The present disclosure relates generally to magnetic resonance imaging (“MRI”), and more specifically, to exemplary embodiments of systems, methods and computer-accessible mediums for construe ting information regarding a distribution of thermal properties of tissue.
Magnetic resonance (“MR”)-based methods have been used which map the electrical property distribution of tissues inside the body. (See e.g., References 1 and 2). These methods can utilize cross-sectional measurements of magnetic fields, perturbed by the presence of the body, to deduce the spatial distribution of electrical conductivity and permittivity responsible for such perturbations. One previously-known method, Local Maxwell Tomography (“LMT”) (see e.g., References 2), in particular, can use measurements of field curvature in distinct MR transmit and receive coils to solve for coil-independent tissue and field related unknowns based on a self-consistent set of equations. However, such method cannot determine a distribution of thermal properties of an object.
Thus, it may be beneficial to provide exemplary systems, methods and computer accessible mediums that can construct a distribution of the thermal properties of an object, such as an anatomical structure, from MR thermometry and which can overcome at least some of the deficiencies described herein above.
An exemplary system, method and computer-accessible medium for constructing information regarding a distribution of thermal properties of an object(s), can be provided. For example, data related to a temperature of the object(s) can be received at multiple points in time and space at which a portion(s) of the object(s) can be heated or cooled. The information can be constructed based on a bio-heat, equation, which can be a Pennes' bio-heat equation.
The temperature data can be generated using magnetic resonance thermometry or positron emission tomography, and the temperature data can include information about a pixel or a voxel associated with an image of the object(s). The construction of the information can be performed by inverting the Pennes' bio-heat equation. In certain exemplary embodiments of the present disclosure, the data can be based on progressive temperature measurements of the portion(s) of the object(s). The construction can be performed by measuring spatial and temporal variations in the temperature measurement as the object(s) is heated or cooled.
In some exemplary embodiments of the present disclosure, the construction of the information can be performed by discrediting the bio-heat equation in a matrix form, where rows or columns of the matrix can correspond to different acquisition times of the spatial variations of the temperature data. The matrix can have a form of, for example:
According to further certain exemplary embodiments of the present disclosure, the information can relate to a perfusion of the object(s), which can be based on
The information can relate to a metabolic energy of the object(s), which can be based on
The information can also relate to a heat diffusivity of the object(s), which can be based on
The object(s) can include an anatomical structure, and the anatomical structure can be fat, muscle, or cerebellum.
In still further exemplary embodiments of the present disclosure, the information can be two-dimensional information, three-dimensional information, or four-dimensional information. The information can relate to (i) a time invariant perfusion, (ii) a time invariant metabolic energy, or (iii) a time invariant heat diffusivity.
These and other objects, features and advantages of the exemplary embodiments of the present disclosure will become apparent upon reading the following detailed description of the exemplary embodiments of the present disclosure, when taken in conjunction with the appended claims.
Further objects, features and advantages of the present disclosure will become apparent from the following detailed description taken in conjunction with the accompanying Figures showing illustrative embodiments of the present disclosure, in which:
Throughout the drawings, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components, or portions of the illustrated embodiments. Moreover, while the present disclosure will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments and is not limited by the particular embodiments illustrated in the figures, or the appended claims.
An exemplary system, method, and computer-accessible medium, according to an exemplary embodiment of the present disclosure, can be provided to construct and/or reconstruct a distribution of thermal properties of a body from MR thermometry, from positron emission tomography, or other suitable imaging mechanism, at multiple time points. Cross-sectional measurements (e.g., temperature measurements) of magnetic fields perturbed by the presence of the body can be used to determine the spatial distribution of electrical conductivity and permittivity responsible for such perturbations. The exemplary system, method, and computer-accessible medium, according to an exemplary embodiment of the present disclosure, can solve the Pennes' bio-heat equation (See e.g., Reference 3), or other equation (e.g., a bio-heat equation, a heat transfer equation, a heat transport equation, a heat equation, or a further bio-heat equation) to determine temperature measurements at distinct time points during the body's heating and/or cooling. Thermal properties of a body, which can be based on spatial and temporal data at multiple points, can be constructed and/or reconstructed by heating an object (e.g., plasma) and measuring spatial and temporal variations in temperature distribution using MR thermometry as the exemplary object cools down. The thermal properties of the body can also be constructed and/or reconstructed by measuring spatial and temporal variations in temperature distribution using MR thermometry as the exemplary object is heated.
Pennes bio-heat equation (See e.g., Reference 3) can relate temperature change to perfusion, diffusion, heat capacity and metabolic energy, and can be written, for example, as follows, in the absence of an external source of heating:
where, ρ can be the density of tissue in kg/m3, c can be the specific heat capacity in J/kg/C, k can be the thermal conductivity in W/m/C, T can be temperature, i can be time, w can be perfusion in mL/100 g/min and Qm can be the metabolic energy generated by the body, for example in
Equation 1 above can be discretized in space and in time (see e.g., reference 4), which can yield the following exemplary matrix equation, in which each row can correspond to a different acquisition time during cooling:
This exemplary formalism can utilize the fact that heat diffusion, perfusion, and metabolic heat terms can be a time invariant. The linear system of equations can have a solution using matrix
inversion, which can yield estimates of the heat diffusivity
and the quantities
The exemplary system, method, and computer-accessible medium according to an exemplary embodiment of the present disclosure can utilize an exemplary four channel transmit coil provided around an exemplary phantom with 3 different tissue compartments (e.g., cerebellum, fat and muscle), which can be modeled (see e.g.,
Qm
at procedure 330,
at procedure 325 and/or
at procedure 320), and which can be based on an exemplary least squares solution to the bio-heat equation. The images constructed and/or generated for each contrast can contain information about each pixel or voxel of the patient or phantom that is being imaged. Additionally, the value for each contrast at each pixel or voxel can be based on neighboring pixels or voxels (e.g., 7 neighbor voxels for a single voxel).
which can be measured in units of m2/s, can be referred to as “heat diffusivity.”
which can be measured in units of mL-m3-C)/(100g-min-J), can be measured in conjunction with the perfusion of tissue w, heat capacity c and the density of the tissue ρ.
which, can be measured in units of c/s, can be the ratio of the metabolic energy term Q over heat capacity c and tissue density ρ.
can be the ratio of the metabolic energy Q over the heat capacity c and tissue density ρ, with the addition of SAR over the heat capacity c.
The exemplary procedure, can described herein with reference to
The exemplary system, method, and computer-accessible medium according to an exemplary embodiment of the present disclosure, can facilitate a construction and/or reconstruction of tissue thermal properties based on progressive MR-based temperature measurements. In contrast to LMT, where incomplete measurements of RF magnetic fields require supplementing the set of electrical property unknowns with unknowns such as the absolute RF reference phase, the exemplary system, method and computer-accessible medium, according to an exemplary embodiment of the present disclosure, can provide all the interior measurements necessary to invert the discretized bioheat equation (see, e.g., Equation 1), which can describe the response of the system to thermal perturbation.
As shown in
Further, the exemplary processing arrangement 502 can be provided with or include an input/output arrangement 514, which can include, e.g., a wired network, a wireless network, the internet, an intranet, a data collection probe, a sensor, etc. As shown in
The foregoing merely illustrates the principles of the disclosure. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. It will thus be appreciated that those skilled in the art will be able to devise numerous systems, arrangements, and procedures which, although not explicitly shown or described herein, embody the principles of the disclosure and can be thus within the spirit and scope of the disclosure. Various different exemplary embodiments can be used together with one another, as well as interchangeably therewith, as should be understood by those having ordinary skill in the art. In addition, certain terms used in the present disclosure, including the specification, drawings and claims thereof, can be used synonymously in certain instances, including, but not limited to, e.g., data and information. It should be understood that, while these words, and/or other words that can be synonymous to one another, can be used synonymously herein, that there can be instances when such words can be intended to not be used synonymously. Further, to the extent that the prior art knowledge has not been explicitly incorporated by reference herein above, it is explicitly incorporated herein in its entirety. All publications referenced are incorporated herein by reference in their entireties.
The following publications are hereby incorporated by reference in their entireties.
This application relates to and claims priority from U.S. Patent Application No. 61/808,869, filed on Apr. 5, 2013, the entire disclosure of which is incorporated herein by reference.
Number | Date | Country | |
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61808869 | Apr 2013 | US |