Coil for Microscale Imaging

Abstract

The aim of this work was to design a coil for magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) to analyze the morphology of cells in vitro. This newly developed hardware, due to compatibility to the 1.5-Tesla MRI scanner (GE Healthcare, Boston, MA, USA), allows for the characterization of cell cultures in vitro. To adapt a designed coil on the 1.5-Tesla MRI scanner, some changes in hardware and software were carried out. The advantage of the designed receiving circuit is the ability to perform MRI with a resolution of 80 μm × 80 μm pixel size. Additionally, this coil can be used to visualize cell cultures and tissue sections, which, due to their small dimensions, could not be imaged on standard MRS and MRI coils at 1.5 Tesla.

1. Introduction

Magnetic resonance imaging (MRI) is a measurement technique which entered the field of medicine and changed its standards almost completely [1]. An MRI scanner is a type of diagnostic machine used to test and create images of every structure and organ inside the body. This measurement can be quantitative or qualitative. Briefly, MRI is built from magnet hardware and radio wave software to produce images on a computer. MRI does not use ionizing radiation. Images produced by an MRI scan can show with diagnostics quality the size and structure of organs, bones, muscles and blood vessels [2,3]. Most important is that MRI is a non-invasive imaging technology that produces three-dimensional detailed anatomical images.

The MRI scanner uses a special magnet that generates a strong static magnetic field in the area of examination. For this field to be useful, it must be as uniform as possible in the area of examination and constant over time. The requirements in this respect are extremely high. The spatial inhomogeneity of the static field cannot be greater than 1 to 10 ppm (~0.0001–0.001%) in an area with a diameter of about 40 cm. Obtaining such high field uniformity requires extraordinary precision in the magnet’s manufacture. The temporal drift of the field intensity should not exceed 0.1 ppm/h.

In the MRI technique, the unit of Tesla (1 T-10,000 Gauss) is used to describe the intensity of the magnetic field. The intensity of Earth’s magnetic field is about 0.05 mT (0.5 G), while that of a typical permanent magnet is about 0.5 T (5000 G). The static magnetic field in modern MRI equipment has an intensity in the range of 0.5 T–3 T, although equipment with a 4 T field is also used. The use of such strong magnetic fields is related to the signal-to-noise ratio (SNR) in the measuring part of the equipment. In addition to the useful voltage, the nuclear magnetic resonance (NMR) signal, there are various types of noise and interference originating from both the patient and the measuring and processing systems of the NMR signal. The ratio of the useful signal to noise determines the quality of imaging and is linearly dependent on the intensity of the magnetic field. Therefore, the higher the field intensity, the more accurately the NMR signal can be measured, and thus the better quality the image can be obtained [1,2,3].

A very important requirement for permanent magnets in MRI systems is the homogeneity of the magnetic field in the area of examination. This can only be achieved by the very precise arrangement of the magnet coils. This results from the well-known properties of the magnetic field generated by the coils. It is known that in the case of a single coil, the field is directed along its axis and can be expressed as a sum of the harmonics of the spherical fields. The first component of this sum is a constant representing the desired constant magnetic field. The subsequent harmonics correspond to the components of the field that disturb its spatial homogeneity. A system of two coaxial coils of the same diameter placed at a distance equal to their radius (Helmholtz pair) allows for the elimination of the first three harmonics. In this way, using, for example, six coils, the first twelve harmonics can be eliminated, obtaining the required field homogeneity around the coil axis. In practice, in order to obtain the highest possible field homogeneity, correction coils are additionally used. These are small resistive coils that correct the field distribution in the area of examination. During the installation of the MRI system, a map of the field distribution in the examination area is created, and then the operation of the correction coils is programmed in such a way as to eliminate previously detected inhomogeneities.

In order to create an MRI image, it is necessary to introduce information about the position of the source of this signal into the NMR signal. This is the only way to reconstruct the image of the examined object. Encoding information about the position of the NMR signal source is performed by introducing magnetic field gradients in three directions. The axis of the static field coils is assumed to be treated as the z-axis. For each direction in the Cartesian coordinate system, so-called gradient coils are introduced in MRI systems, i.e., coils generating a magnetic field gradient in each of the three directions [1,2,3,4].

The Z-gradient coil is usually wound on a cylinder surrounding the patient in such a way that in the center the turns occur far from each other, and as they approach the edge, they become denser and form a spiral. The method of winding the X- and Y-gradient coils is slightly more complicated.

Creating an MRI image requires creating fast sequences of gradient fields. This means quickly turning the coils on and off. The possibilities of fast switching determine the imaging parameters of the MRI system. In typical systems, the gradient coil has a resistance of about 1 Ohm, an inductance of 1 mH and must be switched from 0 to 10 mT/m in 0.5 ms. In this case, the current must change from 0 to 100 A in 0.5 ms, which results in the dissipation of about 20 kW of power. Since the switching moments in the measurement sequence are relatively short, heating of the coils is not a problem. The switching itself, however, places extremely high demands on the coil power supply systems.

RF coils generate a changing magnetic field BRF, which causes the magnetization vector to rotate, i.e., magnetic resonance imaging. They can also be used to measure transverse magnetization because its precession takes place in the XY-plane. RF coils used in MRI can be divided into three categories:

• transmit coils;
• transmit–receive coils;
• receive coils.

Transmitter–receive coils are used both to generate the RF electromagnetic field and to measure the RF energy coming from the imaged object. Instead of transmit–receive coils, pairs of coils (transmitter and receiver) are sometimes used. In the latter arrangement, the functions of providing excitation and measuring the NMR signal are separated. MRI scanners usually have multiple RF coils that are used for different types of images. The appropriate set of coils is used depending on the type of image to be obtained.

Current MRI scanners allow for the imaging of the human body in a way that is unattainable by other modalities, including computed tomography (CT) [4]. MRI scanners are particularly well suited to image the non-bony parts or soft tissues of the body. In CT, the negative side effect is the large dose of ionizing radiation to the patient. Another CT inconvenience is the relatively low tissue resolution, which MRI systems do not have [4]. Although MRI does not emit ionizing radiation like that found in X-ray and CT imaging, it does employ a strong magnetic field. MRI allows for the differentiation of soft tissues with a resolution that cannot be obtained with other methods. The possibilities of MRI are constantly growing [5]. However, one of the most difficult challenges that MRI technicians face is obtaining a clear image, especially when the measured sample is small. A multitude of sequences makes this modality unmatched in terms of diagnostic possibilities. Magnetic resonance spectroscopy (MRS) allows us to record changes in metabolism without the need to use other expensive methods [6]. Only a limited number of molecules with protons are observable in MRS (

Table 1. Principal metabolites measured by MRS in vivo.

Role	Metabolite
Glial marker	Myoinositol [7]
Cell membrane metabolism marker	Choline [8]
Energy metabolism marker serves as the reference peak as it is~constant	Creatine [9] Phosphocreatine [10]
Intracellular neurotransmitter marker	Glutamate Glutamine [11]
Healthy neuron marker	N-Acetyl-Aspartate [12]
Pyogenic abscess	Succinate [13]
Abscess	Acetate [14]
Meningioma and abscess	Alanine [15]
Ischemia, convulsions, tumors, and mitochondrial cytopathies	Lactate [16]
Necrotic tumor (high grade)	Free lipids [17]
Pyogenic abscess	Amino acids [18]

). MRS allows for the non-invasive detection of in vivo metabolites and allowed for the study of the molecular composition of cells and tissue. This is important to detect certain metabolites at the molecular level. All metabolites are involved in physiological or pathophysiological processes. MRS of metabolites can be performed and focuses mostly on hydrogen ¹H, carbon ¹³C, nitrogen ¹⁵N, phosphorus ³¹P, sodium ²³Na and fluorine ¹⁹F nuclei. However, ¹H MRS is the most widely studied in clinical MRI. The number of detected metabolites in cells and tissue samples is very dependent from the time to echo (TE) of the used sequence. Generally, the longer the TE (135 or 270 ms), the longer T₂ it takes for metabolites to be selected. With a short TE (15 to 20 ms), the spectrum will be more complex because of the greater number of superimposed peaks, producing a number of problems for quantification and interpretation. Table 1 presents the principal metabolites detected in healthy and diseased tissues in vivo (Table 1).

MRI and MRS have the potential to bring the full capabilities of the scanner to specified localized positions within small samples.

MRI is most often associated with examining patients. Equipped with a set of transmitting–receiving coils or only receiving coils, it is used to diagnose patients. Coils adapted to the anatomical regions being examined allow for precise diagnostics. Imaging is better the closer the object being examined is to the receiving elements of the coil. Therefore, it became necessary to construct a series of coils of different shapes. It is in them that the power and quality of imaging is largely hidden.

This work demonstrates some possibilities of measurements available through the combination of micro-coil receivers, strong gradients, and pulsing schemes designed to maximize the signal-to-noise ratio. Figure 1 presents the MR OPTIMA 360MR system manufactured by GEMS (Boston, MA, USA). This is a system with a magnetic field induction of 1.5 Tesla (T), which makes it a standard system in most hospitals. A magnetic field of this intensity allows for diagnostics at a very good level. This is ensured by the coil systems supplied with the delivery, which cover the entire area of the human body with their imaging. It should be added that these elements are refined to the limits of their possibilities; they are high-class electronic devices. Despite continuous progress in their design, such as moving the receiving circuits and analog–digital processing systems inside them, they cannot image very small objects with satisfactory quality and resolution. This paper describes the design of a single-channel coil for conducting MRI on cell cultures located in an “Ependorff” test tube.

2. Design

The design of the coil for MRI and MRS of small objects consisted of making receiving circuits geometrically matched to the tested volumes. A solenoid coil was made, inside which the tested objects were placed. The choice of the coil’s design and shape was dictated by its properties. The solenoid coil has a uniform magnetic field inside it. Its internal relatively high field homogeneity allows for conducting both MRI and MRS studies. A certain alternative to this design is surface coils; however it should be noted that they have very uneven sensitivity characteristics. The sensitivity of the surface coil decreases rapidly with increasing distance from its imaging plane. The sensitivity of the solenoid coil can be determined by the ratio of the B₁ field to the current.

$${\displaystyle \frac{B_1\left(y\right)}{i}}=n{\mu }_0\left[{\displaystyle \frac{0.5+\frac{y}{l_c}}{\sqrt{d_c^2+{(l_c+2y)}^2}}}+{\displaystyle \frac{0.5-\frac{y}{l_c}}{\sqrt{d_c^2+{(l_c-2y)}^2}}}\right]$$

(1)

where B₁—the radiofrequency field, y—the long axis of the coil, d_c—the diameter of the coil, l_c—the length of the coil; n—the number of coil turns, and μ₀—the magnetic permeability of vacuum (Figure 2). The field deviation in the vicinity of the solenoid edge is described by Formula (1) [19].

The basic parameter of the coil is inductance. It can be determined from an empirical formula that approximates the actual value relatively well. The result of the calculations is obtained in microhenries. In addition to inductance L, there are two more important parameters: resistance and capacitance C_L—these are parasitic parameters, but they affect the resonance frequency.

$$L={\displaystyle \frac{n^2{d}_c^2}{46d_c+100l_c}}$$

(2)

$$C_L=d_c(0.1126{\displaystyle \frac{l_c}{d_c}}+0.08+0.27\sqrt{({\displaystyle \frac{d_c}{l_c}})})$$

(3)

The entire circuit is tuned with variable value capacitors. The letter designations of the coil parameters are identical to the designations of Equation (1). The resonance capacitance can be determined.

$$C={\displaystyle \frac{1}{4{\pi }^2{f}_0^{2}L}}$$

(4)

The quality factor of a circuit can be determined in several ways. However, from a practical point of view, when tuning a resonant circuit, it is convenient to use the passband. This is because the tuning process itself is performed using a spectrum analyzer equipped with a tracking generator. The quality factor of a circuit can be defined as

$$Q={\displaystyle \frac{{\omega }_0}{{\omega }_{-3dB}}}$$

(5)

This is the ratio of the resonance frequency value to the band at a 3 dB signal drop. The choice of this method is dictated by the fact that it automatically takes into account all the elements of the circuit in a natural way. Calculating the quality factor of the circuit from RLC parameters is relatively difficult due to the fact that they are not known exactly. From a practical point of view, the values defined by Formulas (2) and (3) are approximate values. The actual values of inductance, capacitance and resistance are influenced by a number of factors: the length of the paths, the distance between the paths, the geometry of the paths themselves, the material from which the laminate was made and the geometry of the coil. The factors influencing the resistance value should also include the skin effect in the conductor material, i.e., copper from which all the conductive parts were made. Contrary to appearances, this is an important parameter because it affects the resistance value quite clearly. The skin effect itself is a phenomenon of current displacement to the outer part of the conductor. This displacement depends on the current frequency. To describe the phenomenon analytically, the Bessel function should be used. It is often used in physics to describe various phenomena. It has been thoroughly studied and described, and the extensive literature available allows for detailed familiarization with it. Bessel functions are a broad issue that significantly exceeds the scope of this article and will not be discussed here.

A feature of the skin effect is its dependence on frequency. Its increase causes a relatively rapid displacement of current to the outer parts of the conductor. Considering for simplicity a conductor with a circular cross-section, it is known that as a result of the phenomenon, high-frequency electric current flows as if through a “pipe”. Its highest values are on the circumference of the conducting element, while in the central part the current value is very small. It can be assumed with good approximation that the wall thickness of this “pipe” is

$$\delta =\sqrt{{\displaystyle \frac{2}{{\omega }_0\mu \sigma }}}$$

(6)

where ω₀—current pulsation, μ—a magnetic permeability of the medium of 1.25664 × 10⁻⁶ H/m, and σ—a specific conductivity of 5.86 × 10⁷ Ω∙m⁻¹. For the frequency f₀ = 63 MHz and the material copper, the value is δ = 8.3 μm.

Since the function describing the value of the current as a function of, for example, the radius of a circular cross-section wire is continuous, it means that the skin boundary is not a boundary beyond which the current does not flow. The number δ denoting the thickness of the skin layer is the distance from the edge of the conductor at which the current value drops to 37% of the maximum value. This results from Formula (7).

$$J_{\delta }=J_{max}\cdot e^{-1}$$

(7)

In the case of conductors with a circular cross-section, the analytical solution is relatively easy, while in the case of conductors with other shapes, e.g., rectangular, such a conductor is, for example, a conducting path, so it is convenient to use numerical methods.

The effect is one of the well-described problems in the scientific and technical literature, from which one can distinguish the items cited in the bibliography [20,21,22,23].

3. Build Instructions

The entire system was assembled on a PCB, which was made for this purpose using the photochemical method. This is a standard method of making printed circuits that allows for the easy production of very good quality connections on PCBs. The design uses elements dedicated to work in this type of application and in a non-magnetic version. The constructed coil was tested using a spectrum analyzer manufactured by RIGOL, type: DSA815. This is a device that can analyze waveforms in the band from 9 kHz to 1.5 GHz (Figure 3). It has a built-in tracking generator, the frequency sweep range of which can be changed depending on the needs of the analysis. Additionally, it is possible to adjust the power of the transmitted frequency. The relatively large number of available functions related to measurements, in particular measurements of the signal level, frequency and band ranges, makes it very useful for these applications. In the case of testing the coil, the analysis range from 30 MHz to 100 MHz was selected. The center frequency was set very close to the resonance frequency of the MR system, i.e., 63.88 MHz. The analysis shows that the transfer band of the receiving circuit is about 2.6 MHz. This is completely sufficient due to the narrow range of frequencies generated and received in the MR system. Figure 4 shows the transfer characteristic of the receiving circuit.

4. Operating Instructions

Figure 5A shows the coil with the material for testing, while part B shows the single-channel coil adapter to which the designed receiving circuit is connected with a coaxial cable with an impedance of 50 Ω using a BNC connector. Electronic components adapted to work in magnetic resonance systems were used to build the coil. The receiving circuit was assembled on a board manufactured using the copper etching method. This method is the standard for manufacturing printed circuits today.

5. Validation

Figure 6a shows the result of imaging using the designed and manufactured coil. The subject of imaging was a phantom (Figure 6c). Its design is based on 10 capillaries immersed in distilled water and placed in an “Eppendorf” tube. The capillaries were made of plastic. The outer diameter was 2.3 mm; the wall thickness was 0.3 mm; the inner diameter was 1.7 mm. The entire study was performed using the T2FSE sequence. The basic parameters of the sequence are FOV = 40 mm; acquisition resolution: 512 × 512; image matrix resolution: 512 × 512; TR = 3000 ms; T = 35 ms; and layer thickness: 2 mm. The spatial resolution in the imaging plane, calculated as the ratio of the FOV to the acquisition matrix, was 78 μm. This resolution is within the range of magnetic resonance microscopy. Figure 6b shows the measurement of the capillary diameter using a caliper.

Figure 7 shows the representative results of MRS performed using the designed receiver coil. The sample contained 0.75 mL of an aqueous solution of ethanol and Ophiobolin A (1:4). The study was performed at a time to repetition (TR) of 1600 ms, a time to echo (TE) of 55 ms and a voxel size of 7 × 7 × 7 mm³. The chemical shift, measured in ppm, corresponds to a change in the resonance frequency of the nuclei within the molecules as a function of their chemical bonds. Ppm is expressed as parts per million and represents a value that is independent of the amplitude of the magnetic field. The value of the chemical shift thus provides information about the molecular group carrying the hydrogen nuclei. The presence of an electron cloud constitutes an electronic shield that slightly lowers the B0 magnetic field to which the nucleus would normally be subjected to.

The relation of the resonance frequency of the studied molecule, the resonance frequency of the reference molecule and the chemical shift value in ppm is presented in Equation (8).

$$d_m={\displaystyle \frac{{\omega }_m-{\omega }_{ref} }{{\omega }_{ref}}} {10}^6$$

(8)

Abbreviation used in Equation (8) are

ω_m—the resonance frequency of the studied molecule;

ω_ref—the resonance frequency of the reference molecule;

d_m—the chemical shift value in ppm.

Presented below is the MRS hydrogen ¹H spectra of ophiobolin A obtained at 1.5 Tesla. The compound ophiobolin A is a sesterterpenoid that is ophiobolane with a hydroxy group at position 3 and two -oxo groups at positions 5 and 25, double bonds at positions 7–8 and 19–20, and an oxygen link between positions 14 and 18. Ophiobolin A is an oxaspiro compound, an enal, a cyclic ketone, a tertiary alcohol and a sesterterpenoid. Ophiobolin A is a chemical compound, specifically a metabolite produced by fungi of the Bipolaris genus, which attack crop plants, especially cereals. It is a calmodulin antagonist and has anti-cancer activity. In addition, it is considered a plant toxin (phytotoxin).

MRS spectrum quality is evaluated according to two main criteria: The first criterium is the signal-to-noise ratio (height of metabolite peaks in relation to background noise). The second is spectral resolution (peak width, which determines whether the different metabolites can be separated). MRS provides greater feasibility in the experimental and clinical practice setting, and the indications for MRS are multiplying. Usually, MRS yields diagnostic data for the following: tumoral pathologies with the detection of choline, myo-inositol (gliomas), free lipids (necrotic tumor: glioblastoma, metastasis…), alanine (meningioma) and lactate; demyelinating inflammatory pathologies with the detection of myo-inositol; infectious diseases with the detection of free acetate and amino acids in certain abscesses; a reduction in NAA and VIH encephalopathy with the detection of metabolic pathologies, such as myo-inositol and glutamine/glutamate in hepatic encephalopathy, lactate and diffuse cerebral distress; and finally epilepsy to diagnose brain maturation and degenerative diseases. The possibility to obtain MRS of small samples is valuable due to a few reasons: The small sample may be helpful in more situations because of the lower possibility of errors and increased validity. Small samples give quick results. A large number of small studies can be performed easily in different setups, and if they point toward the same direction, a safe, possibly more robust, conclusion can be drawn through a meta-analysis (Supplementary Materials). The small samples may be enough to show the presence of an effect but not for estimating the effect size.

6. Conclusions

The resolution in MRI is one of the key parameters in revealing the microstructures of objects. Enhancing the resolution has been the main interest of many MR researchers. As a result of the design and construction work, a coil for the imaging of the small samples was obtained. The creation of this device resulted in the possibility of the use of a standard MR clinical system for the imaging of small objects with a volume of only 1.0–1.5 mL. The created possibility to perform MRS study at 1.5 T significantly increased the potential scope of scanner application. The created electronic circuit is already another improved system for examining small objects. This work shows that clinical MRI systems are perfectly suited for conducting research from a range beyond their assumptions. Although they require hardware adaptation as well as the modification of the sequence, the benefits resulting from the adaptation are significant.