Physics and mathematics of magnetic resonance imaging for nanomedicine: An overview

Abstract

Magnetic resonance imaging (MRI), magnetic resonance angiography (MRA) and magnetic resonance spectroscopy (MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the principle of nuclear magnetic resonance (NMR). Over the years, various laboratories around the world have applied different numerical techniques based on the Bloch NMR equations to solve specific problems in physics, biology, chemistry, engineering and medicine. The ultimate goal of any physician is to obtain maximum physical, biophysical, chemical and biological information on any tissue or cell under examination. This goal can be achieved by solving the Bloch NMR flow equations analytically. In this review, we present the basic principle of NMR/MRI in a way that can be easily understood by any researcher who needs an NMR concept to solve a specific medical problems. After a very brief history of the subject, a second order, non homogeneous, time-dependent differential equation derived from the Bloch NMR equation is presented. This equation has the basic intrinsic properties of MRI, MRA and MRS that can be extracted by means of classical and quantum mechanics for possible application in nanomedicine.

Keywords: Bloch flow equations; Rotational diffusion; Molecular dynamics of biological fluids; Nuclear magnetic resonance diffusion equation; Rotational correlation time; Spherical harmonics; Molecular flow

Core tip: Magnetic resonance imaging is one of the most powerful methods for investigating structural and dynamics of biological matter. Based on quantum mechanical principles applied to Bloch nuclear magnetic resonance (NMR) flow equations, we aimed to apply the analytical solutions obtained from the Bloch NMR flow equations to nanomedicine. This may trigger research towards the design of nano devices that capable of delivering drugs directly to specifically targeted cells, with the possibility of very early diagnosis of diseases and treating them with powerful drugs at the pathological site alone, reducing any harmful side effects.