applied Mathematics. New Jersey: Princeton University Press, 2015, pp. 9.
[13] World Society for Stereotactic and Functional Neurosurgery, about, definitions of SFN, http://www.wssfn.org [accessed: May 22, 2017].
[14] Grunert P Sr, Keiner D, Oertel J. Remarks upon the term stereotaxy: a linguistic and historical note. Stereotact. Funct. Neurosurg. 2015; 93(1): 42-9.
[15] Talairach J and Tournoux P (eds) Co-planar Stereotaxic Atlas of the Human Brain, 3-Dimentional Proportional System: An Approach to Cerebral Imaging. New York: Georg Thieme Verlag-Thieme Medical Publishers, 1988, pp. vii, 1.
[16] Sharan AD and Andrews DW. Stereotactic Frames: Technical Considerations. In: Schulder M (ed) Handbook of Stereotactic and Functional Neurosurgery. Neurological Disease and Therapy. Boca Raton: CRC Press-Taylor & Francis Group, 2003, pp. 11, 12.
[17] European Society for Stereotactic and Functional Neurosurgery, about, history, http://www.essfn.org [accessed: May 22, 2017].
[18] Mavridis IN. Mavridis’ Area: A Modern Stereotactic Microanatomic Guide for Deep Brain Stimulation of the Nucleus Accumbens. In: Costa A and Villalba E (eds) Horizons in Neuroscience Research. Volume 27. Horizons in Neuroscience Research. New York: Nova Biomedical-Nova Science Publishers, 2016, pp. 39, 62.
[19] Mavridis IN. [Stereotactic neurosurgical anatomy of the nucleus accumbens]. PhD Thesis, National and Kapodistrian University of Athens (School of Medicine), Athens, Greece, 2012, doi: 10.12681/eadd/27603. Greek, pp. 17, 32, 62, 151-4.
[20] Mavridis IN. Deep Brain Stimulation for Treating Neuropsychiatric Disorders: Nucleus Accumbens Targeting and the Role of Mavridis’ Area. In: Costa A and Villalba E (eds) Horizons in Neuroscience Research. Volume 23. Horizons in Neuroscience Research. New York: Nova Biomedical-Nova Science Publishers, 2015, pp. 135, 139.
[21] Levy R. A Short History of Stereotactic Neurosurgery.
Cyber Museum of Neurosurgery, http://www.neurosurgery.org/ cybermuseum/stereotactichall/stereoarticle.html [accessed: May 22, 2017].
[22] Nowinski WL. Modified Talairach landmarks. Acta Neurochir (Wien) 2001; 143(10): 1045-57.
[23] Maciunas RJ, Galloway RL Jr, Latimer JW. The application accuracy of stereotactic frames. Neurosurgery 1994; 35(4): 682-94; discussion 694-5.
[24] The CRW Precision™ Arc system, Integra NeuroSciences, Integra LifeSciences Corporation, Plainsboro, New Jersey, USA,
2009, http://www.integralife.com/products/pdfs/crwprecisionarc_ brochure_480.pdf [accessed: May 22, 2017].
[25] Yang KJ, Long H, Yuan YW, Qi ST, Xu BT, Wang KW, Song Y. Stereotactic neurosurgical technique and electrophysiological study in ablating the ventromedial shell of the nucleus accumbens. Stereotact. Funct. Neurosurg. 2014; 92(1): 37-43.
[26] Zhang C, Wei NL, Wang Y, Wang X, Zhang JG, Zhang K. Deep brain stimulation of the nucleus accumbens shell induces anti-obesity effects in obese rats with alteration of dopamine neurotransmission. Neurosci. Lett. 2015; 589: 1-6.
[27] Mavridis IN. Mavridis’ area and the mathematical science of subnuclear accumbens targeting: precision matters. World Neurosurg. 2016; 90: 691-2.
[28] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.
[29] Mavridis IN. Anatomic guidance for stereotactic microneurosurgery: a modern necessity and the example of Mavridis’ area. Surg. Radiol. Anat. 2015; 37(1): 119-20.
[30] Mavridis IN. Mavridis’ area as a target for either selective or combined accumbens/ventral internal capsule deep brain stimulation. Acta Neurochir. (Wien) 2015; 157(2): 347-8.
[31] Mavridis IN. Mavridis’ area and electrode target localization in nucleus accumbens deep brain stimulation. World Neurosurg. 2015; 83(2): 259-60.
[32] Mavridis IN. Surgical anatomy of the human nucleus accumbens: Mavridis’ area and other clarifications in stereotactic space. Stereotact. Funct. Neurosurg. 2015; 93(4): 297-8.
[33] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.

Chapter 1

[1] McCrea WH (ed) Analytical Geometry of Three Dimensions, 2nd ed. Dover Books on Mathematics. Mineola: Dover Publications, 2006, pp. 1.
[2] Gelfand IM, Glagoleva EG, Kirillov AA (eds) The Method of Coordinates. Dover Books on Mathematics. Mineola: Dover Publications, 2011, pp. 2, 12.
[3] Cartesian Coordinates, Review B: Coordinate Systems. Department of Physics. Massachusetts Institute of Technology, pp. B-2-3, http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf [accessed: May 22, 2017].
[4] Gibilisco S (ed) Pre-Calculus Know-It-ALL, 1st ed. New York: The McGraw-Hill Companies, 2010, pp. 3, 111.
[5] Mavridis IN. [Stereotactic neurosurgical anatomy of the nucleus accumbens]. PhD Thesis, National and Kapodistrian University of Athens (School of Medicine), Athens, Greece, 2012, doi: 10.12681/eadd/27603. Greek, pp. 22, 76, 77.
[6] Mavridis IN. Mavridis’ Area of the Human Brain: Mathematics Applied to Anatomy Offers Microsurgical Accuracy in Stereotactic Neurosurgery. In: Baswell AR (ed) Advances in Mathematics Research. Volume 22. Advances in Mathematics Research. New York: Nova-Nova Science Publishers, 2017 (at press).
[7] Schaltenbrand G and Wahren W (eds) Guide to the Atlas for Stereotaxy of the Human Brain. Stuttgart: Georg Thieme Verlag, 1977, pp. 2, 6-8.
[8] Levy R. A Short History of Stereotactic Neurosurgery. Cyber Museum of Neurosurgery, http://www.neurosurgery.org/ cybermuseum/stereotactichall/stereoarticle.html [accessed: May 22, 2017].
[9] Talairach J and Tournoux P (eds) Co-planar Stereotaxic Atlas of the Human Brain, 3-Dimentional Proportional System: An Approach to Cerebral Imaging. New York: Georg Thieme Verlag-Thieme Medical Publishers, 1988, pp. vii, 2, 5.
[10] Parizel PM and De la Porte C. Stereotaxic target calculation. Theory and practice. Acta Neurochir. (Wien) 1993; 124(1): 34-6.
[11] Nowinski WL. Modified Talairach landmarks. Acta Neurochir. (Wien) 2001; 143(10): 1045-57.
[12] Mai JK, Majtanik M, Paxinos G (eds) Atlas of the Human Brain, 4th ed. London: Academic Press-Elsevier, 2016, pp. 87, 93.
[13] Blomstedt P, Olivecrona M, Sailer A, Hariz MI. Dittmar and the history of stereotaxy; or rats, rabbits, and references. Neurosurgery 2007; 60(1): 198-201; discussion 201-2.
[14] Stereotactic Frames: Technical Considerations. What-when-how.com, In Depth Tutorials and Information. The-Crankshaft Publishing, http://what-when-how.com/stereotactic-and-functional-neurosurgery/stereotactic-frames-technical-considerations [accessed: May 22, 2017].
[15] Barnett G. Stereotactic Frame-Application and Use. In: Introduction to Cranial Neurosurgery and Advanced Radiosurgery, Participant’s Manual, Cleveland Clinic Gamma Knife Center, October 17-21, 2016, Cleveland Clinic, Cleveland, Ohio, USA, pp. 34.
[16] Neyman G. Stereotactic Radiosurgery Physics. In: Introduction to Cranial Neurosurgery and Advanced Radiosurgery, Participant’s Manual, Cleveland Clinic Gamma Knife Center, October 17-21, 2016, Cleveland Clinic, Cleveland, Ohio, USA, pp. 78.
[17] Sharan AD and Andrews DW. Stereotactic Frames: Technical Considerations. In: Schulder M (ed) Handbook of Stereotactic and Functional Neurosurgery. Neurological Disease and Therapy. Boca Raton: CRC Press-Taylor & Francis Group, 2003, pp. 19.
[18] Leksell Stereotactic System® Overview. Elekta, Stockholm, Sweden, 2012, www.elekta.com/dam/jcr:d34290d4-3bfb-4ac6-b87a-6c3c664ce0cc/Leksell-Stereotactic-System-Overview.pdf [accessed: May 22, 2017].
[19] CRW Precision™ Arc stereotactic system. Integra NeuroSciences, Integra LifeSciences Corporation, Plainsboro, New Jersey, USA, 2009, http://www.integralife.com/products/pdfs/crwprecisionarc_ brochure_480.pdf [accessed: May 22, 2017].
[20] Mavridis IN. Mavridis’ Area: A Modern Stereotactic Microanatomic Guide for Deep Brain Stimulation of the Nucleus Accumbens. In: Costa A and Villalba E (eds) Horizons in Neuroscience Research. Volume 27. Horizons in Neuroscience Research. New York: Nova Biomedical-Nova Science Publishers, 2016, pp. 49.
[21] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.
[22] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.

Chapter 2

[1] Gelfand IM, Glagoleva EG, Kirillov AA (eds) The Method of Coordinates. Dover Books on Mathematics. Mineola: Dover Publications, 2011, pp. 5, 7, 12, 32, 34, 51.
[2] McCrea WH (ed) Analytical Geometry of Three Dimensions, 2nd ed. Dover Books on Mathematics. Mineola: Dover Publications, 2006, pp. 4.
[3] Gibilisco S (ed) Pre-Calculus Know-It-ALL, 1st ed. New York: The McGraw-Hill Companies, 2010, pp. 111, 112.
[4] Cartesian Coordinates, Review B: Coordinate Systems. Department of Physics. Massachusetts Institute of Technology, pp. B-2-3, http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf [accessed: May 22, 2017].
[5] Knill O. Math S21a: Multivariable calculus. Harvard University, 2014, http://www.math.harvard.edu/~knill/teaching/summer2014/ handouts/week1.pdf [accessed: May 22, 2017].
[6] Eisenhart LP (ed) Coordinate Geometry. Dover Books on Mathematics. Mineola: Dover Publications, 2005, pp. 73, 74.
[7] Schaltenbrand G and Wahren W (eds) Atlas for Stereotaxy of the Human Brain: With an Accompanying Guide, 2nd ed. Stuttgart: Georg Thieme Verlag, 1977, plate 18.
[8] Talairach J and Tournoux P (eds) Co-planar Stereotaxic Atlas of the Human Brain, 3-Dimentional Proportional System: An Approach to Cerebral Imaging. New York: Georg Thieme Verlag-Thieme Medical Publishers, 1988, pp. 59, 83.
[9] Mai JK, Majtanik M, Paxinos G (eds) Atlas of the Human Brain, 4th ed. London: Academic Press-Elsevier, 2016, pp. 87, 88, 93, 98, 407.
[10] Sharan AD and Andrews DW. Stereotactic Frames: Technical Considerations. In: Schulder M (ed) Handbook of Stereotactic and Functional Neurosurgery. Neurological Disease and Therapy. Boca Raton: CRC Press-Taylor & Francis Group, 2003, pp. 12.
[11] Neyman G. Stereotactic Radiosurgery Physics. In: Introduction to Cranial Neurosurgery and Advanced Radiosurgery, Participant’s Manual, Cleveland Clinic Gamma Knife Center, October 17-21, 2016, Cleveland Clinic, Cleveland, Ohio, USA, pp. 78.
[12] Mavridis IN. Mavridis’ Area of the Human Brain: Mathematics Applied to Anatomy Offers Microsurgical Accuracy in Stereotactic Neurosurgery. In: Baswell AR (ed) Advances in Mathematics Research. Volume 22. Advances in Mathematics Research. New York: Nova-Nova Science Publishers, 2017 (at press).
[13] Mavridis IN. [Stereotactic neurosurgical anatomy of the nucleus accumbens]. PhD Thesis, National and Kapodistrian University of Athens (School of Medicine), Athens, Greece, 2012, doi: 10.12681/eadd/27603. Greek, pp. 22.
[14] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.
[15] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.

Chapter 3

[1] McCrea WH (ed) Analytical Geometry of Three Dimensions, 2nd ed. Dover Books on Mathematics. Mineola: Dover Publications, 2006, pp. 3-5, 17, 27, 30.
[2] Eisenhart LP (ed) Coordinate Geometry. Dover Books on Mathematics. Mineola: Dover Publications, 2005, pp. 71, 74, 88-90, 92, 101.
[3] Gelfand IM, Glagoleva EG, Kirillov AA (eds) The Method of Coordinates. Dover Books on Mathematics. Mineola: Dover Publications, 2011, pp. 32, 33, 52.
[4] Gibilisco S (ed) Pre-Calculus Know-It-ALL, 1st ed. New York: The McGraw-Hill Companies, 2010, pp. 112, 320.
[5] Cartesian Coordinates, Review B: Coordinate Systems. Department of Physics. Massachusetts Institute of Technology, pp. B-2-3, http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf [accessed: May 22, 2017].
[6] Knill O. Math S21a: Multivariable calculus. Harvard University, 2014, http://www.math.harvard.edu/~knill/teaching/summer2014/ handouts/week1.pdf [accessed: May 22, 2017].
[7] Dawkins P. Calculus III. Beaumont: Paul Dawkins, 2007 (last updated: February 7, 2016), pp. 5, http://tutorial.math.lamar.edu/ getfile. aspx?file=B,11,N [accessed: May 22, 2017].
[8] Mavridis IN. Mavridis’ Area of the Human Brain: Mathematics Applied to Anatomy Offers Microsurgical Accuracy in Stereotactic Neurosurgery. In: Baswell AR (ed) Advances in Mathematics Research. Volume 22. Advances in Mathematics Research. New York: Nova-Nova Science Publishers, 2017 (at press).
[9] Parizel PM and De la Porte C. Stereotaxic target calculation. Theory and practice. Acta Neurochir. (Wien) 1993; 124(1): 34-6.
[10] Stereotactic Frames: Technical Considerations. What-when-how.com, In Depth Tutorials and Information. The-Crankshaft Publishing, http://what-when-how.com/stereotactic-and-functional-neurosurgery/stereotactic-frames-technical-considerations [accessed: May 22, 2017].
[11] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.
[12] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.
[13] Mavridis IN. [Stereotactic neurosurgical anatomy of the nucleus accumbens]. PhD Thesis, National and Kapodistrian University of Athens (School of Medicine), Athens, Greece, 2012, doi: 10.12681/eadd/27603. Greek, pp. 140.

Chapter 4

[1] Gelfand IM, Glagoleva EG, Kirillov AA (eds) The Method of Coordinates. Dover Books on Mathematics. Mineola: Dover Publications, 2011, pp. 13, 33, 34.
[2] Gibilisco S (ed) Pre-Calculus Know-It-ALL, 1st ed. New York: The McGraw-Hill Companies, 2010, pp. 113, 114, 116, 118, 120, 124, 345.
[3] Cartesian Coordinates, Review B: Coordinate Systems. Department of Physics. Massachusetts Institute of Technology, pp. B-2-3, http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf [accessed: May 22, 2017].
[4] Knill O. Math S21a: Multivariable calculus. Harvard University, 2014, http://www.math.harvard.edu/~knill/teaching/summer2014/ handouts/week1.pdf [accessed: May 22, 2017].
[5] Eisenhart LP (ed) Coordinate Geometry. Dover Books on Mathematics. Mineola: Dover Publications, 2005, pp. 72, 73, 77, 82-4, 286, 287.
[6] McCrea WH (ed) Analytical Geometry of Three Dimensions, 2nd ed. Dover Books on Mathematics. Mineola: Dover Publications, 2006, pp. 2-5, 14, 27.
[7] Maciunas RJ, Galloway RL Jr, Latimer JW. The application accuracy of stereotactic frames. Neurosurgery 1994; 35(4): 682-94; discussion 694-5.
[8] Levy R. A Short History of Stereotactic Neurosurgery. Cyber Museum of Neurosurgery, http://www.neurosurgery.org/ cybermuseum/stereotactichall/stereoarticle.html [accessed: May 22, 2017].
[9] Schulder M. Stereotactic Surgery with the Radionics Frame. In: Schulder M (ed) Handbook of Stereotactic and Functional Neurosurgery. Neurological Disease and Therapy. Boca Raton: CRC Press-Taylor & Francis Group, 2003, pp. 21, 22.
[10] Sharan AD and Andrews DW. Stereotactic Frames: Technical Considerations. In: Schulder M (ed) Handbook of Stereotactic and Functional Neurosurgery. Neurological Disease and Therapy. Boca Raton: CRC Press-Taylor & Francis Group, 2003, pp. 19.

Chapter 5

[1] McCrea WH (ed) Analytical Geometry of Three Dimensions, 2nd ed. Dover Books on Mathematics. Mineola: Dover Publications, 2006, pp. 10, 11.
[2] Eisenhart LP (ed) Coordinate Geometry. Dover Books on Mathematics. Mineola: Dover Publications, 2005, pp. 149, 166, 167.
[3] Gibilisco S (ed) Pre-Calculus Know-It-ALL, 1st ed. New York: The McGraw-Hill Companies, 2010, pp. 152, 157, 159, 160, 163, 165, 166.
[4] Scheinerman ER (ed) Mathematical Notation – A Guide for Engineers and Scientists. Baltimore: Edward R. Scheinerman, 2011, pp. 22, 23.
[5] Grunert P. From the idea to its realization: the evolution of minimally invasive techniques in neurosurgery. Minim. Invasive. Surg. 2013; 2013: 171369.
[6] Lichterman BL. Roots and routes of Russian neurosurgery (from surgical neurology towards neurological surgery). J. Hist. Neurosci. 1998; 7(2): 125-35.
[7] Konovalov A and Potapov A. Neurosurgery in Russia and USSR. Int. Neurosci. J. 2015; 1(1): e870.
[8] Levy R. A Short History of Stereotactic Neurosurgery.
Cyber Museum of Neurosurgery, http://www.neurosurgery.org/ cybermuseum/stereotactichall/stereoarticle.html [accessed: May 22, 2017].
[9] Schulder M. Stereotactic Surgery with the Radionics Frame. In: Schulder M (ed) Handbook of Stereotactic and Functional Neurosurgery. Neurological Disease and Therapy. Boca Raton: CRC Press-Taylor & Francis Group, 2003, pp. 21.
[10] RM Stereotactic System, Stereotactic Systems, Functional Neurosurgery, Products. Inomed, Emmendingen, Germany, http://www.en.inomed.com/products/functional-neurosurgery/stereotactic-systems/rm-stereotactic-system/ [accessed: May 22, 2017].
[11] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.
[12] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.

Chapter 6

[1] Mavridis IN. [Stereotactic neurosurgical anatomy of the nucleus accumbens]. PhD Thesis, National and Kapodistrian University of Athens (School of Medicine), Athens, Greece, 2012, doi: 10.12681/eadd/27603. Greek, pp. 24, 28, 77-80, 85, 112-6, 138, 151-4, 163.
[2] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.
[3] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.
[4] Mavridis IN. Mavridis’ Area of the Human Brain: Mathematics Applied to Anatomy Offers Microsurgical Accuracy in Stereotactic Neurosurgery. In: Baswell AR (ed) Advances in Mathematics Research. Volume 22. Advances in Mathematics Research. New York: Nova-Nova Science Publishers, 2017 (at press).
[5] Schaltenbrand G and Wahren W (eds) Guide to the Atlas for Stereotaxy of the Human Brain. Stuttgart: Georg Thieme Verlag, 1977, pp. 1, 11, 16, 17, 19, 20.
[6] Schaltenbrand G and Wahren W (eds) Atlas for Stereotaxy of the Human Brain: With an Accompanying Guide, 2nd ed. Stuttgart: Georg Thieme Verlag, 1977, plates 4-8, 12-8, 25-9, 35-49, 51-5, 57-63.
[7] Mavridis I and Anagnostopoulou S. The safest electrode trajectory for deep brain stimulation of the human nucleus accumbens: a stereotactic anatomic study. Minim. Invasive Neurosurg. 2011; 54(1): 16-20.
[8] Mavridis I and Anagnostopoulou S. The human nucleus accumbens as a target for deep brain stimulation: Anatomical study of electrode

s target point and stereotactic coordinates. Minim. Invasive Neurosurg. 2009; 52(5-6): 212-5.
[9] Mavridis IN. Mavridis’ area of the human brain: mathematically analysed anatomy assists stereotactic neurosurgery. OA Anat. 2014; 2(2): 11.
[10] Mavridis IN.

Mavridis’ Area: A Modern Stereotactic Microanatomic Guide for Deep Brain Stimulation of the Nucleus Accumbens. In: Costa A and Villalba E (eds) Horizons in Neuroscience Research. Volume 27. Horizons in Neuroscience Research. New York: Nova Biomedical-Nova Science Publishers, 2016, pp. 44-8.

Chapter 7

[1] Mavridis IN. Mavridis’ area of the human brain: mathematically analysed anatomy assists stereotactic neurosurgery. OA Anat. 2014; 2(2): 11.
[2] Mavridis IN. Anatomic guidance for stereotactic microneurosurgery: a modern necessity and the example of Mavridis’ area. Surg. Radiol. Anat. 2015; 37(1): 119-20.
[3] Mavridis IN. [Stereotactic neurosurgical anatomy of the nucleus accumbens]. PhD Thesis, National and Kapodistrian University of Athens (School of Medicine), Athens, Greece, 2012, doi: 10.12681/eadd/27603. Greek, pp. 62, 107, 154, 172.
[4] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human nucleus accumbens: from applied mathematics to microsurgical accuracy. Surg. Radiol. Anat. 2011; 33(7): 583-94.
[5] Mavridis IN. Deep Brain Stimulation for Treating Neuropsychiatric Disorders: Nucleus Accumbens Targeting and the Role of Mavridis’ Area. In: Costa A and Villalba E (eds) Horizons in Neuroscience Research. Volume 23. Horizons in Neuroscience Research. New York: Nova Biomedical-Nova Science Publishers, 2015, pp. 135, 139, 142.
[6] Mavridis IN. Anatomizing the “King of Neurosciences”. World J. Neurol. 2013; 3(2): 4-6.
[7] Mavridis IN. Mavridis’ area

targeting for deep brain stimulation in psychiatric disorders: Stereotactic microanatomy and technical aspects. J. Minim. Invasive Surg. Sci. 2016; 5(2): e34147.
[8] Mavridis IN. Mavridis’ area as a target for either selective or combined accumbens/ventral internal capsule deep brain stimulation. Acta Neurochir. (Wien) 2015; 157(2): 347-8.
[9] Mavridis IN. Mavridis’ area and electrode target localization in nucleus accumbens deep brain stimulation. World Neurosurg. 2015; 83(2): 259-60.
[10] Mavridis IN. Surgical anatomy of the human nucleus accumbens: Mavridis’ area and other clarifications in stereotactic space. Stereotact. Funct. Neurosurg. 2015; 93(4): 297-8.
[11] Mavridis IN. Stereotactic neurosurgical anatomy of the nucleus accumbens: four-year outcomes. Surg. Radiol. Anat. 2013; 35(7): 637-8.
[12] Mavridis IN. Nucleus accumbens stereotactic surgery: achieving accuracy through area M. World J. Neurol. 2013; 3(2): 7-9.
[13] Mavridis IN.

Stereotactic microanatomy of the nucleus accumbens stimulation for obsessive-compulsive disorder: Reported coordinates and Mavridis’ area. Neurosurgery

2015; 77(1): E155-6.
[14] Mavridis I, Boviatsis E, Anagnostopoulou S. Stereotactic anatomy of the human subthalamic nucleus: providing coordinates for accurate electrode placement. J. Neurol. Surg. A Cent. Eur. Neurosurg. 2014; 75(4): 289-98.
[15] Mavridis IN.

Mavridis’ Area: A Modern Stereotactic Microanatomic Guide for Deep Brain Stimulation of the Nucleus Accumbens. In: Costa A and Villalba E (eds) Horizons in Neuroscience Research. Volume 27. Horizons in Neuroscience Research. New York: Nova Biomedical-Nova Science Publishers, 2016, pp. 44-8, 53, 54, 56,
62, 63.
[16] Rezai AR, Sederberg PB, Bogner J, Nielson DM, Zhang J, Mysiw WJ, Knopp MV, Corrigan JD. Improved Function After Deep Brain Stimulation for Chronic, Severe Traumatic Brain Injury. Neurosurgery 2016; 79(2): 204-11.
[17] Gibson WS, Cho S, Abulseoud OA, Gorny KR, Felmlee JP, Welker KM, Klassen BT, Min HK, Lee KH. The Impact of Mirth-Inducing Ventral Striatal Deep Brain Stimulation on Functional and Effective Connectivity. Cereb. Cortex 2017; 27(3): 2183-94.
[18] Salgado S and Kaplitt MG. The Nucleus Accumbens: A Comprehensive Review. Stereotact. Funct. Neurosurg. 2015; 93(2): 75-93.
[19] Mavridis IN. Mavridis’ Area of the Human Brain: Mathematics Applied to Anatomy Offers Microsurgical Accuracy in Stereotactic Neurosurgery. In: Baswell AR (ed) Advances in Mathematics Research. Volume 22. Advances in Mathematics Research. New York: Nova-Nova Science Publishers, 2017 (at press).
[20] Implant manual. Reclaim DBS therapy for OCD. 3391 Lead Kit for deep brain stimulation. Medtronic, 2012, pp. 7, 8, 13 (Manual Document Number: M945749A008).
[21] Kuhn J, Lenartz D, Huff W, Mai JK, Koulousakis A, Maarouf M, Lee SH, Klosterkoetter J, Sturm V. Transient manic-like episode following bilateral deep brain stimulation of the nucleus accumbens and the internal capsule in a patient with Tourette syndrome. Neuromodulation 2008; 11(2): 128-31.
[22] Nachev P, Lopez-Sosa F, Gonzalez-Rosa JJ, Galarza A, Avecillas J, Pineda-Pardo JA, Lopez-Ibor JJ, Reneses B, Barcia JA, Strange B. Dynamic risk control by human nucleus accumbens. Brain 2015; 138(Pt 12): 3496-502.
[23] Yang KJ, Long H, Yuan YW, Qi ST, Xu BT, Wang KW, Song Y. Stereotactic neurosurgical technique and electrophysiological study in ablating the ventromedial shell of the nucleus accumbens. Stereotact. Funct. Neurosurg. 2014; 92(1): 37-43.
[24] Zhang C, Wei NL, Wang Y, Wang X, Zhang JG, Zhang K. Deep brain stimulation of the nucleus accumbens shell induces anti-obesity effects in obese rats with alteration of dopamine neurotransmission. Neurosci. Lett. 2015; 589: 1-6.
[25] Mavridis IN. Mavridis’ area and the mathematical science of subnuclear accumbens targeting: precision matters. World Neurosurg. 2016; 90: 691-2.

The principal audiences for this book are expected to range from graduate and postgraduate students to postdoctoral fellows and professors and include neurosurgeons, neuroanatomists, basic and clinical neuroscientists and mathematicians. This book is considered to be useful, among others, to clinicians and researchers working in neurosurgery departments and neuroanatomy laboratories.

If you have any questions or comments with regards to this book, please fill out the form below. Thank you!

You have not viewed any product yet.