It is the goal of this paper to present general strategy for using fractional operators to model the magnetic relaxation in complex environments revealing time and spacial disorder. Such systems have anomalous temporal and spacial response (non-local interactions and long memory) compared to systems without disorder. The systems having no memory can be modeled by linear differential equations with constant coefficients (exponential relaxation); the differential equations governing the systems with memory are known as Fractional Order Differential Equations (FODE).
The relaxation of the spin system is best described phenomenologically by so-called Bloch's equations, which detail the rate of change of the magnetization M of the spin system. The Ordinary Order Bloch's Equations (OOBE) are a set of macroscopic differential equations of the first order describing the magnetization behavior under influence of static, varying magnetic fields and relaxation. It is assumed that spins relax along the z axis and in the x-y plane at different rates, designated as R1 and R2 (R1=1/T1,R2=1/T2) respectively, but following first order kinetics.
To consider heterogeneity, complex structure, and memory effects in the relaxation process the Ordinary Order Bloch's Equations were generalized to Fractional Order Bloch's Equations (FOBE) through extension of the time derivative to fractional (non-integer) order.
To investigate systematically the influence of “fractionality” (power order of derivative) on the dynamics of the spin system a general approach was proposed. The OOBE and FOBE were successively solved using analytical (Laplace transform), semi-analytical (ADM - Adomian Decomposition Method) and numerical methods (Grunwald- Letnikov method for FOBE). Solutions of both OOBE and FOBE systems of equations were obtained for various sets of experimental parameters used in spin !! NMR and EPR spectroscopies. The physical meaning of the fractional relaxation in magnetic resonance is shortly discussed.
Sławomir Wąsik, Michał Arabski, Karolina Maciejec, Grażyna Suchanek and Anna Świercz
temperatures. Materials Chemistry and Physics , 21 , 67-84.
Dworecki K., Ślęzak A., Drabik M., Ornal-Wąsik B., Wąsik S. (2006). Determination of the membrane permeability coefficient under concentration polarisation conditions, Desalination , 198 , 326-334.
Dworecki K., Ślęzak A., Ornal-Wąsik B., Wąsik S. (2005). Evolution of concentration field in a membrane system. J. Biochem. Biophys. Methods , 62 , 153-162.
Dworecki K., Ślęzak A., Wąsik S. (2003). Temporal and spatial structure of the concentration boundary layers in membrane system. Physica A , 326 , 360
Volha Anatol’evna Mezhnina and Aksana Yuryeuna Urbanovich
, Guiard J, Zhang D. Assessing temporal changes in genetic diversity of maize varieties using microsatellite markers, Theoretical and Applied Genetics., 2005, 110(2): 294-302.
15. Xie H, Sui Y, Chang FQ, Xu Y, Ma RC. SSR allelic variation in almond (Prunus dulcis Mill.), Theoretical and Applied Genetics., 2006, 112(2): 366-372.
Yeltay Rakhmanov, Paolo Enrico Maltese, Alessandra Zulian, Tommaso Beccari, Munis Dundar and Matteo Bertelli
Martin SS Shapiro EP Mukherjee M Atrial septal defects - clinical manifestations, echo assessment, and intervention Clin Med Insights Cardiol 2015 23 8 Suppl 1 93 8
7 Botto LD, Correa A, Erickson JD. Racial and temporal variations in the prevalence of heart defects. Pediatrics 2001; 107(3): E32. 10.1542/peds.107.3.e32 11230613
Botto LD Correa A Erickson JD Racial and temporal variations in the prevalence of heart defects Pediatrics 2001 107 3 E32
8 Chen B, Gagnon M, Shahangian S, Anderson NL, Howerton DA, Boone JD
Martin Vanek, Filip Mravec, Martin Szotkowski, Dana Byrtusova, Andrea Haronikova, Milan Certik, Volha Shapaval and Ivana Marova
used as imaging technique when studying S. cerevisiae as a model organism. Lipids are accumulated in all eukaryotic cells as lipid bodies (LB), which are not a simple warehouse, but rather one of the principal compartments with function including protein degradation, temporal protein storage and also signaling ( 8 , 9 , 10 ).
One reason for study such a complex system with LSCM was proposed as statement ( 11 ), that morphological alteration of LB is affected by processes maintaining neutral lipid and phospholipid homeostasis. Some of the red yeasts were found
gently inserted to retract the eyelids of the rabbit. Where necessary due to a narrow palpebral aperture, the globe was exposed by incisions at the lateral and medial canthi, removing the nictitating membrane and reflecting the eyelids. The “tracer-gel” attached to the ultrasound transducer was placed in contact with the limbal region on the temporal side of the eye. The transducer was activated to deliver the 40 kHz ultrasound for a period of 1-2 minutes. For each eye of 3 rabbits a different therapeutic molecule was tested, either incorporated directly into the
Anthony Singer, Eleni Markoutsa, Alya Limayem, Subhra Mohapatra and Shyam S. Mohapatra
to ensure complete removal
NIR Fluorescence-Enhanced Diffuse Optical Tomography – multimodal use of real-time computed tomography & MRI
- Tumor targeted NCs incorporating fluorescent NPs
- Real-time temporal and spatial 3D imaging for the identification of biological & genetic causalities of disease - Earlier detection & removal of tumors
Theranostics for Tumor Ablation in Cancer Patients
Stimuli-responsive nanoparticles are being incorporated into nanoformulations that are targeted for tumor cells, and upon radiation
Elena Manara, Paolo E. Maltese, Giulia Guerri, Giuseppe Marceddu, Natale Capodicasa, Andi Abeshi and Matteo Bertelli
Molecular diagnosis relieves patients of uncertainty, aids informed decisions about health and reproductive choices, and helps them join clinical trials or access available therapy. Genetic testing by next generation sequencing (NGS) is the suggested choice for a wide variety of disorders with heterogeneous phenotypes, alleles and loci. The development of a NGS service at MAGI Balkans, through the support of a partner, increases the availability of forefront genetic testing in Albania with great advantages for patients and their families. Here we report the NGS tests performed in collaboration with MAGI Euregio, Italy, for the diagnosis of rare genetic disease in seven probands and their families. The diseases/manifestations included ichthyosis, familial adenomatous polyposis, diabetes, syndromic craniosynostosis, fronto-temporal dementia, fragile X syndrome and ataxia. We obtained an overall detection rate of 57%. For 4/7 probands we identified a pathogenic or likely pathogenic variant, while for the others, the results did not completely explain the phenotype. All variants were confirmed by Sanger sequencing. Segregation of the variant with the affected phenotype was also evaluated.
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2. Li E, Weng X, Han Y, Wu S, Zhuang J, Chen C, Feng L, Zhang K. Asymmetry of brain functional activation: fMRI study under language and music stimulation. Chin Med J 2000; 113:154-158.
3. Sammler D, Koelsch S, Friederici AD. Are left fronto-temporal brain areas a prerequisite for normal music-syntactic processing? Cortex 2011; 47:659-673.
4. Osborne K, Gale A Bilateral EEG
Niyazi Acer, Nazan Dolu, Gokmen Zararsiz, Mehmet Sait Dogan, Kazim Gumus, Sevgi Ozmen, Ali Yucel Kara, Handan Soysal, Huseyin Per and Mehmet Bilgen
, Doganay S, Per H, Gorkem SB, Canpolat M, Bayram AK, Coskun A. Brain diffusion tensor imaging in children with tuberous sclerosis. Diagn Interv Imaging 2016; 97(2): 171-6.
21. Miller MI, Beg MF, Ceritoglu C, Stark C. Increasing the power of functional maps of the medial temporal lobe by using large deformation diffeomorphic metric mapping. Proc Natl Acad Sci U S A, 2005; 102(27): 9685-90.
22. Oishi K, Faria A, Jiang H, Li X, Akhter K, Zhang J, Hsu JT, Miller MI, van Zijl PC, Albert M, Lyketsos CG, Woods R, Toga AW, Pike GB, Rosa-Neto P