About me

Quantum perturbation theory and quantum scattering theory play a central role in the understanding of the theory behing medical radiation dosimetry.

In radiation oncology, we employ medical ionizing radiation (in radiotherapy) for the treatment of locoregional cancers. The said ionising radiations are either uncharged (photons or neutrons) creating secondary charged particles through interactions with atoms in the tissue (tumors and or surrounding healthy tissues) or charged (electrons, positrons, protons or heavy ions). However, in both cases, the outcome of the medical irradiation is always a flux of energetic charged particles within tissues and which lose their kinetic energy through interactions with the atoms within these tissues.

It is important to point out that there are two general categories of energy loss when ionizing radiation interact with matter (human body or tissues here in the case of medical physics or radiation oncology): one of these categories is called the radiative energy loss of bremsstrahlung and the other one is that of the energy loss of a moving charged particle as the result of collisions with atomic electrons.

• The radiative energy loss of bremsstrahlung is the process by which x-ray photons are created through the electromagnetic interaction between the charged particle and the nuclear Coulomb field and then, any absorbed dose (for diagnosis or for treatment) that ultimately results from this interaction will be the consequence of a subsequent interaction of the photon with an atom and the ejection of an atomic electron which decelerates and transfers energy to the tissues (tumors or healthy tissues). But, the radiative energy loss of bremsstrahlung has no importance in medical physics (diagnosis and treatment) because for electron energies of a few MeV, which are typical of Compton-scattered electrons set in motion by the megavoltage photons used in therapy, radiative energy losses are at least an order of magnitude less than those occurring through collisions; while for the diagnosis, (diagnostic nuclear medicine and radiology), the resulting electron energies are of only a few tens or hundreds of keV at most, and the radiative component of the total stopping power is several orders of magnitude less than the collision component, meaning, negligible. So, as a medical radiation physicist, I do not pay attention to this class of energy loss (radiative energy loss of bremsstrahlung). ​​​​​​​​​​​​
• The class of energy loss of interest in medical physics is the energy loss of a moving charged particle as the result of collisions with atomic electrons. Energy transfer to the tissues through these collisions leads to local energy deposition and to nonlocal energy deposition which is due to secondary recoil electrons with sufficient kinetic energy to travel from the original interaction site and deposit their kinetic energies at a distance. ​

So, what is the point here with this class of energy loss of interest in medical physics? The knowledge of the collision stopping power is of great importance for an accurate medical radiation dosimetry.

The collision stopping power is a unique dosimetric quantity providing it is not an empirical quantity, but instead, it is almost entirely a theoretical quantity. Therefore, that characteristic of the collision stopping power makes the theoretical foundations of calculating charged particle energy loss the foci of patient care and safety [1].

Now, from this point, a medical physicist in his/her daily routine work has two possible roads s/he can follow:

1. The easiest road is to just and simply extract stopping power data for elements and compounds of radiological interest from existing tables such as those provided in various reports of the International Commission on Radiological Units and Measurements (ICRU) or, from the website of the National Institute of Science and Technology (NIST). As usually done in practice, someone can easily use these already available data without understanding or appreciation of the theoretical developments which led to their calculation. So, is that easiest road good and honorable for a research medical radiation physicist? My personal answer is "no, it is not”.
2. The other road, the hardest and most complicated one for a research medical physicist interested or involved in the design of dosimetry devices or who uses Monte Carlo codes available for medical radiation transport calculations (Geant4, Fluka, ...) needs to understand the theory of collision energy loss in order to select the appropriate modeling to use and to be able to interpret the results. That is why Quantum perturbation theory and quantum scattering theory play a central role in the understanding of the theory behind medical radiation dosimetry.​

Modern megavoltage radiotherapy machines actually in use are capable of delivering advanced techniques, such as modulated arc therapy (Tomotherapy^®, VMAT, and RapidArc^®) and stereotactic radiotherapy (Cyberknife^® and Gamma Knife^®). But, the calibration of these machines is extremely challenging as they are based on new techniques that use beams not complying with conventional reference dosimetry protocols and therefore were given the designation nonstandard, denoting either small fields or modulated photon beams. Modern radiotherapy relies on accurate dose delivery to the prescribed target volume.

The International Commission on Radiological Units and Measurements (ICRU) recommends an overall accuracy in tumour dose delivery of 5 %, based on an analysis of dose response data and an evaluation of errors in dose delivery in a clinical setting. In fact, an accurate dose delivery to the tumour with external photon or electron beams is governed by a chain consisting of the following main links:

• Basic output calibration of the beam.
• Procedures for measuring the relative dose data.
• Equipment commissioning and quality assurance.
• Treatment planning.
• Patient set-up on the treatment machine.

And here comes the sweetest part known as the Cavity theory approach: To calibrate radiotherapy beams, the quantity of interest to medical radiation physicists is the absorbed dose at a point in water. To determine this quantity, measurements involve the use of a detector having a cavity (or sensitive volume) of finite dimensions which is not constituted of water. What initiated the need for a theory supporting absorbed dose measurement are the two following characteristics of a radiation detector: (1) the fact that the detector cavity is finite (i.e., not a point) and (2) the fact that it is not constituted of the surrounding medium. This approach is referred to as cavity theory. Cylindrical ionization chambers are used in clinical photon and electron beam dosimetry.

Therefore, in dose measurements, the relationship of the dose to water and the dose to air in water are based on the cavity theory [2] or the Spencer–Attix cavity theory.

Let present things in details as they are applied in a clinical routine: in modern radiotherapy techniques such as intensity-modulated radiation therapy (IMRT) and volume modulated arc therapy (VMAT), the quality assurance (QA) process is vital; so, careful pretreatment checks with a patient‐related QA protocol is a crucial step in the pretreatment process in radiation therapy, because of treatment plan complexity and high sophisticated technology behind the radiation delivery.

Several tools are available for a two dimensional evaluation, and among these tools we can find arrays of diodes, (e.g. MapCHECK) or arrays of ionization chambers, (e.g. PTW Octavius^®‐4D). For example, in a research project published in August 17, 2020, I worked with OCTAVIUS 4D system (PTW) [3]. This system consists of an ion chamber array embedded in a cylindrical phantom which, assisted by an inclinometer, rotates synchronously with the LINAC’S gantry. For VMAT plans (as it is the case for that publication), it measures planar dose distributions as a function of gantry angle in order to compute the resulting 3D dose distribution. There are two options for the ion chamber array:

Octavius 729 (general purpose) used in that paper and Octavius 1000 SRS (small field size, high resolution). With this setup, a perfect isotropic measurement geometry is achieved. The software acquires the dose inside the entire, cylindrical volume and allows dose planes to be extracted for further analysis. The measured data can be visualized in relation to patient contours and organ structures. OCTAVIUS 4D also allows the reconstruction of a volumetric dose distribution.

The (gamma) γ-metric is the standard technique used to evaluate the agreement between the planned (calculated) dose (in the treatment planning system –TPS, in the publication cited here, I employed the Pinnacle³ as TPS) and measured dose (in OCTAVIUS 4D) and can be obtained not only in a 2D array but also 3D, allowing the evaluation of the whole volumetric dose distribution. Plan dose perturbation (PDP) uses the difference between the measured and TPS calculated dose (TPS dose map) in phantom to perturb the 3D TPS calculated patient dose and create a corrected 3D dose distribution in the patient geometry. In Octavius 4D phantom, the PDP is performed using the VeriSoft software; (for comparison, another software named 3DVH is used for the same purpose for MapCHECK).

This method does not require a forward calculation algorithm. It relies on the measurement to create the perturbation matrix for correcting the TPS generated plan. This can be seen as follow: "a measurement is made on the phantom (Octavius 4D or MapCHECK for example) and compared to a TPS dose map using a software such as VeriSoft or 3DVH; and this results in a dose error map in the QA phantom in the specific plane of measurement and at the detector locations in the VeriSoft.

When the dose error is applied to the original TPS dose value (calculated or planned dose), the result constitutes the measured dose plan. The TPS dose calculation results from a dosimetry model that has been initially commissioned with the LINAC. Since the detector location in (x,y,z) coordinates is known with respect to the radiation source, the dose correction factor at each detector location can be applied to the TPS dose rays intersecting the detector and the target.

So, to summarize the above: in perturbation of a modeled dose, we have: a 3D dose function in the TPS that has been approved for treatment, i.e., unperturbed planed dose D(x,y,z), a delivery system or TPS modeling error that perturbs the planned dose function, i.e., perturbation operator “d(x,y,z)”, a QA phantom measurement of the dose delivery that results in a 3D correction technique that allows an approximate solution to the 3D perturbed dose D'(x,y,z), i.e., that which was delivered. Hence we get a good approximation to the Solution of the plan dose that has been perturbed, i.e., Plan Dose Perturbation (PDP) [4]. The presence of tissue heterogeneities, such as air cavities, lungs, bony structures, and prostheses, can greatly impact the calculated dose distribution.

The change in dose is due to the perturbation of the transport of primary and scattered photons and that of the secondary electrons set in motion from photon interactions. Depending on the energy of the photon beam and the shape, size, and constituents of the inhomogeneities, the resultant change in dose can be large. Perturbation of photon transport is more noticeable for lower-energy beams.

There is usually an increase in transmission, and therefore dose, when the beam traverses a low-density inhomogeneity. The reverse applies when the inhomogeneity has a density higher than that of water. However, the change in dose is complicated by the concomitant decrease or increase in the scatter dose [5].

With the above in mind, it appears that Monte Carlo simulations of the radiation transport and the radiation interaction with matter (human tissues in the case of radiotherapy) are extremely important and useful in medical radiation physics, particularly when the evaluation of radiation absorbed doses is considered.

This is the reason why Monte Carlo methods using Markov chain and Quantum field theory (QFT) are particularly appealing to me and constitute my primary research area of interest in Theoretical Physics.

References:

[1] McParland, B.J.. (2014). Medical Radiation Dosimetry: Theory of Charged Particle Collision Energy Loss. DOI: 10.1007/978-1-4471-5403-7. ISBN 978-1-4471-5402-0.​

[2] Bouchard, H., Seuntjens, J., Duane, S., Kamio, Y., & Palmans, H. (2015). Detector dose response in megavoltage small photon beams. I. Theoretical concepts. Medical Physics, 42(10), 6033-6047. doi:10.1118/1.4930053.

[3] Bogmis, A.I., Popa, A.R., Adam, D., Ciocâltei, V., Guraliuc, N.A., Ciubotaru, F. and Chiricuță, I.-C. (2020) Complex Target Volume Delineation and Treatment Planning in Radiotherapy for Malignant Pleural Mesothelioma (MPM). International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 9, 125-140. https://doi.org/10.4236/ijmpcero.2020.93012.

[4] Nelms et al. United States Patent. Patent No.: US 7,945,022 B2. Date of Patent: May 17, 201.

[5] Halperin, Edward C, David E. Wazer, Carlos A. Perez, and Luther W. Brady. Perez & Brady's Principles and Practice of Radiation Oncology. 2019. 7th Edition. ISBN-10: 1496386795.

In medical physics, radiotherapy is one of the main treatments for cancer, used in 50% of cancer treatments, and a multi-disciplinary field of research, mostly involving medicine, physics, mathematics, and computer science.

My goal when choosing to specialize in radiotherapy for my residency training program is to help make improvement in radiotherapy treatment delivery to cancer patients.

==> My current research areas of interest are the ​

• Markov Chain Monte Carlo methods
  • in Medical Radiation Physics,
  • in Quantum field theory (QFT);
• development of new treatment planning algorithms for radiotherapy;
• study of the radiobiological mechanisms underlying the FLASH effect for FLASH radiotherapy using the Geant4-DNA code.

Below are the abstracts of my 2 MSc's Theses and 5 selected academic projects in R and MATLAB programming.