The cross product between two vectors, , 3, is represented by a matrix multiplication [��]�� = �� , where:[�Ρ���]=(0?��3��2��30?��1?��2��10)The n-dimensional unit sphere embedded in n+1 is denoted as n = x n+1: xTx = 1. Members of SO(3) are often parametrized Dasatinib BMS-354825 in terms of a rotation, �� , about a fixed axis, e?.gif” border=”0″ alt=”e” title=”"/> 2, by the map, : �� 2 �� SO(3), defined as:u(��,e��):=I+sin(��)[e����]+(1?cos(��))[e����]2(1)Hence, a unit quaternion, q 3, is defined as:q:=(cos��2e��sin��2)=(q0q��)��S3(2)q?.gif” bor
For biomedical applications, superconducting quantum interference devices (SQUIDs) have been used for noninvasive anatomical and functional medical diagnostics involving imaging, and magnetic marker monitoring of disintegrating and non-disintegrating tablets, capsules and pellets in the gastrointestinal tract [1�C4].
The SQUIDs are the most sensitive magnetic field sensors currently available. They operate at low temperature based on two effects: flux quantization and Josephson effects, thus these sensors need a sophisticated infrastructure that increases their size and cost. Giant magnetoresistive Inhibitors,Modulators,Libraries (GMR) and Hall sensors have been used for medical diagnosis and bioscreening through electrical detection and biological labeling of superparamagnetic particles (magnetic beads) [5�C7]. Inhibitors,Modulators,Libraries In addition, GMR sensors have been used in hyperthermia therapy for cancer treatment. These sensors can estimate magnetic fluid weight density inside large tumors [8,9]. However, GMR sensors have temperature dependence and offset, and can be damaged by magnetic flux density close to 1 T [10].
On the other hand, magnetic field sensors based on magnetoelectric (ME) composites could be used for biomagnetic measurements in the picotesla regime [11�C15]. Recently, several research groups have studied the performance of these sensors [11�C21]. They use piezoelectric and magnetostritive laminate composites Inhibitors,Modulators,Libraries and could be Inhibitors,Modulators,Libraries candidates for noninvasive medical imaging like magneto-encephalography (MEG) or -cardiography (MCG) [11,13,14]. These sensors have advantages of low cost, and high sensitivity and high spatial resolution [11,14,15]. Their resolution can be increased with further improvements in sensor design, vacuum encapsulation, and the use of Microelectro-mechanical Systems (MEMS) or Nanoelectromechanical Systems (NEMS) technologies [11,14�C16].
Atomic magnetic field sensors are also near-room-temperature devices with suitable sensitivity Dacomitinib for biomagnetic applications such as MEG and MCG [17�C21]. They measure magnetic flux density by establishing an average electron spin polarization in an atomic vapour and sensing the resulting flux-dependent shifts in optical properties. These sensors can achieve sub-femtotesla (sub-fT) sensitivities and could be a promising non-cryogenic, low-cost candidate to replace sellekchem SQUID sensors.