MR based electric properties imaging for hyperthermia treatment planning and MR safety purposes - 2. Electric properties imaging

UvA-DARE (Digital Academic Repository)

MR based electric properties imaging for hyperthermia treatment planning and

MR safety purposes

Balidemaj, E.

Publication date

2016

Document Version

Final published version

Link to publication

Citation for published version (APA):

Balidemaj, E. (2016). MR based electric properties imaging for hyperthermia treatment

planning and MR safety purposes.

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2 Electric properties imaging

2.1 Electric properties

Tissue electric properties determine the behavior of electromagnetic fields in biological

tissue. Electric properties are tissue dependent and are described by the magnetic

permeability (𝜇), the permittivity (𝜀) and the electric conductivity (𝜎). Magnetic

permeability describes the degree of magnetization that a material obtains in response

to an applied magnetic field. As the magnetization of human tissue is negligible [28], the

permeability of free space (𝜇

) is assumed for all biological tissue types.

Tissue conductivity and permittivity are frequency and temperature dependent and are

determined by blood and water content, ionic concentrations [29] and ionic mobility in

tissue. Various studies have shown that tumor tissue generally has a higher conductivity

than normal tissue due to physiological differences between tumor and normal tissue.

These differences have been shown for breast tumors and normal breast [31–33],

normal liver, malignant liver tumors and cirrhotic liver [34,30], bladder tumors [35] and

gliomas and the normal brain [36].

Currently used values in patient models are mostly based on ex vivo measurements

of animal and human tissues [37,38]. Furthermore, there is a large variation in reported

values between the different studies shown in a review of the literature [39]. This

variation can be explained by the inclusion of tissues of various species and differences

in measuring conditions (tissue temperature, in vivo, in vitro and ex vivo). Due to practical

and ethical reasons, human in vivo electric property (EP) measurements are scarce. Only

easily accessible tissue types (e.g. skin, tongue) [37] and liver [30] have been measured in

vivo. Various studies have shown that in vivo conductivity values are higher than ex vivo

[40,41]. Hence, determination of in vivo electric properties has recently received

increasing attention since these properties are essential for more accurate SAR

assessment and subsequent computation of the temperature distribution. In particular

the use of an MR system is preferred for this purpose as it is a non-invasive technique

and can be easily integrated in the current clinical workflow.

2.2 Magnetic Resonance Imaging

Magnetic Resonance Imaging (MRI) is a non-invasive medical imaging technique which

is based on the interaction between radiofrequency (RF) fields and certain atomic nuclei

(i.e. 1H hydrogen) in the body when they are subjected to a strong magnetic field, which

is referred to as B0 field. In the presence of this magnetic field, the nuclear spins will

Chapter 2

precess around the B0 field at the Larmor frequency which depends on the strength of

the magnetic field as

𝜔 = 𝛾𝐵

(1)

with 𝜔 the Larmor frequency and 𝛾 the gyromagnetic ratio (𝛾

= 42.576 MHzT). To

create an MR image the transmitter RF coil generates a pulse at the Larmor frequency

of a certain nucleus corresponding to the present magnetic field strength. For instance,

the Larmor frequency of a 1H hydrogen nucleus is 64, 128, and 298 MHz when

subjected to a magnetic field strength of 1.5, 3.0, and 7.0 Tesla, respectively. The RF

pulse is an electromagnetic pulse consisting of an electric and magnetic field

component. The magnetic field of the RF, which is referred to as the 𝐵

field, is

perpendicular to the B0 field and, therefore, flips the alignment of the nuclear spins

towards the 𝐵

field. The degree of the flip angle is dependent on the shape of the

applied RF pulse. For a rectangular RF pulse the flip angle is computed by

𝛼(𝒙) = 𝛾𝐵

(𝒙)𝜏 (2)

where 𝐵

the magnetic field of the transmit RF coil and 𝜏 is the pulse duration.

After the pulse, the nuclear spins return to their original state through the longitudinal

and transverse planes. This process is called relaxation. The relaxation times in each

plane, referred to as T1 and T2, are tissue dependent and determine the intensity and

contrast of MR images. The signal generated by the nuclear spins during relaxation is

received by a receive RF coil, which in some cases is the same RF coil as used for

transmitting. The received magnetic field is referred to as 𝐵

.

To obtain high quality MR images, a homogeneous B1 field in the volume of

interest is required. A birdcage coil can produce a homogeneous field over a large

volume within the coil. The homogeneity of the B1 field decreases with field strength

and antenna arrays are therefore used to increase the homogenization at higher field

strengths. Phase and amplitude steering of the RF pulses is used aiming at increasing

the B1 field homogenization, however, care should be taken to prevent high electric

fields that might lead to unwanted tissue heating. Therefore, the acquisition of

patient-specific electric tissue properties is valuable not only for hyperthermia, but also for MR

safety purposes at high field strengths.

2.3 Electric Properties Tomography

The interaction between the magnetic component of the RF field and tissue can be

exploited to determine the electric properties. Electric Properties Tomography (EPT)

is an MR-based method that uses B1 maps to derive the electric properties at the Larmor

frequency [42–45]. EPT requires both the amplitude and phase of the 𝐵

field. In MR

systems the amplitude of the B1 field can be measured by various B1 mapping

techniques [46–48]. The phase of the 𝐵

field is not directly measurable. However, the

measurable MR signal phase (𝜑

) contains contributions from the transmit phase

(𝜑

= arg(𝐵

_{)), receive phase (𝜑}

_{= arg(𝐵}

1−

)) and resonance effects. The

off-resonance effects are reduced by using spin echo acquisition [49]. Using the modern

multi-transmit MR systems it is possible to separate the transmit and receive phases

[50,51]. Most clinical systems use single or double channel quadrature coil, therefore,

separation of the transmit and the receive phase is limited. In general, when using such

systems, the contributions of transmit and receive phases are assumed identical. This

assumption was investigated for the head at various field strength [43], and was shown

to hold up to 3T. The central equation of the EPT method is the homogeneous

Helmholtz equation

𝛻

_𝐵

𝐵

= −𝜇

𝜀

𝜀

𝜔

− 𝑖𝜇

𝜎𝜔 (3)

where 𝐵

is the complex transmit field (𝐵

= |𝐵

|𝑒

+

), 𝜔 is the Larmor angular

frequency, 𝜇

and 𝜀

are the permeability and permittivity of vacuum, respectively, and

𝜀

and 𝜎 are the unknown relative permittivity and conductivity of the object of interest,

respectively. Using the measured |𝐵

| and the 𝜑

distribution the conductivity can be

reconstructed by

𝜎 = 𝐼𝑚 (

𝛻

(|𝐵

|𝑒

)

|𝐵

_|𝑒

)

1

−𝜇

𝜔

(4)

and the relative permittivity by

𝜀

= 𝑅𝑒 (

𝛻

(|𝐵

|𝑒

)

|𝐵

_|𝑒

)

1

−𝜇

𝜀

𝜔

∙ (5)

Implementation of EPT involves spatial differentiation of the generally noisy B1 field,

hence, the quality of the reconstructed electric property maps depends on the

Signal-to-Noise Ratio (SNR) of the MR signal and the kernel size of the differential operator

[52]. Furthermore, a piece-wise homogenous medium is assumed in the derivation of

Equation (3) which affects the reliability of EPT at tissue boundaries [42]. To reduce

the boundary artifacts various ad hoc solutions have been introduced involving gradient

map of EP profiles in conjunction with a multi-channel transmit/receive array RF coil

[44] or by using arbitrary-shaped kernels based on voxel position [53]. In Chapters 3-5

the conventional EPT method is used. A novel approach to solve the boundary issues

is introduced in the next section and described in more detail in Chapter 6.

Chapter 2

2.4 Contrast Source Inversion – Electric Properties Tomography

(CSI-EPT)

CSI-EPT reconstructs electric properties in an iterative manner and is based on the

Contrast Source Inversion method by Van den Berg and Kleinman (1997) [54]. This

method was later applied for oil exploration purposes [55] and tissue properties

mapping [56] where EM measurements were performed outside the object of interest.

The unique situation that MR systems are able to measure fields inside the object of

interest brought us to the idea to use CSI in a completely new MRI inversion setting. In

this new constellation every measured voxel represents a virtual receiving antenna. The

large number of “receiving antennas” combined with measured data inside the object

of interest leads to a “less” ill-posed problem compared to the measuring conditions

the CSI method is currently applied upon.

CSI-EPT is based on the global integral representations for the EM field quantities

and therefore is less sensitive to noise since integral operators act on the measured field

data. Finally, this method is assumption-free regarding the local variations of electric

properties. The reader is referred to 6.2 for a more detailed description of the

implemented algorithm in this study. A more general description of CSI-EPT can be

found in 7.2.

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