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Current Medicinal Chemistry

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ISSN (Print): 0929-8673
ISSN (Online): 1875-533X

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Review Article

The Fractal Viewpoint of Tumors and Nanoparticles

Author(s): Athanasios Alexiou*, Christos Tsagkaris, Stylianos Chatzichronis, Andreas Koulouris, Ioannis Haranas, Ioannis Gkigkitzis, Georgios Zouganelis, Nobendu Mukerjee, Swastika Maitra, Niraj Kumar Jha, Gaber El-Saber Batiha, Mohammad Amjad Kamal, Michail Nikolaou and Ghulam Md Ashraf

Volume 30, Issue 3, 2023

Published on: 30 September, 2022

Page: [356 - 370] Pages: 15

DOI: 10.2174/0929867329666220801152347

Price: $65

Abstract

Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.

Keywords: Box-Counting Algorithm, Chaos Theory, Cancer, Drug Delivery, Fractal Dimension, Fractality, Imaging Data, Lacunarity, Pharmacokinetics, Quantum Tunneling, Nanoparticles, Scanning Tunneling Microscope, Succolarity

« Previous
[1]
Rahman, M; Abdullah, SA; Alharbi, KS; Beg, S; Sharma, K; Anwar, F; Al-Abbasi, FA; Kumar, V Ganoderic acid loaded nano-lipidic carriers improvise treatment of hepatocellular carcinoma. Drug Delivery, 2019, 26(1), 629-640.
[http://dx.doi.org/10.1080/10717544.2019.1606865]
[2]
Pandey, P.; Rahman, M.; Bhatt, P.C.; Beg, S.; Paul, B.; Hafeez, A.; Al-Abbasi, F.A.; Nadeem, M.S.; Baothman, O.; Anwar, F.; Kumar, V. Implication of nano-antioxidant therapy for treatment of hepatocellular carcinoma using PLGA nanoparticles of rutin. Nanomedicine (Lond.), 2018, 13(8), 849-870.
[http://dx.doi.org/10.2217/nnm-2017-0306] [PMID: 29565220]
[3]
Rahman, M.; Beg, S.; Verma, A.; Kazmi, I.; Patel, D.K.; Anwar, F.; Al Abbasi, F.A.; Kumar, V. Therapeutic applications of liposomal based drug delivery and drug targeting for immune linked inflammatory maladies: A contemporary view point. Curr. Drug Targets, 2017, 18(13), 1558-1571.
[http://dx.doi.org/10.2174/1389450118666170414113926] [PMID: 28413980]
[4]
Rahman, M.; Ahmad, M.Z.; Kazmi, I.; Akhter, S.; Afzal, M.; Gupta, G.; Sinha, V.R. Emergence of nanomedicine as cancer targeted magic bullets: Recent development and need to address the toxicity apprehension. Curr. Drug Discov. Technol., 2012, 9(4), 319-329.
[http://dx.doi.org/10.2174/157016312803305898] [PMID: 22725687]
[5]
Rahman, M.; Ahmad, M.Z.; Kazmi, I.; Akhter, S.; Afzal, M.; Gupta, G.; Jalees Ahmed, F.; Anwar, F. Advancement in multifunctional nanoparticles for the effective treatment of cancer. Expert Opin. Drug Deliv., 2012, 9(4), 367-381.
[http://dx.doi.org/10.1517/17425247.2012.668522] [PMID: 22400808]
[6]
Pucci, C.; Martinelli, C.; Ciofani, G. Innovative approaches for cancer treatment: Current perspectives and new challenges. E Cancer Med. Sci., 2019, 13, 961.
[7]
Jabir, N.R.; Tabrez, S.; Ashraf, G.M.; Shakil, S.; Damanhouri, G.A.; Kamal, M.A. Nanotechnology-based approaches in anticancer research. Int. J. Nanomedicine, 2012, 7, 4391-4408.
[http://dx.doi.org/10.2147/IJN.S33838] [PMID: 22927757]
[8]
Pavlović Mavić, M.; Šeparović, R.; Tečić Vuger, A.; Vazdar, L. Difference in estimation of side effects of chemotherapy between physicians and patients with early-stage breast cancer: The use of patient reported outcomes (PROs) in the evaluation of toxicity in everyday clinical practice. Cancers, 2021, 13(23), 5922.
[9]
Ali, R.; Mirza, Z.; Ashraf, G.M.; Kamal, M.A.; Ansari, S.A.; Damanhouri, G.A.; Abuzenadah, A.M.; Chaudhary, A.G.; Sheikh, I.A. New anticancer agents: Recent developments in tumor therapy. Anticancer Res., 2012, 32(7), 2999-3005.
[PMID: 22753764]
[10]
Azhar, A.; Ashraf, G.M.; Zia, Q.; Ansari, S.A.; Perveen, A.; Hafeez, A.; Saeed, M.; Kamal, M.A.; Alexiou, A.; Ganash, M.; Yarla, N.S.; Baeesa, S.S.; Alfiky, M.M.; Bajouh, O.S. Frontier view on nanotechnological strategies for neuro-therapy. Curr. Drug Metab., 2018, 19(7), 596-604.
[http://dx.doi.org/10.2174/1389200219666180305144143] [PMID: 29512448]
[11]
Alexiou, A.; Vairaktarakis, C.; Tsiamis, V.; Ashraf, G.M. Application of efficient nanoparticles for early diagnosis and treatment of cancer. Curr. Drug Metab., 2015, 16(8), 662-675.
[http://dx.doi.org/10.2174/1389200216666150602145310] [PMID: 26560321]
[12]
Beg, S.; Rahman, M.; Jain, A.; Saini, S.; Midoux, P.; Pichon, C.; Ahmad, F.J.; Akhter, S. Nanoporous metal organic frameworks as hybrid polymer-metal composites for drug delivery and biomedical applications. Drug Discov. Today, 2017, 22(4), 625-637.
[http://dx.doi.org/10.1016/j.drudis.2016.10.001] [PMID: 27742533]
[13]
Rahman, M.; Kumar, V.; Beg, S.; Sharma, G.; Katare, O.P.; Anwar, F. Emergence of liposome as targeted magic bullet for inflammatory disorders: Current state of the art. Artif. Cells Nanomed. Biotechnol., 2016, 44(7), 1597-1608.
[http://dx.doi.org/10.3109/21691401.2015.1129617] [PMID: 26758815]
[14]
Ahmad, J.; Akhter, S.; Rizwanullah, M.; Amin, S.; Rahman, M.; Ahmad, M.Z.; Rizvi, M.A.; Kamal, M.A.; Ahmad, F.J. Nanotechnology-based inhalation treatments for lung cancer: State of the art. Nanotechnol. Sci. Appl., 2015, 8(8), 55-66.
[PMID: 26640374]
[15]
Ahmad, J.; Amin, S.; Rahman, M.; Rub, R.A.; Singhal, M.; Ahmad, M.Z.; Rahman, Z.; Addo, R.T.; Ahmad, F.J.; Mushtaq, G.; Kamal, M.A.; Akhter, S. Solid matrix based lipidic nanoparticles in oral cancer chemotherapy: Applications and pharmacokinetics. Curr. Drug Metab., 2015, 16(8), 633-644.
[http://dx.doi.org/10.2174/1389200216666150812122128] [PMID: 26264206]
[16]
Rahman, M.; Akhter, S.; Ahmad, M.Z.; Ahmad, J.; Addo, R.T.; Ahmad, F.J.; Pichon, C. Emerging advances in cancer nanotheranostics with graphene nanocomposites: Opportunities and challenges. Nanomedicine (Lond.), 2015, 10(15), 2405-2422.
[http://dx.doi.org/10.2217/nnm.15.68] [PMID: 26252175]
[17]
Aneja, P.; Rahman, M.; Beg, S.; Aneja, S.; Dhingra, V.; Chugh, R. Cancer targeted magic bullets for effective treatment of cancer. Recent Pat Antiinfect Drug Discov., 2014, 9(2), 121-135.
[http://dx.doi.org/10.2174/1574891X10666150415120506] [PMID: 25876849]
[18]
Rahman, M.; Ahmad, M.Z.; Ahmad, J.; Firdous, J.; Ahmad, F.J.; Mushtaq, G.; Kamal, M.A.; Akhter, S. Role of graphene nano-composites in cancer therapy: Theranostic applications, metabolic fate and toxicity issues. Curr. Drug Metab., 2015, 16(5), 397-409.
[http://dx.doi.org/10.2174/1389200215666141125120633] [PMID: 25429670]
[19]
Ahmad, M.Z.; Akhter, S.; Anwar, M.; Kumar, A.; Rahman, M.; Talasaz, A.H.; Ahmad, F.J. Colorectal cancer targeted Irinotecan-Assam Bora rice starch based microspheres: A mechanistic, pharmacokinetic and biochemical investigation. Drug Dev. Ind. Pharm., 2013, 39(12), 1936-1943.
[http://dx.doi.org/10.3109/03639045.2012.719906] [PMID: 23013140]
[20]
Ahmad, M.Z.; Akhter, S.; Ahmad, I.; Rahman, M.; Anwar, M.; Jain, G.K.; Ahmad, F.J.; Khar, R.K. Development of polysaccharide based colon targeted drug delivery system: Design and evaluation of Assam Bora rice starch based matrix tablet. Curr. Drug Deliv., 2011, 8(5), 575-581.
[http://dx.doi.org/10.2174/156720111796642327] [PMID: 21696349]
[21]
Akhter, S.; Ahmad, Z.; Singh, A.; Ahmad, I.; Rahman, M.; Anwar, M.; Jain, G.K.; Ahmad, F.J.; Khar, R.K. Cancer targeted metallic nanoparticle: Targeting overview, recent advancement and toxicity concern. Curr. Pharm. Des., 2011, 17(18), 1834-1850.
[http://dx.doi.org/10.2174/138161211796391001] [PMID: 21568874]
[22]
Ahmad, M.Z.; Akhter, S.; Jain, G.K.; Rahman, M.; Pathan, S.A.; Ahmad, F.J.; Khar, R.K. Metallic nanoparticles: Technology overview & drug delivery applications in oncology. Expert Opin. Drug Deliv., 2010, 7(8), 927-942.
[http://dx.doi.org/10.1517/17425247.2010.498473] [PMID: 20645671]
[23]
Rahman, M.; Beg, S.; Ahmed, A.; Swain, S. Emergence of functionalized nanomedicines in cancer chemotherapy: Recent advancements, current challenges and toxicity considerations. Recent Pat. Nanomed., 2013, 2, 128-139.
[24]
Rahman, M.; Ahmed, M.Z.; Kazmi, I. Novel approach for the treatment of cancer: Theranostic nanomedicines. Pharmacologia., 2012, 3, 371-376.
[http://dx.doi.org/10.5567/pharmacologia.2012.371.376]
[25]
Kumar, V.; Bhatt, P.C.; Rahman, M.; Kaithwas, G.; Choudhry, H.; Al-Abbasi, F.A.; Anwar, F.; Verma, A. Fabrication, optimization, and characterization of umbelliferone β-D-galactopyranoside-loaded PLGA nanoparticles in treatment of hepatocellular carcinoma: In vitro and in vivo studies. Int. J. Nanomedicine, 2017, 12, 6747-6758.
[http://dx.doi.org/10.2147/IJN.S136629] [PMID: 28932118]
[26]
Singh, V.; Sahebkar, A.; Kesharwani, P. Poly (propylene imine) dendrimer as an emerging polymeric nanocarrier for anticancer drug and gene delivery. Eur. Polym. J., 2021, 158, 110683.
[27]
Mittal, P.; Saharan, A.; Verma, R.; Altalbawy, F.M.A.; Alfaidi, M.A.; Batiha, G.E-S.; Akter, W.; Gautam, R.K.; Uddin, M.S.; Rahman, M.S. Dendrimers: A new race of pharmaceutical nanocarriers. BioMed Res. Int., 2021, 2021, e8844030.
[28]
Dubey, S.K.; Kali, M.; Hejmady, S.; Saha, R.N.; Alexander, A.; Kesharwani, P. Recent advances of dendrimers as multifunctional nano-carriers to combat breast cancer. Eur. J. Pharmaceut. Sci., 2021, 164, 105890.
[http://dx.doi.org/10.1016/j.ejps.2021.105890]
[29]
Karimi, S.; Namazi, H. Fe3O4@PEG-coated dendrimer modified graphene oxide nanocomposite as a pH-sensitive drug carrier for targeted delivery of doxorubicin. J. Alloys Compd., 2021, 879, 160426.
[30]
Fatima, M.; Sheikh, A.; Hasan, N.; Sahebkar, A.; Riadi, Y.; Kesharwani, P. Folic acid conjugated poly(amidoamine) dendrimer as a smart nanocarriers for tracing, imaging, and treating cancers over-expressing folate receptors. Eur. Polym. J., 2022, 170, 111156.
[31]
Mignani, S.; Shi, X.; Rodrigues, J.; Tomas, H.; Karpus, A.; Majoral, J-P. First-in-class and best-in-class dendrimer nanoplatforms from concept to clinic: Lessons learned moving forward. Eur. J. Med. Chem., 2021, 219, 113456.
[http://dx.doi.org/10.1016/j.ejmech.2021.113456] [PMID: 33878563]
[32]
Yu, Z.; Gao, L.; Chen, K.; Zhang, W.; Zhang, Q.; Li, Q.; Hu, K. Nanoparticles: A new approach to upgrade cancer diagnosis and treatment. Nanoscale Res. Lett., 2021, 16(1), 88.
[http://dx.doi.org/10.1186/s11671-021-03489-z] [PMID: 34014432]
[33]
Chen, J.; Qiu, M.; Ye, Z.; Nyalile, T.; Li, Y.; Glass, Z.; Zhao, X.; Yang, L.; Chen, J.; Xu, Q. In situ cancer vaccination using lipidoid nanoparticles. Sci. Adv., 2021, 7(19), eabf1244.
[http://dx.doi.org/10.1126/sciadv.abf1244] [PMID: 33952519]
[34]
Montaseri, H.; Kruger, C.A.; Abrahamse, H. Inorganic nanoparticles applied for active targeted photodynamic therapy of breast cancer. Pharmaceutics, 2021, 13(3), 296.
[http://dx.doi.org/10.3390/pharmaceutics13030296]
[35]
Thi, T.T.H.; Suys, E.J.A.; Lee, J.S.; Nguyen, D.H.; Park, K.D.; Truong, N.P. Lipid-based nanoparticles in the clinic and clinical trials: From cancer nanomedicine to COVID-19 vaccines. Vaccines (Basel), 2021, 9(4), 359.
[http://dx.doi.org/10.3390/vaccines9040359] [PMID: 33918072]
[36]
Jiang, X.; He, C.; Lin, W. Supramolecular metal-based nanoparticles for drug delivery and cancer therapy. Cur. Opin. Chem. Biol., 2021, 61, 143-153.
[http://dx.doi.org/10.1016/j.cbpa.2021.01.005]
[37]
Kateb, B.; Chiu, K.; Black, K.L.; Yamamoto, V.; Khalsa, B.; Ljubimova, J.Y.; Ding, H.; Patil, R.; Portilla-Arias, J.A.; Modo, M.; Moore, D.F.; Farahani, K.; Okun, M.S.; Prakash, N.; Neman, J.; Ahdoot, D.; Grundfest, W.; Nikzad, S.; Heiss, J.D. Nanoplatforms for constructing new approaches to cancer treatment, imaging, and drug delivery: What should be the policy? Neuroimage, 2011, 54(1), S106-S124.
[http://dx.doi.org/10.1016/j.neuroimage.2010.01.105] [PMID: 20149882]
[38]
Jiang, X.; Fitch, S.; Wang, C.; Wilson, C.; Li, J.; Grant, G.A.; Yang, F. Nanoparticle engineered TRAIL-overexpressing adipose-derived stem cells target and eradicate glioblastoma via intracranial delivery. Proc. Natl. Acad. Sci. USA, 2016, 113(48), 13857-13862.
[http://dx.doi.org/10.1073/pnas.1615396113] [PMID: 27849590]
[39]
Stephan, M.T.; Moon, J.J.; Um, S.H.; Bershteyn, A.; Irvine, D.J. Therapeutic cell engineering with surface-conjugated synthetic nanoparticles. Nat. Med., 2010, 16(9), 1035-1041.
[http://dx.doi.org/10.1038/nm.2198] [PMID: 20711198]
[40]
Yafout, M.; Ousaid, A.; Khayati, Y.; El Otmani, I.S. Gold nanoparticles as a drug delivery system for standard chemotherapeutics: A new lead for targeted pharmacological cancer treatments. Sci. Am., 2021, 11, e00685.
[41]
Huang, P.; Wang, D.; Su, Y.; Huang, W.; Zhou, Y.; Cui, D.; Zhu, X.; Yan, D. Combination of small molecule prodrug and nanodrug delivery: Amphiphilic drug-drug conjugate for cancer therapy. J. Am. Chem. Soc., 2014, 136(33), 11748-11756.
[http://dx.doi.org/10.1021/ja505212y] [PMID: 25078892]
[42]
Chen, T.C.; da Fonseca, C.O.; Levin, D.; Schönthal, A.H. The monoterpenoid perillyl alcohol: Anticancer agent and medium to overcome biological barriers. Pharmaceutics, 2021, 13(12), 2167.
[43]
Sokolov, I. Fractals: A possible new path to diagnose and cure cancer? Future Oncol., 2015, 11(22), 3049-3051.
[http://dx.doi.org/10.2217/fon.15.211] [PMID: 26466999]
[44]
Haranas, I.; Gkigkitzis, I.; Alexiou, A. Fractal Growth on the Surface of a Planet and in Orbit around it, Microgravity - Science and Technology; Springer, 2014.
[45]
Michallek, F.; Huisman, H.; Hamm, B.; Elezkurtaj, S.; Maxeiner, A.; Dewey, M. Accuracy of fractal analysis and PI-RADS assessment of prostate magnetic resonance imaging for prediction of cancer grade groups: A clinical validation study. Eur. Radiol., 2022, 32(4), 2372-2383.
[http://dx.doi.org/10.1007/s00330-021-08358-y] [PMID: 34921618]
[46]
Michallek, F.; Huisman, H.; Hamm, B.; Elezkurtaj, S.; Maxeiner, A.; Dewey, M. Prediction of prostate cancer grade using fractal analysis of perfusion MRI: Retrospective proof-of-principle study. Eur. Radiol., 2021, 32(5), 3236-3247.
[PMID: 34913991]
[47]
Spyropoulos-Antonakakis, N.; Sarantopoulou, E.; Trohopoulos, P.N.; Stefi, A.L.; Kollia, Z.; Gavriil, V.E.; Bourkoula, A.; Petrou, P.S.; Kakabakos, S.; Semashko, V.V.; Nizamutdinov, A.S.; Cefalas, A.C. Selective aggregation of PAMAM dendrimer nanocarriers and PAMAM/ZnPc nanodrugs on human atheromatous carotid tissues: A photodynamic therapy for atherosclerosis. Nanoscale Res. Lett., 2015, 10, 210.
[http://dx.doi.org/10.1186/s11671-015-0904-5] [PMID: 25991914]
[48]
Mandelbrot, B.B. The Fractal Geometry of Nature; Freeman: New York, 1983.
[http://dx.doi.org/10.1119/1.13295]
[49]
Zmeskal, O.; Dzik, P.; Vesely, M. Entropy of fractal systems. Comput. Math. Appl., 2013, 66, 135-146.
[http://dx.doi.org/10.1016/j.camwa.2013.01.017]
[50]
Klonowski, W Signal and image analysis using chaos theory and fractal geometry. Machine Graph. Vision, 2001, 9(1), 31.
[51]
Maipas, S.; Nonni, A.; Politi, E.; Sarlanis, H.; Kavantzas, N.G. The Goodness-of-fit of the fractal dimension as a diagnostic factor in breast cancer. Cureus, 2018, 10(11), e3630.
[http://dx.doi.org/10.7759/cureus.3630] [PMID: 30705789]
[52]
Delides, A.; Panayiotides, I.; Alegakis, A.; Kyroudi, A.; Banis, C.; Pavlaki, A.; Helidonis, E.; Kittas, C. Fractal dimension as a prognostic factor for laryngeal carcinoma. Anticancer Res., 2005, 25(3B), 2141-2144.
[PMID: 16158956]
[53]
Smith, T.G.; Lange, G.D.; Marks, W.B. Fractal methods and results in cellular morphology- dimensions, lacunarity and multifractals. J. Neurosci. Methods, 1996, 69(2), 123-136.
[54]
Alexiou, A.; Nizami, B.; Khan, F.I.; Soursou, G.; Vairaktarakis, C.; Chatzichronis, S.; Tsiamis, V.; Manztavinos, V.; Yarla, N.S.; Md Ashraf, G. Mitochondrial dynamics and proteins related to neurodegenerative diseases. Curr. Protein Pept. Sci., 2018, 19(9), 850-857.
[http://dx.doi.org/10.2174/1389203718666170810150151] [PMID: 28799502]
[55]
Alexiou, A.; Soursou, G.; Chatzichronis, S.; Gasparatos, E.; Kamal, M.A.; Yarla, N.S.; Perveen, A.; Barreto, G.E.; Ashraf, G.M. Role of GTPases in the regulation of mitochondrial dynamics in Alzheimer’s disease and CNS-related disorders. Mol. Neurobiol., 2019, 56(6), 4530-4538.
[http://dx.doi.org/10.1007/s12035-018-1397-x] [PMID: 30338485]
[56]
Auger, C.; Vinaik, R.; Appanna, V.D.; Jeschke, M.G. Beyond mitochondria: Alternative energy-producing pathways from all strata of life. Metabolism, 2021, 118, 154733.
[http://dx.doi.org/10.1016/j.metabol.2021.154733] [PMID: 33631145]
[57]
Nunn, A.V.; Guy, G.W.; Bell, J.D. The quantum mitochondrion and optimal health. Biochem. Soc. Trans., 2016, 44(4), 1101-1110.
[http://dx.doi.org/10.1042/BST20160096] [PMID: 27528758]
[58]
Cortassa, S.; O’Rourke, B.; Aon, M.A. Redox-optimized ROS balance and the relationship between mitochondrial respiration and ROS. Biochim. Biophys. Acta, 2014, 1837(2), 287-295.
[http://dx.doi.org/10.1016/j.bbabio.2013.11.007] [PMID: 24269780]
[59]
Bou-Teen, D.; Kaludercic, N.; Weissman, D.; Turan, B.; Maack, C.; Di Lisa, F.; Ruiz-Meana, M. Mitochondrial ROS and mitochondria-targeted antioxidants in the aged heart. Free Radical Biol. Med., 2021, 167, 109-124.
[http://dx.doi.org/10.1016/j.freeradbiomed.2021.02.043]
[60]
Cortassa, S.; Juhaszova, M.; Aon, M.A.; Zorov, D.B.; Sollott, S.J. Mitochondrial Ca2+, redox environment and ROS emission in heart failure: Two sides of the same coin? J. Mol. Cell. Cardiol., 2021, 151, 113-125.
[http://dx.doi.org/10.1016/j.yjmcc.2020.11.013] [PMID: 33301801]
[61]
Kiebish, M.A.; Seyfried, T.N. Absence of pathogenic mitochondrial DNA mutations in mouse brain tumors. BMC Cancer, 2005, 5, 102.
[http://dx.doi.org/10.1186/1471-2407-5-102] [PMID: 16105171]
[62]
Brown, W.M.; George, M., Jr; Wilson, A.C. Rapid evolution of animal mitochondrial DNA. Proc. Natl. Acad. Sci. USA, 1979, 76(4), 1967-1971.
[http://dx.doi.org/10.1073/pnas.76.4.1967] [PMID: 109836]
[63]
Cavalli, L.R.; Liang, B.C. Mutagenesis, tumorigenicity, and apoptosis: Are the mitochondria involved? Mutat. Res., 1998, 398(1-2), 19-26.
[http://dx.doi.org/10.1016/S0027-5107(97)00223-6] [PMID: 9626961]
[64]
Augenlicht, L.H.; Heerdt, B.G. Mitochondria: Integrators in tumorigenesis? Nat. Genet., 2001, 28(2), 104-105.
[http://dx.doi.org/10.1038/88800] [PMID: 11381247]
[65]
Tan, D.J.; Bai, R.K.; Wong, L.J. Comprehensive scanning of somatic mitochondrial DNA mutations in breast cancer. Cancer Res., 2002, 62(4), 972-976.
[PMID: 11861366]
[66]
Fliss, M.S.; Usadel, H.; Caballero, O.L.; Wu, L.; Buta, M.R.; Eleff, S.M.; Jen, J.; Sidransky, D. Facile detection of mitochondrial DNA mutations in tumors and bodily fluids. Science, 2000, 287(5460), 2017-2019.
[http://dx.doi.org/10.1126/science.287.5460.2017] [PMID: 10720328]
[67]
Máximo, V.; Soares, P.; Seruca, R.; Rocha, A.S.; Castro, P.; Sobrinho-Simões, M. Microsatellite instability, mitochondrial DNA large deletions, and mitochondrial DNA mutations in gastric carcinoma. Genes Chromosomes Cancer, 2001, 32(2), 136-143.
[http://dx.doi.org/10.1002/gcc.1175] [PMID: 11550281]
[68]
Hibi, K.; Nakayama, H.; Yamazaki, T.; Takase, T.; Taguchi, M.; Kasai, Y.; Ito, K.; Akiyama, S.; Nakao, A. Mitochondrial DNA alteration in esophageal cancer. Int. J. Cancer, 2001, 92(3), 319-321.
[http://dx.doi.org/10.1002/ijc.1204] [PMID: 11291064]
[69]
Jones, J.B.; Song, J.J.; Hempen, P.M.; Parmigiani, G.; Hruban, R.H.; Kern, S.E. Detection of mitochondrial DNA mutations in pancreatic cancer offers a massive advantage over detection of nuclear DNA mutations. Cancer Res., 2001, 61(4), 1299-1304.
[PMID: 11245424]
[70]
Polyak, K.; Li, Y.; Zhu, H.; Lengauer, C.; Willson, J.K.; Markowitz, S.D.; Trush, M.A.; Kinzler, K.W.; Vogelstein, B. Somatic mutations of the mitochondrial genome in human colorectal tumours. Nat. Genet., 1998, 20(3), 291-293.
[http://dx.doi.org/10.1038/3108] [PMID: 9806551]
[71]
Okochi, O.; Hibi, K.; Uemura, T.; Inoue, S.; Takeda, S.; Kaneko, T.; Nakao, A. Detection of mitochondrial DNA alterations in the serum of hepatocellular carcinoma patients. Clin. Cancer Res., 2002, 8(9), 2875-2878.
[PMID: 12231530]
[72]
Ha, P.K.; Tong, B.C.; Westra, W.H.; Sanchez-Cespedes, M.; Parrella, P.; Zahurak, M.; Sidransky, D.; Califano, J.A. Mitochondrial C-tract alteration in premalignant lesions of the head and neck: A marker for progression and clonal proliferation. Clin. Cancer Res., 2002, 8(7), 2260-2265.
[PMID: 12114429]
[73]
Kumimoto, H.; Yamane, Y.; Nishimoto, Y.; Fukami, H.; Shinoda, M.; Hatooka, S.; Ishizaki, K. Frequent somatic mutations of mitochondrial DNA in esophageal squamous cell carcinoma. Int. J. Cancer, 2004, 108(2), 228-231.
[http://dx.doi.org/10.1002/ijc.11564] [PMID: 14639607]
[74]
Sanchez-Cespedes, M.; Parrella, P.; Nomoto, S.; Cohen, D.; Xiao, Y.; Esteller, M.; Jeronimo, C.; Jordan, R.C.; Nicol, T.; Koch, W.M.; Schoenberg, M.; Mazzarelli, P.; Fazio, V.M.; Sidransky, D. Identification of a mononucleotide repeat as a major target for mitochondrial DNA alterations in human tumors. Cancer Res., 2001, 61(19), 7015-7019.
[PMID: 11585726]
[75]
Rejniak, K.A.; Anderson, A.R. Hybrid models of tumor growth. Wiley Interdiscip. Rev. Syst. Biol. Med., 2011, 3(1), 115-125.
[http://dx.doi.org/10.1002/wsbm.102] [PMID: 21064037]
[76]
Slattery, K.; Woods, E.; Zaiatz-Bittencourt, V.; Marks, S.; Chew, S.; Conroy, M.; Goggin, C.; MacEochagain, C.; Kennedy, J.; Lucas, S.; Finlay, D.K.; Gardiner, C.M. TGFβ drives NK cell metabolic dysfunction in human metastatic breast cancer. J. Immunother. Cancer, 2021, 9(2), e002044.
[http://dx.doi.org/10.1136/jitc-2020-002044]
[77]
Peng, Y.; Liu, H.; Liu, J.; Long, J. Post-translational modifications on mitochondrial metabolic enzymes in cancer. Free Radical Biol. Med., 2022, 179, 11-23.
[http://dx.doi.org/10.1016/j.freeradbiomed.2021.12.264]
[78]
Kopinski, P.K.; Singh, L.N.; Zhang, S.; Lott, M.T.; Wallace, D.C. Mitochondrial DNA variation and cancer. Nature Rev. Cancer, 2021, 21(7), 431-445.
[http://dx.doi.org/10.1038/s41568-021-00358-w]
[79]
Pérez-Amado, C.J.; Bazan-Cordoba, A.; Hidalgo-Miranda, A.; Jiménez-Morales, S. Mitochondrial heteroplasmy shifting as a potential biomarker of cancer progression. Int. J. Mol. Sci., 2021, 22(14), 7369.
[http://dx.doi.org/10.3390/ijms22147369]
[80]
Anderson, A.R.A.; Chaplain, M.A.J. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol., 1998, 60(5), 857-899.
[http://dx.doi.org/10.1006/bulm.1998.0042] [PMID: 9739618]
[81]
Alexiou, A.; Rekkas, J. The quantum human central neural system. In: Advances in Experimental Medicine and Biology; Vlamos, P.; Alexiou, A., Eds.; Springer International Publishing: Switzerland, 2014; p. 821.
[82]
Alexiou, A.; Rekkas, J. Superconductivity in Human Body; Myth or Necessity In: Advances in Experimental Medicine and Biology; Vlamos, P.; Alexiou, A., Eds.; In: Advances in Experimental Medicine and Biology; Vlamos, P.; Alexiou, A., Eds.; Springer International Publishing: Switzerland, 2014; p. 821.
[83]
Metze, K.; Adam, R.; Florindo, J.B. The fractal dimension of chromatin - a potential molecular marker for carcinogenesis, tumor progression and prognosis. Expert Rev. Mol. Diagn., 2019, 19(4), 299-312.
[http://dx.doi.org/10.1080/14737159.2019.1597707] [PMID: 31006377]
[84]
Hakim, A.; Awale, R.N. Identification of breast abnormality from thermograms based on fractal geometry features. In: IOT Smart Sys; , 2022; 2022, pp. 393-401.
[http://dx.doi.org/10.1007/978-981-16-3945-6_38]
[85]
Sebők, D.; Vásárhelyi, L.; Szenti, I.; Vajtai, R.; Kónya, Z.; Kukovecz, Á. Fast and accurate lacunarity calculation for large 3D micro-CT datasets. Acta Mater., 2021, 214, 116970.
[http://dx.doi.org/10.1016/j.actamat.2021.116970]
[86]
Ashcroft, P.; Michor, F.; Galla, T. Stochastic tunneling and metastable states during the somatic evolution of cancer. Genetics, 2015, 199(4), 1213-1228.
[http://dx.doi.org/10.1534/genetics.114.171553] [PMID: 25624316]
[87]
Melo, R.; Conci, A. Succolarity: Defining a method to calculate this fractal measure. Genetics, 2008, 2008, 291-294.
[http://dx.doi.org/10.1109/IWSSIP.2008.4604424]
[88]
Borys, P.; Krasowska, M.; Grzywna, Z.J.; Djamgoz, M.B.; Mycielska, M.E. Lacunarity as a novel measure of cancer cells behavior. Biosystems, 2008, 94(3), 276-281.
[http://dx.doi.org/10.1016/j.biosystems.2008.05.036] [PMID: 18721854]
[89]
Römer, H. Weak quantum theory and the emergence of time. MindMatter, 2004, 2, p8.
[90]
Hershey, D.; Lee, W.E. Correspondence: Excess entropy (EE) and excess entropy production (EEP) in aging, evolving systems. Syst. Res., 1988, 5, 261-263.
[http://dx.doi.org/10.1002/sres.3850050309]
[91]
Binnig, G.; Rohrer, H. Scanning tunneling microscopy. IBM J. Res. Develop., 1986, 30(4), 355-369.
[92]
Trixler, F. Quantum tunnelling to the origin and evolution of life. Curr. Org. Chem., 2013, 17(16), 1758-1770.
[http://dx.doi.org/10.2174/13852728113179990083] [PMID: 24039543]
[93]
de Broglie, L. The wave nature of the electron. Nobel Lecture., 1929, 12, 244-256.
[94]
Schrödinger, E. Quantisierung als Eigenwertproblem I. Ann. Phys., 1926, 79, 361-376.
[http://dx.doi.org/10.1002/andp.19263840404]
[95]
Schrödinger, E. Quantisierung als Eigenwertproblem II. Ann. Phys., 1926, 79, 489-527.
[http://dx.doi.org/10.1002/andp.19263840602]
[96]
Schrödinger, E. Quantisierung als Eigenwertproblem III. Ann. Phys., 1926, 80, 734-756.
[97]
Schrödinger, E. Quantisierung als Eigenwertproblem IV. Ann. Phys., 1926, 81, 109-139.
[http://dx.doi.org/10.1002/andp.19263861802]
[98]
Gneiting, T.; vSevvc’ikov’a, H.; Percival, D.B. Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data. 2012.
[99]
Milosevic, N.; Ristanovic, D. The box-counting method as an efficient tool for 2D fractal analysis of neuronal dendritic arbor. 5th International Symposium “Fractals in Biology and Medicine", March 2008 Locarno, Italy.
[100]
Kazemi Korayem, A.; Ghamami, S.; Bahrami, Z. Fractal properties and morphological investigation of Nano hydrochlorothiazide is used to treat hypertension. BMC Pharmacol. Toxicol., 2018, 19(1), 70.
[http://dx.doi.org/10.1186/s40360-018-0259-5] [PMID: 30413182]
[101]
Cerofolini, G.F.; Narducci, D.; Amato, P.; Romano, E. Fractal nanotechnology. Nanoscale Res. Lett., 2008, 3(10), 381-385.
[http://dx.doi.org/10.1007/s11671-008-9170-0]
[102]
Benoit - Fractal Analysis Software. Available from: http://www.trusoft-international.com
[103]
Crampton, S. A Java Applet to compute fractal dimensions. Available from: http://www.stevec.org/fracdim
[104]
Karperien, A. FracLac for ImageJ. Available from: http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm
[105]
Sasaki, H.; Shibata, S.; Hatanaka, T. An evaluation method of ecotypes of japanese lawn grass for three different ecological functions. Bull. Natl. Grassl. Res. Inst., 1994, 49, 17-24.
[106]
The virtual fractal Lab. 2014. Available from: http://fractal-lab.org
[107]
Gneiting, T.; Sevcikova, H.; Percival, D.B. Estimators of fractal dimension: Assessing the smoothness of time series and spatial data. Stat. Sci., 2012, 27(2), 247-277.
[http://dx.doi.org/10.1214/11-STS370]
[108]
Fractalyse fractal analysis software. Available from: http://www.fractalyse.org
[109]
Gwyddion - Free SPM data analysis software. Available from: http://gwyddion.net
[110]
Zmeškal, O.; Veselý, M.; Nežádal, M.; Buchníček, M. Fractal analysis of image structures. HarFA - Harmonic and Fractal Image Analysis, 2001, 3-5.
[111]
Hausdorff (Box-Counting) Fractal Dimension, Alceu Costa (2013) in MathWorks
[112]
Ruiz de Miras, J.; Navas, J.; Villoslada, P.; Esteban, F.J. UJA-3DFD: A program to compute the 3D fractal dimension from MRI data, Computer Methods and Programs in Biomedicine 2011, 104(3), 452-460.
[113]
Ristanović, D.; Nedeljkov, V.; Stefanović, B.D.; Milosević, N.T.; Grgurević, M.; Stulić, V. Fractal and nonfractal analysis of cell images: Comparison and application to neuronal dendritic arborization. Biol. Cybern., 2002, 87(4), 278-288.
[http://dx.doi.org/10.1007/s00422-002-0342-1] [PMID: 12386743]
[114]
Losa, G.A. The fractal geometry of life. Riv. Biol., 2009, 102(1), 29-59.
[PMID: 19718622]
[115]
Baish, J.W.; Jain, R.K. Fractals and cancer. Cancer Res., 2000, 60(14), 3683-3688.
[PMID: 10919633]
[116]
Ashraf, G.M.; Chatzichronis, S.; Alexiou, A.; Kyriakopoulos, N.; Alghamdi, B.S.A.; Tayeb, H.O.; Alghamdi, J.S.; Khan, W.; Jalal, M.B.; Atta, H.M. BrainFD: Measuring the intracranial brain volume with fractal dimension. Front. Aging Neurosci., 2021, 13, 765185.
[http://dx.doi.org/10.3389/fnagi.2021.765185] [PMID: 34899274]
[117]
Di leva, A.; Esteban, F. J.; Grizzi, F.; Klonowski, W.; Martín-Landrove, M. Fractals in the neurosciences, Part II: Clinical applications and future perspectives. Neuroscientist, 2015, 21, 30-43.
[http://dx.doi.org/10.1177/1073858413513928]
[118]
Varley, T.F.; Craig, M.; Adapa, R.; Finoia, P.; Williams, G.; Allanson, J.; Pickard, J.; Menon, D.K.; Stamatakis, E.A. Fractal dimension of cortical functional connectivity networks & severity of disorders of consciousness. PLoS One, 2020, 15(2), e0223812.
[http://dx.doi.org/10.1371/journal.pone.0223812] [PMID: 32053587]
[119]
Pruess, S.A. Some remarks on the numerical estimation of fractal dimension. Fractals. In: The Earth Sciences; Barton, C.C.; La Pointe, P.R., Eds.; Springer: Boston, 1995; pp. 65-75.
[http://dx.doi.org/10.1007/978-1-4899-1397-5_3]
[120]
Ohri, S.; Dey, P.; Nijhawan, R. Fractal dimension in aspiration cytology smears of breast and cervical lesions. Anal. Quant. Cytol. Histol., 2004, 26(2), 109-112.
[PMID: 15131899]
[121]
Zhang, P.; Chen, L.; Xu, T.; Liu, H.; Liu, X.; Meng, J.; Yang, G.; Jiang, L.; Wang, S. Programmable fractal nanostructured interfaces for specific recognition and electrochemical release of cancer cells. Adv. Mater., 2013, 25(26), 3566-3570.
[http://dx.doi.org/10.1002/adma.201300888] [PMID: 23716475]
[122]
Hadzieva, E.; Bogatinoska, D.C.; Petroski, R.; Shuminoska, M.; Gjergjeska, L.; Karadimce, A.; Trajkova, V. Is the fractal dimension of the contour-lines a reliable tool for classification of medical images? MATEC Web Conf., 2016, 76, p. 05002.
[http://dx.doi.org/10.1051/matecconf/20167605002]
[123]
Dokukin, M.E.; Guz, N.V.; Woodworth, C.D.; Sokolov, I. Emerging of fractal geometry on surface of human cervical epithelial cells during progression towards cancer. New J. Phys., 2015, 17(3), 033019.
[http://dx.doi.org/10.1088/1367-2630/17/3/033019] [PMID: 25844044]
[124]
Sokolov, I.; Dokukin, M.E. Fractal analysis of cancer cell surface. Methods Mol. Biol., 2017, 1530, 229-245.
[http://dx.doi.org/10.1007/978-1-4939-6646-2_13] [PMID: 28150205]
[125]
Metze, K. Fractal dimension of chromatin: Potential molecular diagnostic applications for cancer prognosis. Expert Rev. Mol. Diagn., 2013, 13(7), 719-735.
[http://dx.doi.org/10.1586/14737159.2013.828889] [PMID: 24063399]
[126]
Metze, K.; Castro de Mattos, A.; Adam, R. Fractal dimension of chromatin is an independent prognostic factor for survival in patients with small cell neuroendocrine carcinoma of the lung. Virchows Arch., 2018, 473, S114.
[127]
Bedin, V.; Adam, R.L.; de Sá, B.C.; Landman, G.; Metze, K. Fractal dimension of chromatin is an independent prognostic factor for survival in melanoma. BMC Cancer, 2010, 10, 260.
[http://dx.doi.org/10.1186/1471-2407-10-260] [PMID: 20525386]
[128]
Losa, G.A.; Castelli, C. Nuclear patterns of human breast cancer cells during apoptosis: Characterisation by fractal dimension and co-occurrence matrix statistics. Cell Tissue Res., 2005, 322(2), 257-267.
[http://dx.doi.org/10.1007/s00441-005-0030-2] [PMID: 16059703]
[129]
Dey, P.; Sharma, N.; Samanta, S. Fractal dimension of cervical intraepithelial lesions on cytology smear. Anal. Quant. Cytol. Histol., 2010, 32(6), 320-322.
[PMID: 21456343]
[130]
Dey, P.; Banik, T. Fractal dimension of chromatin texture of squamous intraepithelial lesions of cervix. Diagn. Cytopathol., 2012, 40(2), 152-154.
[http://dx.doi.org/10.1002/dc.21631] [PMID: 22246932]
[131]
Sedivy, R.; Windischberger, C.; Svozil, K.; Moser, E.; Breitenecker, G. Fractal analysis: An objective method for identifying atypical nuclei in dysplastic lesions of the cervix uteri. Gynecol. Oncol., 1999, 75(1), 78-83.
[http://dx.doi.org/10.1006/gyno.1999.5516] [PMID: 10502430]
[132]
Mincione, G.; Di Nicola, M.; Di Marcantonio, M.C.; Muraro, R.; Piattelli, A.; Rubini, C.; Penitente, E.; Piccirilli, M.; Aprile, G.; Perrotti, V.; Artese, L. Nuclear fractal dimension in oral squamous cell carcinoma: A novel method for the evaluation of grading, staging, and survival. J. Oral Pathol. Med., 2015, 44(9), 680-684.
[http://dx.doi.org/10.1111/jop.12280] [PMID: 25367085]
[133]
Vasilescu, C.; Giza, D.E.; Petrisor, P.; Dobrescu, R.; Popescu, I.; Herlea, V. Morphometrical differences between resectable and non-resectable pancreatic cancer: A fractal analysis. Hepatogastroenterology, 2012, 59(113), 284-288.
[PMID: 22260836]
[134]
Metze, K.; Ferreira, R.C.; Adam, R.L.; Leite, N.J.; Ward, L.S.; de Matos, P.S. Chromatin texture is size dependent in follicular adenomas but not in hyperplastic nodules of the thyroid. World J. Surg., 2008, 32(12), 2744-2746.
[http://dx.doi.org/10.1007/s00268-008-9736-0] [PMID: 18787892]
[135]
Ferro, D.P.; Falconi, M.A.; Adam, R.L.; Ortega, M.M.; Lima, C.P.; de Souza, C.A.; Lorand-Metze, I.; Metze, K. Fractal characteristics of May-Grünwald-Giemsa stained chromatin are independent prognostic factors for survival in multiple myeloma. PLoS One, 2011, 6(6), e20706.
[http://dx.doi.org/10.1371/journal.pone.0020706] [PMID: 21698234]
[136]
Metze, K.; Mello, M.R.B.; Albanez, K.B. Chromatin texture and molecular features in acute myeloid leukemia. Histopathology, 2012, 61(S1), 49-50.
[137]
Adam, R.L.; Silva, R.C.; Pereira, F.G.; Leite, N.J.; Lorand-Metze, I.; Metze, K. The fractal dimension of nuclear chromatin as a prognostic factor in acute precursor B lymphoblastic leukemia. Cell. Oncol., 2006, 28(1-2), 55-59.
[PMID: 16675881]
[138]
Noy, S.; Vlodavsky, E.; Klorin, G.; Drumea, K.; Ben Izhak, O.; Shor, E.; Sabo, E. Computerized morphometry as an aid in distinguishing recurrent versus nonrecurrent meningiomas. Anal. Quant. Cytol. Histol., 2011, 33(3), 141-150.
[PMID: 21980617]
[139]
Pantic, I.; Paunovic, J.; Perovic, M.; Cattani, C.; Pantic, S.; Suzic, S.; Nesic, D.; Basta-Jovanovic, G. Time-dependent reduction of structural complexity of the buccal epithelial cell nuclei after treatment with silver nanoparticles. J. Microsc., 2013, 252(3), 286-294.
[http://dx.doi.org/10.1111/jmi.12091] [PMID: 24118045]
[140]
Nikolovski, D.; Dugalic, S.; Pantic, I. Iron oxide nanoparticles decrease nuclear fractal dimension of buccal epithelial cells in a time-dependent manner. J. Microsc., 2017, 268(1), 45-52.
[http://dx.doi.org/10.1111/jmi.12585] [PMID: 28543185]
[141]
Pantic, I.; Petrovic, D.; Paunovic, J.; Vucevic, D.; Radosavljevic, T.; Pantic, S. Age-related reduction of chromatin fractal dimension in toluidine blue-stained hepatocytes. Mech. Ageing Dev., 2016, 157, 30-34.
[http://dx.doi.org/10.1016/j.mad.2016.07.002] [PMID: 27412950]
[142]
Pantic, I.; Paunovic, J.; Vucevic, D.; Radosavljevic, T.; Dugalic, S.; Petkovic, A.; Radojevic-Skodric, S.; Pantic, S. Postnatal developmental changes in fractal complexity of Giemsa-stained chromatin in mice spleen follicular cells. Microsc. Microanal., 2017, 23(5), 1024-1029.
[http://dx.doi.org/10.1017/S1431927617012545] [PMID: 28918768]
[143]
Pantic, I.; Basta-Jovanovic, G.; Starcevic, V.; Paunovic, J.; Suzic, S.; Kojic, Z.; Pantic, S. Complexity reduction of chromatin architecture in macula densa cells during mouse postnatal development. Nephrology (Carlton), 2013, 18(2), 117-124.
[http://dx.doi.org/10.1111/nep.12003] [PMID: 23088294]
[144]
Pantic, I.; Harhaji-Trajkovic, L.; Pantovic, A.; Milosevic, N.T.; Trajkovic, V. Changes in fractal dimension and lacunarity as early markers of UV-induced apoptosis. J. Theor. Biol., 2012, 303, 87-92.
[http://dx.doi.org/10.1016/j.jtbi.2012.03.013] [PMID: 22763132]
[145]
Grbatinić, I.; Milošević, N.T. Incipient UV-induced structural changes in neutrophil granulocytes: Morphometric and texture analysis of two dimensional digital images. Microsc. Microanal., 2016, 22(2), 387-393.
[http://dx.doi.org/10.1017/S1431927616000532] [PMID: 26906218]
[146]
Finan, J.D.; Leddy, H.A.; Guilak, F. Osmotic stress alters chromatin condensation and nucleocytoplasmic transport. Biochem. Biophys. Res. Commun., 2011, 408(2), 230-235.
[http://dx.doi.org/10.1016/j.bbrc.2011.03.131] [PMID: 21463604]
[147]
Pantic, I.; Nesic, D.; Basailovic, M.; Cetkovic, M.; Mazic, S.; Suzic-Lazic, J.; Popevic, M. Chromatin fractal organization, textural patterns, and circularity of nuclear envelope in adrenal Zona fasciculata cells. Microsc. Microanal., 2016, 22(6), 1120-1127.
[http://dx.doi.org/10.1017/S1431927616011910] [PMID: 27821221]
[148]
Daniel, M.; Baskar, S.; Latha, M.M. Fractal dimension and tertiary structure of proteins. Phys. Scr., 2006, 60, 270.
[http://dx.doi.org/10.1238/Physica.Regular.060a00270]
[149]
Pereira, L.M. Fractal pharmacokinetics. Comput. Math. Methods Med., 2010, 11(2), 161-184.
[http://dx.doi.org/10.1080/17486700903029280] [PMID: 20461596]
[150]
Carstensen, J.T.; Franchini, M. The use of fractal geometry in pharmaceutical systems. Drug Dev. Ind. Pharm., 1993, 19, 1-2, 85-100.
[http://dx.doi.org/10.3109/03639049309038762]
[151]
Todoroff, N.; Kunze, J.; Schreuder, H.; Hessler, G.; Baringhaus, K.H.; Schneider, G. Fractal dimensions of macromolecular structures. Mol. Inform., 2014, 33(9), 588-596.
[http://dx.doi.org/10.1002/minf.201400090] [PMID: 26213587]
[152]
Jelinek, H.F.; Fernandez, E. Neurons and fractals: How reliable and useful are calculations of fractal dimensions? J. Neurosci. Methods, 1998, 81(1-2), 9-18.
[153]
Dey, P. Basic principles and applications of fractal geometry in pathology: A review. Anal. Quant. Cytol. Histol., 2005, 27(5), 284-290.
[PMID: 16447821]
[154]
Ramya, R.; Shridhar, R.; Latha, K.C.; Balasubramanian, S. Endometrial cancer detection using fractal based texture analysis: A box counting Algorithm. IJAR, 2016, 2(7), 243-245.
[155]
Reza, S.M.; Mays, R.; Iftekharuddin, K.M. Multifractal detrended texture feature for brain tumor classification. Med. Imag., Comput.-Aided Diagn., 2015, 9414, 941410.
[156]
Jitaree, S.; Phinyomark, A.; Boonyaphiphat, P.; Phukpattaranont, P. Cell type classifiers for breast cancer microscopic images based on fractal dimension texture analysis of image color layers. Scanning, 2015, 37(2), 145-151.
[http://dx.doi.org/10.1002/sca.21191] [PMID: 25689353]
[157]
Šoštarić-Zuckermann, I.C.; Severin, K.; Huzak, M.; Hohšteter, M.; Gudan Kurilj, A.; Artuković, B.; Džaja, A.; Grabarević, Ž. Quantification of morphology of canine circumanal gland tumors: A fractal based study. EJH, 2016, 60(2), 2609.
[http://dx.doi.org/10.4081/ejh.2016.2609] [PMID: 27349313]
[158]
Zook, J.M.; Iftekharuddin, K.M. Statistical analysis of fractal-based brain tumor detection algorithms. Magn. Reson. Imaging, 2005, 23(5), 671-678.
[http://dx.doi.org/10.1016/j.mri.2005.04.002] [PMID: 16051042]
[159]
Baetke, S.C.; Lammers, T.; Kiessling, F. Applications of nanoparticles for diagnosis and therapy of cancer. Br. J. Radiol., 2015, 88(1054), 20150207.
[http://dx.doi.org/10.1259/bjr.20150207] [PMID: 25969868]
[160]
Marcos Luciano Bruschi. 5 - Mathematical models of drug release, Strategies to Modify the Drug Release from Pharmaceutical Systems; Woodhead Publishing: Sawston, UK, 2015, pp. 63-86.
[http://dx.doi.org/10.1016/B978-0-08-100092-2.00005-9]
[161]
Farin, D.; Avnir, D. Use of fractal geometry to determine effects of surface morphology on drug dissolution. J. Pharm. Sci., 1992, 81(1), 54-57.
[http://dx.doi.org/10.1002/jps.2600810111] [PMID: 1619570]
[162]
Noyes, A.A.; Whitney, W.R. The rate of solution of solid substances in their own solutions. J. Am. Chem. Soc., 1897, 19, 930-934.
[http://dx.doi.org/10.1021/ja02086a003]
[163]
Demetzos, C.; Pippa, N. Fractal geometry as a new approach for proving nanosimilarity: A reflection note. Int. J. Pharm., 2015, 483(1-2), 1-5.
[164]
Pippa, N.; Dokoumetzidis, A.; Demetzos, C.; Macheras, P. On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: A review. Int. J. Pharm., 2013, 456(2), 340-352.
[165]
Meng, Z.; Hashmi, S.M.; Elimelech, M. Aggregation rate and fractal dimension of fullerene nanoparticles via simultaneous multiangle static and dynamic light scattering measurement. J. Colloid Interface Sci., 2013, 392, 27-33.
[http://dx.doi.org/10.1016/j.jcis.2012.09.088] [PMID: 23211871]
[166]
Pippa, N.; Pispas, S.; Demetzos, C. The fractal hologram and elucidation of the structure of liposomal carriers in aqueous and biological media. Int. J. Pharm., 2012, 430(1-2), 65-73.
[http://dx.doi.org/10.1016/j.ijpharm.2012.03.048] [PMID: 22486958]
[167]
Jasmine, M.J.; Prasad, E. Fractal growth of PAMAM dendrimer aggregates and its impact on the intrinsic emission properties. J. Phys. Chem. B, 2010, 114(23), 7735-7742.
[http://dx.doi.org/10.1021/jp100837h] [PMID: 20496918]
[168]
Sabín, J.; Prieto, G.; Ruso, J.M.; Sarmiento, F. Fractal aggregates induced by liposome-liposome interaction in the presence of Ca2+. Eur. Phys. J. E, 2007, 24(2), 201-210.
[http://dx.doi.org/10.1140/epje/i2007-10231-3] [PMID: 18000643]
[169]
Sabín, J.; Prieto, G.; Ruso, J.M.; Messina, P.; Sarmiento, F. Aggregation of liposomes in presence of La3+: A study of the fractal dimension. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 2007, 76(1 Pt 1), 011408.
[http://dx.doi.org/10.1103/PhysRevE.76.011408] [PMID: 17677442]
[170]
Macheras, P. A fractal approach to heterogeneous drug distribution: Calcium pharmacokinetics. Pharm. Res., 1996, 13(5), 663-670.
[http://dx.doi.org/10.1023/A:1016031129053] [PMID: 8860420]
[171]
Samioti, S.E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I. Two dimensional drug diffusion between nanoparticles and fractal tumors. J. Phys. Conf. Ser., 2017, 931(1), 012034.
[http://dx.doi.org/10.1088/1742-6596/931/1/012034]
[172]
Kosmidis, K.; Argyrakis, P.; Macheras, P. Fractal kinetics in drug release from finite fractal matrices. J. Chem. Phys., 2003, 19(12), 6373-7.57.
[http://dx.doi.org/10.1063/1.1603731]
[173]
Robert, A. Data Models. Remote Sensing In: (Third Edition); Schowengerdt, Robert A., Ed.; Academic Press, 2007, pp. 127-XV.
[http://dx.doi.org/10.1016/B978-012369407-2/50007-3]
[174]
Yaffe, M.J.; Boyd, N.F. Quantitative image analysis for estimation of breast cancer risk. In: Handbook of Medical Image Processing and Analysis; Elsevier, 2009.
[175]
Stylianopoulos, T.; Munn, L.L.; Jain, R.K. Reengineering the physical microenvironment of tumors to improve drug delivery and efficacy: From mathematical modeling to bench to bedside. Trends Cancer, 2018, 4(4), 292-319.
[http://dx.doi.org/10.1016/j.trecan.2018.02.005] [PMID: 29606314]
[176]
Karamanos, K.; Mistakidis, S.; Massart, T.; Mistakidis, I. Entropy production of entirely diffusional Laplacian transfer and the possible role of fragmentation of the boundaries. Fractals, 2015, 23, 15500267.
[http://dx.doi.org/10.1142/S0218348X15500267]
[177]
Liu, S; Wang, Y; Xu, K; Wang, Z; Fan, X; Zhang, C; Li, S; Qiu, X; Jiang, T Relationship between necrotic patterns in glioblastoma and patient survival: Fractal dimension and lacunarity analyses using magnetic resonance imaging. Sci. Reports, 2017, 7(1), 8302.50.
[http://dx.doi.org/10.1038/s41598-017-08862-6]
[178]
Hadzieva, E.; Bogatinoska, D.C.; Gjergjeska, L.; Shuminoska, M.; Petroski, R. Review of the software packages for estimation of the fractal dimension. Seman. Scholor, 2015, 2015, 53988051.
[179]
Korolj, A.; Wu, H-T.; Radisic, M. A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems. Biomaterials, 2019, 219, 119363.
[http://dx.doi.org/10.1016/j.biomaterials.2019.119363] [PMID: 31376747]

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