Unified Dosimetry Quality Audit Index: an integrated Monte Carlo model-based quality assurance ranking for radiotherapy treatment of glioblastoma multiforme

In the present research, we have developed a Unified Dosimetry Quality Audit Index (UDQAI) decision support system supplemented with treatment planning systems for radiation oncologists. This will aid the radiotherapy treatment of Glioblastoma Multiforme and is based on the Integrated Monte Carlo Model (IMC). IMC model is a quality assurance strategy for the computation of total dose, scatter dose deposition at the GBM site and healthy tissues/layers within the brain. It is a combination of Proliferation-Hypoxia-Invasion-Necrosis-Angiogenesis-Radiotherapy-Quality Assurance model, Radiation-induced damage-Quality Assurance model, Boltzmann radiation transport, Talaraich Tournoux image coordinate system for positioning of the tumour from the CT image and GBM treatment environments/patient case reports. The IMC model was validated by recreating GBM patient treatment environments on a novel computational heterogeneous phantom, the Mathematical Anthropomorphic Brain (MAB) phantom. Dose computations accomplished through water phantom, tissue-equivalent head phantoms are neither cost effective; nor patient-specific and are non-customised and less accurate. Thirty-Eight patient-specific GBM treatment environments were recreated on the MAB phantom. MAB phantom synthesis requires mimicking real human brain tissues/layers. Open-source protein databases such as UniProt, Swiss-model and Peptide were atlas employed to compute the elemental composition of different brain layers/tissues. Brain layers and tissues were synthesised as slabs using the Constructive Solid Geometry technique within the MAB phantom on the Electron Gamma Shower radiation transport platform. Phantom slab dimensions were computed by superimposing CT scan images of the brain with GBM and associated comorbidities on Talairach-Tournoux coordinate system. Slab surfaces of the phantom were defined by constructive solid geometry approach using quadratic equations. Energy deposition inside different slabs of phantom is calculated by Analog Monte Carlo game. Computed total dose and scatter dose deposition within the tumour and normal tissues/brain layers were graded by UDQAI which ensures planned dose delivery to the tumour site for radiation-induced cancer cell death minimising healthy tissue damages. The results of the present experimentation show that the proposed framework is promising and outperforms other recent deep learning-based decision systems. Deep learning-based decision systems are a hidden process which is unaware of the physical transport process of charged particles. UDQAI classification of treatment environments predicts that 76.32% of the total environs deposited a substantial amount of dose to the GBM locus. During treatment, healthy tissues and brain layers receive a part of transported energy. This fact is reinforced by the average deviation at the GBM site −8.2% on the contrary, healthy tissues encircling GBM reported −3.909%. These encouraging results would pave the way for the development of a biomathematical tumour growth model and Monte Carlo radiation transport-linked decision assist algorithm for radiation oncologists in the near future.

In the present research, we have developed a Unified Dosimetry Quality Audit Index (UDQAI) decision support system supplemented with treatment planning systems for radiation oncologists. This will aid the radiotherapy treatment of Glioblastoma Multiforme and is based on the Integrated Monte Carlo Model (IMC). IMC model is a quality assurance strategy for the computation of total dose, scatter dose deposition at the GBM site and healthy tissues/layers within the brain. It is a combination of Proliferation-Hypoxia-Invasion-Necrosis-Angiogenesis-Radiotherapy-Quality Assurance model, Radiationinduced damage-Quality Assurance model, Boltzmann radiation transport, Talaraich Tournoux image coordinate system for positioning of the tumour from the CT image and GBM treatment environments/patient case reports. The IMC model was validated by recreating GBM patient treatment environments on a novel computational heterogeneous phantom, the Mathematical Anthropomorphic Brain (MAB) phantom. Dose computations accomplished through water phantom, tissue-equivalent head phantoms are neither cost effective; nor patient-specific and are non-customised and less accurate.
Thirty-Eight patient-specific GBM treatment environments were recreated on the MAB phantom. MAB phantom synthesis requires mimicking real human brain tissues/layers. Open-source protein databases such as UniProt, Swiss-model and Peptide were atlas employed to compute the elemental composition of different brain layers/tissues. Brain layers and tissues were synthesised as slabs using the Constructive Solid Geometry technique within the MAB phantom on the Electron Gamma Shower radiation transport platform. Phantom slab dimensions were computed by superimposing CT scan images of the brain with GBM and associated comorbidities on Talairach-Tournoux coordinate system. Slab surfaces of the phantom were defined by constructive solid geometry approach using quadratic equations. Energy deposition inside different slabs of phantom is calculated by Analog Monte Carlo game. Computed total dose and scatter dose deposition within the tumour and normal tissues/brain layers were graded by UDQAI which ensures planned dose delivery to the tumour site for radiation-induced cancer cell death minimising healthy tissue damages.
The results of the present experimentation show that the proposed framework is promising and outperforms other recent deep learning-based decision systems. Deep learning-based decision systems are a hidden process which is unaware of the physical transport process of charged particles. UDQAI classification of treatment environments predicts that 76.32% of the total environs deposited a substantial amount of dose to the GBM locus. During treatment, healthy tissues and brain layers receive a part of transported energy. This fact is reinforced by the average deviation at the GBM site −8.2% on the contrary, healthy tissues encircling GBM reported −3.909%. These encouraging results would pave the way for the development of a biomathematical tumour growth model and Monte Carlo radiation transport-linked decision assist algorithm for radiation oncologists in the near future.

Introduction
Works of literature in the present scenario of Radiotherapy Treatment (RT) of Glioblastoma Multiforme (GBM) could be broadly classified as (a) mathematical modelling of tumour response to radiation therapy and (b) solid phantom dosimetry.
Chaplain (1) presents mathematical modelling of the stages of Glioblastoma Multiforme (GBM) tumour growth and transition from avascular to vascular growth by taking into account tumour angiogenesis factor (TAF) which favours capillary sprout formation and growth. Enderling et al. (2) discuss tumour growth response to radiotherapy treatment taking into account the dispersal of glioma cells, proliferation as well as the loss term for defining the effect of external beam radiotherapy on tumour population. Roniotis et al. (3) focus on the application of the linear-quadratic model for simulating the effects of radiotherapy on an advanced diffusive glioma model considering the heterogeneous velocities of glioma cells in grey and white matter as well as brain atlases used for extracting the proportion of grey and white matter. Modelling Cellular response to radiotherapy as reported by Daphne et al. (4) elaborates the role of oncogenes and tumour suppressor genes, loss of p53 associated with tumour progression leading to disease recurrence and poor response to anticancer therapy. Stamatakos et al. (5) in their study emphasize a fourdimensional computer simulation model of in-vivo response to radiotherapy for wild-type and mutated p53 gene glioblastoma. Hathout et al. (6) feature the anatomical context of tumour response to radiation therapy pivoted on the diffusion-proliferation model of GBM growth and diffusion tensor imaging.
Boltzmann transport equations have been conventional for the interpretation of particle transport for several decenniums as elaborated by Lewis and Miller (7). Ahnesjo and Aspradakis (8) portrayed the classification of dose as primary dose, phantom scatter dose, containment charged particle deposition and head scatter dose. Gifford et al. (9) depict a deterministic method of solving LBTE equations by finite element multigroup discrete ordinates method using Atilla TM solver. Vassiliev et al. (10) brief cartesian grid-based Boltzmann equation solver Acuros TM with higher accuracy and speed than Attila TM . Duclous et al. (11) propose partial differential equation model for electron transport in tissue which gives better results in comparison to PENELOPE Monte Carlo code. Bedford (12) portrays a review of different solution methodologies for Boltzmann transport equations.
To summarise, the mathematical models developed by researchers for predicting tumour growth response to irradiation do not integrate a ranking for quantifying the absorbed dose within the tumour population. Such models do not record the extent of damage caused to healthy tissues and layers of the brain during radiation energy transport to the GBM locus. Complete modelling of tumour response to radiation therapy treatment requires coalescence of energy quality terms with tumour growth response to RT models.
Contemporaneous research directions in solid phantom dosimetry depict phantom synthesis using tissue-mimicking materials and quantifying dose deposition at various points using thermoluminescence dosimetery (TLD).
Ardekkani et al. (13) presented a breast dosimetry phantom with slab geometry synthesised of Cork and Plexi glass as materials. Thompson et al. (14) briefed a head and neck phantom for GBM dosimetry with 15MV 3D conformal radiotherapy incorporating a gel mixture of carboxy methyl cellulose and poly methyl methacrylate (PMMA) in a base of water and agar. Gurjar et al. (15) demonstrated chest dosimetry phantom using a Pinewood slab with dimensions 30 × 30 × 29 cm 3 . Shaiju et al. (16) illustrated the validation of cranial radiotherapy plans utilising PMMA phantom comprising slabs of thickness 10-40 mm. Fuse et al. (17) discussed the applicability of cork phantom with slab geometry for lung dosimetry.
Several validation phantoms are commercially available with different types detectors for External Beam Radiotherapy Treatments (EBRT). Most of them are synthesised from solid/plastic/gel mixtures/water and are not suitable for ensuring quality assurance (QA) for the RT of GBM. Precise solid phantoms like Lucy 3D (18) QA phantom is very expensive. Solid phantoms do not mimic the real human tissue but can only be considered as a substitute. Such phantoms are better suited for assessing beam quality.
First generation of Computational Anthropomorphic (CA) phantoms originated from the works of Fisher and Snyder at Oak Ridge National Laboratory (ORNL) using Constructive Solid Geometry CSG (19) technique. Since the development of anthropomorphic phantoms ICRP reference man (20) methodology was the set de facto standard for the synthesis of such phantoms.
A novel computational phantom for RT of GBM, the Mathematical Anthropomorphic Brain (MAB) phantom is synthesised by adopting slab geometry (21) using CSG methodology for assessing energy deposition within tissues/brain layers quantitatively and qualitatively. The phantom is unique and the first of its kind as it mimics a real human brain with tissue composition and treatment environments of GBM.

Materials and methods
This research defines an Integrated Monte Carlo (IMC) model for quantifying the radiationinduced tumour cell killing and laceration to healthy tissues. IMC model generates predictive assay from dose computations on a quality audit view, by defining a Unified Dosimetry Quality Audit Index. IMC model propounded as an amalgamation of novel Proliferation-Hypoxia-Invasion-Necrosis-Angiogenesis-Radiotherapy-Quality Assurance (PHINART-QA) model, Radiation-induced damage-Quality Assurance (RID-QA) model, Boltzmann radiation transport (BRT), Image coordinate system Talaraich Tournoux for positioning of tumour from the CT image and GBM treatment environments/patient case reports.
UDQAI-based quality audit workflow strategy in the treatment of GBM requires the synthesis of MAB phantom which mimics treatment environments mathematically in similitude to treatment planning systems. MAB phantoms synthesised reconceptualise the chaotic heterogenous treatment environments within the brain.
Thirty-Eight patient-specific MAB phantoms were recreated based on the heterogenity of tissues/materials. Each MAB phantom represents one environment of treatment, simulated on a Monte Carlo platform further irradiated with a 6-MV photon beam. Pareto 80/20 rule-based classification of treatment environments forecast cell death and damage based on a quality audit view. The curative effect for any tumour is possible only if the dose deposited at the tumour site does not go below a threshold value, this enumerates the need for scatter dose quantification within each tissue/tumour site. Predictive assays are generated based on quality audit indices which define the nature of dose deposition within tumour site and healthy brain tissues and layers. Figure 1 illustrates the proposed schema of the IMC model for the dosimetry quality of GBM RT.
Statistical predictive assays generated from simulation outputs hinged on UDQAI with value ranges of 'H (high)' and 'L (Low)'. UDQAI's for radiation-induced cancer cell death RQ g with its cellwise constituents for normoxic cells, hypoxic cells and vascular cells are correspondingly RQ gc , RQ gh and RQ gv . Radiation-induced damage (RID) governed by UDQAI RQ n with its constituents for grey-white matter (healthy tissue surrounding the tumour), pia mater, subarachnoid trabeculae, arachnoid, dura mater, skull and scalp likewise are RQ grwm, RQ pia , RQ subara , RQ arach , RQ dura , RQ skull and RQ scalp . Scatter dose UDQAIs assigned as SDQ gbm , SDQ grwm , SDQ pia , SDQ subara , SDQ arach , SDQ dura , SDQ skull and SDQ scalp correspond to tumour tissue, healthy tissue encircling tumour, pia mater, subarachnoid trabeculae, arachnoid tissue, dura mater, skull and scalp.

PHINART-QA model
The proposed system is defined mathematically for the formulation of MAB phantom based on chaotic tumour micro and macro environments for treatment. Chaotic environments of brain defined by Fisher-Kolmogorov-Petrovsky-Piskunov diffusion-reaction equation, endorsed for RT of GBM formulated by Giovanni Borasi and Alan Nahum (22) modified based on a quality audit perspective as depicted in Equation (1).
D g the spatially resolved diffusion coefficient, a tensor defined on account for the multitudinous geometry and cell migration, g t (x,t) denote the tumour cell density at position x and time t. The term ρ denotes the net proliferation per year, g 0 is the initial distribution of tumour cells. R(x, t)g t (x, t) denotes the tumour cell deviation due to treatment expressed as a function of radiotherapy quality factor RQ g which predict how good the transported energy through brain tissues/layers is deposited as dose at the tumour site. Radiotherapy quality audit factors are discussed in Section 2.1.4. Application of the diffusion-reaction model to the behaviour of normoxic, hypoxic, vascular and necrotic cells within the GBM domain to RT was grounded on the Proliferation-Invasion-Hypoxia-Necrosis-Angiogenesis-Radiotherapy (PHINART) model as formulated by Rockne et al. (23) and Noble et al. (24). Inclusion of Quality Audit (QA) factors reshapes PHINART to PIHNART-QA defined below by Equation (2) to Equation (6). PHINART-QA defines radiotherapy-induced cell death due to treatment 'R' (radiotherapy treatment loss factor) as a function of quality audit factors RQ g c , RQ g h and RQ g v .
Normoxic to hypoxic − α n g n g c Transition of hypoxic, normoxic and vasculature to necrotic Radiated cells to necrotic (4) Net proliferation of vasculature − α n g n g v Conversion of vasculature to necrotic − R(RQ g v )

Diffusion of angiogenic factors
Net consumption of angiogenic factors − λ a g a Decay of angiogenic factors The normoxic glioma cells g c diffuse at a rate D g (x) where x denotes positional dependence and ρ proliferation rate. The diffusion rate D g (x) can be enumerated as of diffusion into grey matter D gr (x) and white matter as D wm (x). Glioma cells migrate faster into the white matter with myelinated axons than in the grey matter D wm (x) > D gr (x). Their battle for existence and dwelling with the other cells, yearning for oxygen is determined by the vasculature supply to the tissue. If the oxygen dispensing becomes scarce normoxic glioma cells g c undergo metamorphosis to hypoxic state g h at rate β c . Further inadequacy of oxygen will lead to hypoxic cells becoming necrotic at rate α h . The above-mentioned two processes are congruous with the metabolic demands of the tumour, so that proliferation rate is proportional to β c and α h . Conversely, if the oxygen demand becomes plenteous at a later time hypoxic glioma cells will transfigure back to the normoxic cells at the rate γ h . Normoxic glioma cells produce angiogenic factors such as Vascular Endothelial Growth Factor (VEGF) at the rate δ c and for hypoxic the same being δ h . Diffusion and decay rates of angiogenic factors correspond to D a and λ a . Also, necrosis can happen to other viable cells when they come in contact with necrotic cells at a rate α n . Vascularisation is a key phenomenon that regulates the growth of the tumour, governed by the diffusion D v (x), and the migration and proliferation of endothelial cells μ e . F n denote the uncleared share of radiotherapy-induced necrosis.

RID-QA model
Healthy tissue/brain layers encircling tumours receive a fraction of transported energy. Rate of concentration change for damned cells X D (t) (25) within healthy tissue and layers of brain quantify the effect of transported energy, governed by quality audit index RQ n as depicted in Equation (7).

Boltzmann radiation transport model
Irradiation of MAB phantom for performing quality scrutiny in the treatment of GBM enclosed by heterogeneous environments of the brain is based on BRT. Considering the GBM tumour volume along with healthy brain layers/tissues as a medium, Boltzmann Radiation Transport Equation (BRTE) describes the conservation of energy during radiation transport through the medium. elucidates the Region of interest (ROI) consisting of tumour tissue. Figure 2 depicts the concept of ROI and Direction of interest (DOI) defined for particle transport within the MAB phantom. Photon (a) undergoes a Compton scattering event in the ROI and traverses in the direction of interest DOI. Since the energy possessed by the photon is less than the binding energy of the electron, the photon changes its direction of travel and its fluence gets added up along with the fluence of other particles. Photon (b) undergoes Compton scattering and ejects a bound electron and the photon is scattered away from the direction of interest. The ejected electron travels in the direction of interest, making its fluence additive to the DOI. Photon (c) is initially incident in the direction of interest but scatters away so that its fluence is not additive. Electron (d) initially present in the DOI, subsequently scattered away from the DOI thus reducing electron fluence. Electron (e) flings into the DOI and hence turns supplemental with the electron fluence.
The following definitions are elucidated; Ω γ Unit normal in the direction of interest, emanating from Region of interest for Photon after collision/scattering events. Ω γ Initial incoming photon direction before collision/scattering events. Ω e Unit normal in the direction of interest, emanating from Region of interest for Electron.
g Position vector defining point of importance within the treatment site consisting of tumour tissue. ψ γ Initial photon energy before collision /scattering event. ψ γ Photon energy of interest after collision /scattering events (final photon energy) ψ e Electron energy of interest ρ c (g) Density of atomic cores at position g. ρ e (g) Electron density at position g. φ γ (g, Ω γ , ψ γ ) Photon fluence at position g with direction Ω γ and Energy ψ γ φ e (g, Ω e , ψ e ) Electron fluence at position g with direction Ω e and Energy ψ e σ ∼ C,γ (ψ γ , ψ γ , Ω γ , Ω γ ). The differential Compton cross-section of a photon initially traversing with energy ψ γ in direction Ω γ undergoes Compton scattering and finally with energy ψ γ in a deflected direction Ω γ . σ ∼ C,e (ψ γ , ψ e , Ω γ , Ω γ ). The differential Compton cross-section of a photon initially traversing with energy ψ γ in the direction Ω γ undergoes Compton scattering, gives birth to an electron traversing with energy ψ e in a deflected direction Ω γ .
σ ∼ M (ψ e , ψ e , Ω e , Ω e ) The differential Moller scattering cross-section of an electron traversing with energy ψ e in the direction Ω γ undergoes Moller scattering and finally with energy ψ e in a deflected direction Ω e .
σ Mott (ψ e , e Ω e ). The differential Mott scattering cross-section of an electron traversing with energy ψ e initially in direction Ω e scatters finally into Ω e . σ tot M (ψ e ) The total Moller scattering cross-section for an electron travelling with energy ψ e σ tot Mott (ψ e ) The total Mott scattering cross-section for an electron travelling with energy ψ e BRTE equation for photons (26) applied within the ROI could be briefed as in Equation (8).
The LHS component ∇φ γ (g, γ , ψ γ ) in the direction ( γ ) denotes the gradient of photon fluence depends on the increase due to photons travelling in a different direction but which Compton scatter into the DOI and the decrease in the photons which scatter out of the DOI. The first term on the RHS represents the increase and the second term with total scattering cross-section represents a loss. BRTE for electrons was deduced by taking into consideration of Compton scattering event Moller scattering event and Mott scattering events briefed in Equation (9). e · ∇φ e (g, e , ψ e ) = ρ e (g) On similar grounds, the LHS term within the transport equation for electrons represents the gradient of electron fluence ∇φ e (g, e , ψ e ) which is the difference between the increase due to electrons scattered into the DOI and the decrease in the electrons scattered out of the DOI. The first term on the RHS side denotes the increase in electrons due to Compton scattering with differential cross section σ ∼ C,e . The second and third terms on RHS denote the increase in electrons due to Moller scattering and Mott scattering with differential crosssections σ ∼ M and σ Mott . The fourth and fifth terms with total Moller (σ tot M ) and Mott scattering (σ tot Mott ) cross-sections symbolise the loss of electrons. The dose deposited within the GBM site is computed by solving BRTE transport equation for photons and electrons. The only process that deposit energy within different layers and tissues within the MAB phantom is Moller scattering. All other processes transfer energy from the primary particles to the secondary particle which then continues to transport through the MAB phantom.
Absorbed dose within the GBM site D(g) and healthy brain layers and tissues D(n) briefed as in Equation (10).
Two sets of boundary conditions were formulated for solving the transport system of equations for both photons and electrons. Boundary condition 1: The MAB phantom surface subdivided into the domain of irradiation by photons and electrons, ROI and the region outside the ROI : = ∪ . The energy spectrum and the angular distribution of photons and electrons within the ROI are known. Boundary conditions depicted in Equation (11).
e (g, e , e )| = 0 e (h, ϒ , e ) for n · e < 0 e (g, e , e )| = 0 for n · e < 0 n , n being the outer normal of and . h is the position in the two-dimensional MAB phantom surface that accounts for intensity modulations in the irradiated surface. Boundary conditions are only defined for fluences going into the MAB phantom, because multiple scattering within the phantom can cause outward fluence. Boundary condition 2: Consistency of tumour mass defined as in Equation (12), such that tumour cell density within the ROI remains constant with a defined value 1.08 g/cm 3 ; no tumour cells leave or enter the site of irradiation .
Deterministic solvers and Monte Carlo simulations are the two alternative methods for solving the same BRTE equations. The deterministic mode of BRTE solving for practical geometries requires standard approximations such as spherical harmonics, Fokker-Planck approximation and continuous slowing down approximation. Since transport equations are continuous, solving the same requires discretisation of space-orientation-energy phase space. The continuous integral is approximated by a series of function evaluations, weighted by suitable weighting factors. Different types of discretisation methods are discrete ordinates (S N ), spherical harmonics (P N ), collision probabilities and nodal method. Discretisation and approximations lead to a reduction of computation time and an increase of systemic errors.
Monte Carlo method of solving BRTE proceeds via (1) constructing a stochastic model in which the expected value of a certain random variable is equivalent to the physical quantity to be determined and (2) simulating the entire physical process and can consider continuous energy, space and orientation, hence eliminating discretisation errors. Deterministic methods are computationally fast but may forgo accuracy, whereas Monte Carlo methods are computationally slow due to the simulation of a large number of particle histories but are arbitrarily accurate. Taking into consideration of the above factors, Analog Monte Carlo game is played for simulating the entire physical process of radiation transport within the MAB phantom.

Unified Dosimetry Quality Audit Index
Radiotherapy quality factor RQ g defines the effect of external beam radiotherapy on the tumour site, with its cellular dosimetry quality status factors RQ gc , RQ gh and RQ gv . Enumerating loss factor 'R' as a function of RQ g .
Radiotherapy quality factor RQ n defines the effect of external beam radiotherapy on normal healthy tissues /brain layers. Expressing RQ n as a function of D(n),

Statistical predictive assay
Statistical predictive assays were generated from simulated dose outputs using a Pareto distribution chart based on the segregation of treatment environments using UDQAI. UDQAI for radiation-induced tumor cell death is defined as follows. Treatment environments within the region to the left side of the intersection of the 80% cut-off mark and cumulative percentage line correspond to a substantial amount of total dose deposition leading to a higher amount of radiation-induced tumour cell killing. Environs inside the region to the right side of the intersection of the 80% cut-off mark and cumulative percentage line correspond to the marginal total dose deposition and lesser radiation-induced cancerous cell death.
for all treatment environments to the left side UDQAI for RID of healthy tissues/brain layers is briefed below. Environs within the region to the left side of the intersection of the 80% cut-off mark and cumulative percentage line in the Pareto distribution chart correspond to a substantial amount of total dose deposition resulting in a higher amount of RID. Environs within the region to the right side of the intersection of the 80% cut-off mark and cumulative percentage line record the marginal total dose deposition and lesser RID.
Scatter doses within the MAB phantom contribute a portion of the total dose deposited. Scatter dose quality audit indices estimate the amount of scatter dose within each tissue/brain layer.
Environs within the region to the left side of the intersection of the 80% cut-off mark and cumulative percentage line in the Environs within the region to the right side of the intersection of 80% cut-off mark and cumulative percentage line record the marginal scatter dose contribution.
SDQ gbm , SDQ grwm , SDQ pia , SDQ subara , SDQ arach , SDQ dura , SDQ skull and SDQ scalp = H for all treatment environments to left side SDQ gbm , SDQ grwm , SDQ pia , SDQ subara , SDQ arach , SDQ dura , SDQ skull and SDQ scalp = L for all treatment environments to right side. Figure 3 illustrates the proposed novel Unified dosimetry Quality Audit Index (UDQAI) index and statistical predictive assay for the treatment quality of GBM.

Designing mathematical anthropomorphic brain phantom: validating the IMC model
Energy deposition on the GBM site could be better assessed by simulating patient-specific treatment environments. The goal is achieved by recreating the treatment plan visualisation mathematically for GBM RT on the MAB phantom with density variations of each tissue/layer commencing from scalp, skull, periosteal dura mater, arachnoid tissue, subarachnoid trabeculae with CSF, pia mater, grey-white matter healthy tissue and tumour tissue. Open-source protein databases such as UniProt (27), Swiss-Model (28) and Peptide Atlas (29) were used to compute the elemental composition of brain layers/tissues. Figure 4 illustrates the data processing architecture for the IMC model.
Elemental and chemical composition refers to the weight percentage of essential biological elements: Carbon, Hydrogen, Nitrogen, Oxygen, Phosphorus, Sulphur (CHNOPS) and trace elements Magnesium, Potassium, Calcium, Sodium, Iron, Chlorine, Zinc, Copper, Selenium, Rubidium and Argon. Mean excitation energy of brain layers/tissues and nonbiological materials were computed from the NIST-ESTAR database (30). The different brain layers/tissues and non-biological materials were virtually resynthesised on the Monte Carlo radiation transport platform EGSnrc (31) using their density correction values and computed mean excitation energy. All simulations were run on a computer with the following configuration: Intel(R) Corei7 9750H CPU @ 2.60 GHz with 8.00 GB RAM and Nvidia GeForce GTX 1650 4 GB RAM. Table 1 catalogues the treatment environments with their codes.
Materials/tissue within the phantom are recognised with their codes as the first two letters representing the tissue, the next two letters representing the composition and the last digits representing lower energy threshold for the knock-on electrons and are preset to 0.521 MeV. Slabs representing tissue/brain layers/comorbidities associated with GBM RT within phantom are identified with their codes. Table 2 illustrates the same. Non-biological materials with their assigned slab codes are explained in the context. MAB Phantom geometry: The geometry module defines the conversion of complex threedimensional heterogeneous geometry of the head into a simple and variable dosimetry model, the stylised head phantom with cylindrical (r-Z) slab geometry. Stylised phantoms are fabricated using CSG methodology where slab surfaces within the phantom are mathematically formulated using linear and second-order quadratic equations. The transition from stylised head phantom to the MAB phantom requires in-depth categorisation of brain tissues and layers by computing individual amino acid compositions using a protein sequence database. Each MAB phantom consists of nine slabs representing different brain layers/tissues or non-biological materials.
Slab geometry is adopted for the phantom due to some of its beneficial features: (a) heterogeneity of brain tissues/layers can be dealt with; (b) to obtain a balance between attenuation factor, scatter components inside each brain layer/tissue and from other layers/tissues; (c) flexibility of dose computation at different brain layers/tissues and any number of further measurement points can be added; (d) flexibility to simulate different sizes of tissues /materials. In short, the MAB phantom is a stylised heterogeneous mathematical representation of the human head which when coupled with Monte Carlo radiation GBM associated calcification GBM 6 7 Remaining GBM after maximal resection and resection cavity filled with cystic fluid GBM 7 8 GBM with Alzheimer's plaque deposit GBM 8 9 GBM hiding behind haematoma GBM 9 10 GBM associated internal haemorrhage GBM 10 11 Remaining GBM after maximal resection, resected cavity air and bone flap replaced GBM 11 12 Remaining GBM after maximal resection, subdural cavity air and bone flap replaced GBM 12 13 Remaining GBM after maximal resection, subarachnoid space air, resected cavity air and bone flap replaced Computing r GGBM (gross tumour radius) = 2.4232 cm, h GGBM (gross tumour depth) = 2.4232 cm.

cm(expanded tumour depth after maximal resection)
Equivalent MAB Phantom CSG assumption 1: The brain phantom defined with calculated radius r GGBM = 2.4232 cm was chosen as the radius of cylindrical phantom R. The height h GGBM = 2.4232 cm, equivalent to the thickness of tumour, also defined as the depth of the slab represented as Z. Here R and Z can be defined as the measurement equivalents on the MAB phantom.
Equivalent MAB Phantom CSG assumption 2: When defining treatment environments with a resected cavity, the further expanded growth of the tumour after resection is taken into consideration such that h EGBM = 1.275 cm. The product of R and Z defines the 2D phase of the tissue /material in the phantom. All tissue/material measurements are normalised with respect to the product of R and Z.
Slab thickness calculation was derived from CT scan neuro images based on the depth of tumour tracked down using the Talairach Tournoux coordinate system (34). CT scan neuro images superimposed on the Talaraich Tournoux grid for manipulating the tumour tissue and grey-white matter thickness within the slab. Calculations are performed based on the gantry position assuming the photon beam incident on the frontal side and tumour location within the frontal lobe. Refer supplementary data [1] for a detailed illustration.
Depth of tumour measured from scalp = 4.41938 cm (CT scan data). Sum of the width of scalp, skull, periosteal dura mater, arachnoid, subarachnoid, pia mater and tumour tissue (known values) = 0.46738 + 0.7 + 0.  Ca = 0.000150, Fe = 0.000010 and Zn = 0.000010 was used to generate the SLSK521 slab with computed mean excitation energy 72.9 eV and assigned density value 1.084 gm/cm 3 . Total scalp depth Z = 0.46738 cm defined by taking into account the thickness of dermis, epidermis and hypodermis and galea (38). Sketch of a simulated treatment environment for GBM 1 is illustrated in Figure 5. SACF521 (44) is defined with a composition comprising 11 elements. Major components constituting CSF are amino acids, glucose, lactate, pyruvate, glutamine, glutamate, gammaaminobutyric acid (GABA), albumin, prealbumin, creatine phosphokinase (CPK), lactate dehydrogenase (LDH), Blood urea nitrogen (BUN), ammonia, water, sodium, potassium, chloride, calcium, bicarbonate, magnesium, phosphorous and iron (45,46). The weight fraction of each element present in each of the above constituent components is calculated by converting their milliequivalent to weight fraction and summed up to deduce the fractional composition of each element. Based on the above configuration of CSF  (49). Disturbance to the homeostasis of heavy metals in the brain could lead to the epigenetic metamorphosis of astrocytic glial cells that could act as a causative agent for GBM (50).
The composition of GLTT521 was derived by taking into consideration all the above aspects of interest. VEGF composition was derived from amino acid sequence Gly-Ala-Leu GBM 2 (54): GLTT521 denote IGBM with parameters same as above, R = 2.4232 cm and Z = 2.4232 cm. Impediment of fluid circulation to cranial space due to IGBM leads to static accumulation of CSF within the ventricle resulting in ventriculomegaly. Of the total CSF volume of 150, 130 mL circulates in the cranial space, 20 mL is retained within the ventricles. IGBM causes compression of interventricular foramen resulting in CSF accumulation which, lead to an increase of volume from 20 to 25 mL within the ventricles. Two-dimensional equivalent transformation reckoned an area of enclosed CSF within the ventricles to 8.5499 cm 2 . Normalising the ventricular area due to accumulation of CSF slab width was deduced as 3.5283 cm. VMCF521 epitomised ventriculomegaly associated with IGBM.
GBM 5: Density values selected for the ARCT521 slab were in the range of 1.025 gm/cm 3 with the compositional equivalence to GLCT521. The cystic fluid composition was (55) used to generate the material, as discussed above in case studies GBM 3 and GBM 4 with a calculated mean excitation energy 75.0 (eV). Arachnoid cyst dimensions 2.3 cm × 2.7 cm × 2.7 cm, (patient data) was transposed to two dimension with a surface area 6.5509 cm 2 . Computed slab dimensions were Z = 2.703 cm and R = 2.4232 cm. GBM 6 (56): GLCC521 slab within the phantom was synthesised with a density of 1.55 g/cm 3 , computed mean excitation energy of 191.00 (eV) as well as calcium composition. The size of the slab was defined based on patient data as 0.3cm × 0.3 cm, and normalised to the phantom dimensional frame yielded Z = 0.03714097 cm and R = 2.4232 cm. GBM 7: The density value of blood plasma 1.025 gm/cm 3 was assigned to the slab on presumption that oedematous fluid is a transudate derived from the blood through capillary fluid exchange. RCCT521; characterises resected cavity with cystic fluid and compositional equivalence to GLCT521.The computed slab dimension was R = 2.4232 cm and Z = 1.755 cm. GBM 8 (57): The gaugeable amyloid-β value was found to be greater in the brain of Alzheimer's patients when compared with the normal group of patients. Amyloid β fibrils of twofold thickness possess a density of 1.7 gm/cm 3

Results
Simulation of treatment environments that was recreated by adopting MAB phantom depicted variations of dose deposited in tumour tissue and healthy tissues. Biological tissues possessed a common build-up region from the scalp through the skull to the periosteal dura mater, followed by a dose absorption region arachnoid, subarachnoid, pia mater and grey-white matter (healthy tissues). Peritumoral oedema, arachnoid cyst and haematoma conjoined with GBM reflected less dose deposition at the tumour site. Trapped air cavities within biological tissues cause larger deviations to its succeeding and preceding slabs of materials/tissues henceforth less dose at the tumour site. Grey white matter healthy tissues encircling tumour receive maximum dose, with least average deviation. Scalp receives the least dose with maximum deviation. Negative deviations depict that the dose deposited is less than the reference dose. Individual simulation outputs of each treatment environment are depicted in supplementary data [2]. Computed dose deviations from MAB phantom simulation outputs are briefed in Figure 6. Statistical analysis portrays that the dose deposited at GBM tissues is very less than the reference dose. This ensures the dosimetric accuracy of the MAB phantom. The Pareto analysis quantifies radiation-induced tumour cell killing and damage to healthy tissues. Figure 7(a) portrays the Pareto distribution chart for total deposited dose corresponding to treatment environments for tumour tissue. Figure 7(b-h) sketch the same corresponding to healthy tissues encircling tumour, pia mater, subarachnoid trabeculae, arachnoid tissue, dura mater, skull and scalp correspondingly.
Pareto distribution chart for scatter dose quantifies the scatter dose deposition at the GBM site and within healthy brain layers/tissues during the transport of radiation energy to the target. Figure 8(a-h) illustrate the same.
Maximum and minimum doses recorded for each tissue within treatment environments derived from Pareto 80/20 classification based on UDQAI illustrated in Table 3.
Maximum and minimum scatter dose recorded for each tissue within the treatment environments derived from Pareto 80/20 classification based on UDQAI illustrated in Table 4.

Discussion
UDQAI assigned grading values L and H based on the dose perceived by the GBM locus. Simulated mathematical treatment environments and statistical analysis corroborate that Treatment environments GLTTGBM 2,9,22,11,13,16,24 and 18 with lesser dose deposition correspondingly quality audit factors RQ g c , RQ g h and RQ g v toggles to 'L' resulting in      GLTTGBM 2,9,22,11,13,16,24 and GLTTGBM 18 Pareto chart region to the right side of cumulative percentage line Marginal amount of dose delivered at GBM site with 21.05% of the total environs. Low -L Radiation-induced GBM cell killing is less GLTTGBM 21,23,12,10,37,4,1,14,35,34,6,8,31,32,33,27,26,28,29,30,20,25,15,17,38,7,19,3,GLTTGBM 5 Pareto chart region to the left side of cumulative percentage line Substantial amount of dose delivered at GBM site with 76.32% of the total environsRadiation-induced High -H GBM cell killing is more less build-up of necrotic camp for dead tumour cells. Necrotic camp build-up highlights as an indicator of the goodness of dose delivery, ensuring conversion of normoxic, hypoxic and vascular endothelial cells to apoptosis. Radiation oncologists should ensure that audit factors attain a value of 'H' ensuring considerable dose deposition. Table 5 exemplifies the predictive assay for the GBM site. Contrarily for healthy tissues and brain layers, Pareto distribution charts particularise the backdrops which cause maximum RID. The majority of treatment environs for healthy tissue (grey and white matter) encircling tumours are with higher dose deposition; RQ grwm assigned an index value 'H' is an indicator for radiation-induced laceration and meningiomas (RIMs). Leptomeninges recorded substantial dose deposition for treatment environs to the left side of the cumulative per cent line, switching RQ arach and RQ pia to an index value 'H' by paving way for cognitive impairment due to prolonged RT of GBM. Table 6 briefs quality audit indices and predictive assays to other brain layers/tissues. Scatter dose average deviation builds up from scalp to tumour site. Pareto 80/20 rule application to simulation output picturises treatment environments to the left of cumulative percentage line generates substantial contribution to scatter dose when compared to the right side. Scatter dose within patient even though feeble, plays a vital role in the curative effect of tumour due to its addition with primary dose Scalp records a lower value of scatter dose 1.08 E-13 and the tumour site reflects comparatively higher range 5.49 E-13, neglecting the marginal decrease from 5.81 E-13 at healthy tissue to 5.49 E-13 at GBM site. Table 7 brief scatter dose quality audit indices.
Neural networks (NN) learn the properties of a given training dataset. There is no a priori guarantee that a trained NN provides a convincing representation of radiation transport underlying the process. Monte Carlo particle transport simulations are entrenched in the underlying physics process. Table 9 enumerates a direct comparison of the proposed UDQAI decision support system and DL-based expert system for RT of GBM.
Various inherent shortcomings of DL-based algorithms need to be addressed such as the black box problem, quality and quantity of dataset and tediousness. The underlying reason for the black box anomaly is that neural networks are non-linear functions whose parameters are the neuron weights which are optimised to best represent training data. Neuron weights have no a priori meaning hence the process is opaque. DL-based ATP requires a comprehensive, rigorous and meticulous quality assurance program to ensure high consistency of generated treatment plans. It requires a blindfold comparison of automated and manual treatment plans. If the automated plans and manual plans are identical, they can be used by the radiation oncologist. It does not provide an insight to plan optimality.
UDQAI system has a distinct quality metric, the Pareto optimality for predicting optimum dose distribution. IMC being a well-defined physical process, it is governed by a performance index. Figure 9 illustrates the same. Performance index is categorised as statistical parameters.

Conclusion
We have demonstrated in this paper a simple UDQAI decision assist for radiation oncologists based on a mathematical approach mimicking treatment plans; with due consideration to the heterogeneity of brain tissues. Prime recommendations of the experimentation are briefed below.
76.32% of the treatment environments deposited a considerable dose to the tumour site and healthy tissue encircling tumour site, the remaining 21.05% reported marginal dose. This annotates that the planned dose will not be delivered at the GBM site, in turn depends on the charged particle transport process. Reduced dose deposition was reflected for treatment environs such as haematoma and pneumocephalus within resection, subarachnoid and subdural spaces. During the course of RT for the GBM site healthy tissues surrounding the GBM mass receive a considerable amount of dose deposition. Healthy tissue encircling tumour recorded an average deviation of −3.909% on the contrary, GBM site reported −8.2%. This can result in considerable damage to healthy tissues resulting in radiationinduced brain necrosis (RIBN). Once the onset of RIBN is initiated it becomes difficult to Average recorded deviations of −9.079% and −9.161% depict higher dose deposition but less than GBM mass and healthy tissues. Continuous exposure during GBM RT paves the way for radiation-induced intracranial aneurysms which lead to subarachnoid haemorrhage.
Arachnoid, Dura mater and Skull reflected similar irradiation patterns with 71.05% of environs with higher dose deposition and 26.32% with lower dose deposition. Average deviations within quite similar range −13.882% and −13.092% for arachnoid and dura mater depict dose build up has reached a stable value. The transition of dose deviation from a value of −40.528% (Skull) to −13.092% (Duramater) picturises the intensity of dose build up.
Conclusively, only three quarters of the total treatment environs were able to deliver the planned dose and the remaining one-quarter reported a lesser value than the threshold. All the treatment environs including substantial and marginal deposit reasonable dose to healthy tissues during the transport process. 76.32% of the total environs delivered considerable scatter dose to the tumour site. 21.05% reported marginal scatter dose. Less scatter dose deposition was reported for Real-time computed tissue/material composition as input From the above survey the dataset consists of CT/CTMRI fusion images with delineated targets and OAR's 3.
Microscopic approach with statistical prediction Macroscopic and peripheral approach. 4.
Well defined transparent physical process Black box system 5.
Efficacy depends on the number of particle histories and the Monte Carlo transport parameters. Simulations performed with 1×10 8 particle histories Efficacy based on the quality of dataset. larger dataset required for more accurate results. Accuracy of results depends on the correct balance between bias and variance 6.
Computation time proportional to the number of particle histories simulated. More number of histories result in more accurate results.
Training time depends on the input dataset size 7.
Tumour growth response to RT biomathematical model linked decision system Treatment plan-based decision system 9.
Self-generated datasets based on tissue composition DL based ATP approach lack quality datasets. Analysis of the above-mentioned ATP research works depict that the available dataset < 300. Unavailability of enough data for model training and testing results in overfitting due an excessive complex model produced from limited dataset 10.
Can predict optimality of dose with Pareto analysis Lack of predicting optimality or selecting a clinically acceptable treatment plan 11.
Quantifies total dose and scatter dose inside each brain layer /tissue No quantification of total dose and scatter dose. Selects a best fit treatment plan based on dataset 12.
Single architecture system. Users can define the composition of tissues/materials and the Monte Carlo particle transport parameters Wrong selection of neural network architecture results in underfitting or overfitting of the model. Several regularisation methods need to be incorporated GBM RT environs with arachnoid cyst, abscess, IGBM, haematoma, pneumocephalus and presence of titanium and PMMA cranial flaps. Healthy tissues encircling GBM suffer a higher scatter dose deposition and have the same treatment environment percentile categorisation as GBM tissue.

Future scope
Out of the total 38 GBM treatment environs only 76.32% was able to deliver substantial dose, this figure could decrease considerably in the case of deep-seated GBM. An extended MAB phantom with more virtually synthesised tissues/brain layers could assess the nature of dose deposition within deep-seated GBM and the RID as they are embedded in the eloquent cortex.
To this end, this study may be further expanded in the future to different chaotic tumour microenvironments. CA phantoms of different organs could predict the nature of dose deposition for tumours within it. The study formulated above is an inexpensive strategy when compared to solid-tissue equivalent phantoms. Further patient-specific CA phantoms depending on age and disease conditions such as cholesterol and blood sugar could be formulated by creating a novel database of tissue composition. A novel IMC model-based predictive treatment planning algorithm could be formulated which employs biomathematical tumour growth response to RT and RID to healthy tissues/brain layers.This could forecast the nature of dose deposition and damage to tissues without subjecting the patient to Computed Tomography scanning frequently for assessing tumour volume shrinkage. The aformentioned results in dose reduction to healthy tissues during Computed Tomography and could balance health risks and medical benefits.

What is known
-Biomathematical models for GBM response to radiotherapy -Biomathematical models for radiation-induced tissue damage -Treatment environments of GBM -Analog Monte Carlo game for radiation transport -Open-source protein database and radiation transport software

What was found
-Biomathematical models linked to Monte Carlo radiation transport by introducing quality audit factors to predict the nature of dose deposition at GBM site by a novel MAB phantom recreated from treatment plans and open-source software and database. -Quantified radiation-induced damage to healthy brain tissues.
-Defined a unified dosimetry quality index for GBM RT.
physical Measurements laboratory ESTAR program for stopping power range of electrons and EGSnrc open-source radiation transport software.

Code availability
Self-developed codes used for EGSnrc open-source software and NIST data.

Notes on contributors
Praveen Kumar C. is a research scholar in the Department of Biomedical Engineering, Indian Institute of Technology (BHU),Varanasi, Uttar Pradesh, India. He has worked as Assistant Professor in the Electrical And Electronics department of NSS College of Engineering, Palakkad, Kerala. His research area is Medical Physics and he started working on computational modelling of energy transport within cancer systems using phantoms for quality assurance in Radiotherapy and Diagnostic Radiology. His areas of interest include Electromagnetic Spectrum interaction on biological and non-biological materials and Cold Plasma application in cancer therapy. Saju Bhasi is currently working as Additional Professor in the Department of Radiation Physics, Regional Cancer Centre, Thiruvananthapuram, Kerala, India. His clinical expertise and area of research include dosimetry, fabrication of dosimetry tools and quality assurance. He has several research papers to his credit.