1. Diffuse Optical Tomography (DOT)

2. Magnetic Resonance Thermometry (MRT)
     PRF of Water  

3. Photo-magnetic Imaging (PMI)
     Forward Problem    Inverse Problem    Procedure:  

4. Applications

5. References

Photo-magnetic Imaging (PMI) is a novel form of imaging that is derivative from Diffuse Optical Tomography (DOT). PMI uses a heat diffusion model and combined photon propagation to determine spatiotemporal temperature distribution due to light absorbed.^[1] By capturing 3D temperature distribution in a medium using a technique known as Magnetic Resonance Thermometry (MRT), PMI can bypass traditional spatial resolution limitations that DOT faces. This effectively allows PMI to image the optical contrast at MRI spatial resolution.

Diffuse Optical Tomography (DOT)

DOT is a non-invasive imaging modality that uses near-infrared light to primarily quantify tissue absorption properties. This is done using multi-wavelength measurements, a technique that allows for identification of the spatial distribution of physiologically significant chromophores. DOT can thus provide important functional information with high sensitivity. Examples of these include total hemoglobin and oxygen saturation maps. On a practical level, DOT’s high sensitivity has allowed for advances in a variety of applications, most prominently in breast cancer imaging.

While DOT remains a valuable technique in imaging, the spatial resolution remains low due to the non-unique solution of the DOT inverse problem. This problem makes the solution especially sensitive to measurement noise. One problem with DOT is that measurements is only obtainable at the boundary. Any internal measurements would require the use of invasive methods.

Magnetic Resonance Thermometry (MRT)

Magnetic Resonance Thermometry (MRT) is a non-invasive temperature measurement technique for real-time temperature monitoring. The most commonly used methods for MRT take advantage of molecules with higher proton resonance frequency (PRF) temperature sensitivity. In most cases, this molecule is water. The PRF of water exhibits temperature linearity for physiologically relevant temperatures as well as has a thermal coefficient that has almost no dependence on the type of tissue. These features allow assessment of temperature change even after the tissue has coagulated.^[2]

PRF of Water

The resonance frequency of a nucleus in a molecule is determined by the local magnetic field it experiences. The field at the nucleus can be written as

Here, s is the shielding constant and is dependent on the chemical environment.

The resonance frequency can be determined using the magnetic field and shielding constant. This results in:

As mentioned previously, the temperature dependent components remain linear in the desired temperature range. It can be expressed as:

Photo-magnetic Imaging (PMI)

Forward Problem

The proposed framework for PMI consists of two parts - the forward problem and the inverse problem

The forward problem can then once again be broken into 2 parts: (1) defining laser light propagation in tissue and (2), defining thermal propagation in tissue due to laser heating.

Photon propagation in tissue can be described by the following equation:^[5]

where is the diffusion coefficient (mm^-1) defined by , is defined as the photon density (W/mm²) while and are the absorption and reduced scattering coefficients of the medium respectively. defines the light source distribution.

Thermal propagation within tissue can then be described by the following equation:^[6]

where represents the thermal energy absorbed from laser heating and has a dependence on the light fluence rate and the absorption distribution.

In PMI, Pennes' bio-heat thermal model shown below is used to model temperature distribution dynamics in tissue:

where is density (g/mm³), is specific heat (J/g°C), is thermal conductivity (W/mm°C), is blood specific heat (J/g°C), is supplying arterial blood temperature (°C) and is thermal energy due to laser irradiation.

When solving for the equation above, the heat sink term is neglected and defined for applications in the absence of blood perfusion.

Since the boundary condition for the heat transfer is complex, only heat convection at the boundary is considered, giving the following equation:

Since boundary condition for heat transfer is complex, only heat convection at boundary is considered, giving us the equation:

where is the heat transfer coefficient (W/mm²°C) between the surface and surrounding medium and (°C) is the temperature of the surrounding medium

Finally, a finite element method (FEM) is used to solve the partial differential equation. Assuming the surrounding temperature to be 22°C allows for simplification of the differential equation to the weak form of the heat transform equation:

Solving this equation gives the solution of the temperature equation:

Inverse Problem

To solve the inverse problem for PMI, the following function is used in order to minimize the difference between the calculated temperature map and measured temperature:

Where i is the number of sources and j is the number of temperature measurements

Procedure:

1. is created using the forward solver
2. The spatial distribution of is used to minimize the error function between and the calculated temperature measurement
3. Different meshes are used for the forward solver and the inverse solver
4. A dual coarse mesh is used
5. can be calculated using the Levenberg-Marquardt method

where,

Applications

At the onset, PMI had most of its applications in pre-clinical imaging due to its unproven capability of probing deep enough into the sample. However, more recent studies have shown increased confidence in PMI applications in the realm of clinical management of cancer. By increasing illumination ports and improving MRT parameters, the probing depth of PMI can be enhanced and thus be applied to the development of smart tumor targeting probes and management of cancer.^[8] In particular, breast cancer monitoring is especially relevant due to previously present problems in DOT imaging such as lowered accuracy when target lesion is not visible from the anatomical image or when optical contrast does not correlate with anatomical contrast^[9]. PMI resolves this issue by directly measuring temperature elevation induced by optical contrast through MRT techniques, thus providing higher optical contrast and resolution.^[10] The next step for PMI is to hopefully expand its applications to in vivo experiments by reconstructing quantitative optical absorption maps by modeling heat diffusion in tissue and photon migration.^[11]

References

• Norodom Yukanthor
• Noroeste de Minas (mesoregion)
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• No Role Modelz
• No Romeo No Juliet
• No rompas más (mi pobre corazón)
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• No Room at the Inn (The Leftovers)
• No Room (song)
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• No Roots (Alice Merton song)
• No Roots (disambiguation)
• No Roots (EP)
• No Roots (Faithless song)
• No Roots (song)
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• Norops biporcatus
• Norops conspersus
• Norops garmani
• Norops grahami