Monaco and GPUMCD: Dose to Medium, Dose to Water, and Clinical Validation

Highly complex radiotherapy requires dose calculation engines that can faithfully represent tissue heterogeneity, fluence variations in modulated fields and penumbras in challenging geometries. For decades, deterministic algorithms such as pencil beam convolution (PBC) and collapsed cone (CC) dominated treatment planning systems (TPS), as they offered computational speed compatible with clinical flow. The advent of stochastic Monte Carlo (MC) in commercial TPS has altered this balance: by explicitly simulating particle-to-particle transport of photons and electrons, MC eliminates geometric approximations that compromise accuracy in low-density regions, tissue-bone interfaces, and small-diameter fields.

The GPUMCD (Hissoiny et al., 2011) was created as a GPU-oriented Monte Carlo platform to transport coupled photons and electrons in voxelized geometries. Clinical literature includes a research version of Monaco evaluated in 2016 and, more recently, Elekta One Planning with GPUMCD, released in March 2025 for treatment planning on Versa HD accelerators. Reported dose magnitude and available resources depend on implementation and version: the 2026 commissioning study, for example, recorded Elekta One Planning calculations as dose in water.

This article reviews, for medical physicists, dosimetrists and radiation oncologists, the physical rationale for GPUMCD, its comparison with other algorithms available in Monaco and competing systems, and the current state of the evidence on clinical performance in heterogeneous tissues. The commissioning procedures described in recent literature and the criteria for choosing calculation parameters in different clinical scenarios are also discussed.

---

What is GPUMCD and why it was created

GPUMCD is a Monte Carlo engine accelerated by GPU whose clinical integration must always be described with the version of the product evaluated. Its origins date back to the recognition that conventional MC methods could require times that were incompatible with clinical flow. The massive parallelization strategy on GPU made it possible to reduce this time substantially, although actual performance depends on hardware, geometry, grid, statistical uncertainty, and implementation.

The development of GPUMCD has been documented in detail by Hissoiny et al. (2011), who describe a new platform for coupled transport of photons and electrons between 0.01 and 20 MeV and its validation results against EGSnrc. GPUMCD and XVMC are distinct Monte Carlo engines; it is not correct to present the first as a simple rewriting or direct descendant of the second. GPU adaptation is technically demanding because particle histories have different branching and memory access patterns.

The clinical motivation was twofold. First, offer an MC algorithm as a routine tool, not just a spot check. Second, make Monaco competitive against advanced deterministic systems such as Acuros XB (Eclipse, Varian) — a method for solving the linear Boltzmann transport equation (LBTE) — and AAA, which at the time already offered acceptable calculation speed with greater accuracy than pencil beam in heterogeneities.

---

How coupled photon-electron transport works in the GPU

MC transport of photons in GPUMCD follows established physics: for each photon, the mean free path to the next interaction (photoelectric effect, Compton scattering or pair creation), the geometry of the interaction and the energy of the secondary products are drawn. Electrons generated in the process are then transported using the condensed history (CH) model, which groups multiple low-energy Coulomb interactions into stochastic macroscopic steps, preserving the angular and energy distribution at the end of each step.

The GPU implementation requires that the code be structured so that parallel threads process different particle histories — not different steps of the same history. This is due to the SIMD model (Single Instruction, Multiple Data) of GPUs: parallel executing divergent paths undergo serialization. The solution adopted in GPUMCD (Hissoiny et al., 2011) is to maintain a pool of active particles, so that when one story ends another is immediately started, minimizing idle parallel .

The CT voxel grid and the assignment of densities and materials form the geometry used by the transport. The exact HU→density conversion and material classification mechanism is specific to the TPS implementation and must be verified in the documentation of the commissioned version. This step has direct implications for accuracy, especially in lung, bone and high-density materials.

The statistical uncertainty of the final result is controlled by the number of simulated stories (or the variance per voxel), configurable by the user in Monaco. Reducing uncertainty from 2% to 1% requires, in principle, four times as many stories, implying more calculation time. The choice of an appropriate threshold is, therefore, a compromise between accuracy and time — a topic returned to in a later section.

---

GPUMCD, XVMC and collapsed cone: differences that matter

Pencil beam, collapsed cone, XVMC and GPUMCD represent calculation families found in different TPS, versions and studies. XVMC and GPUMCD are both Monte Carlo, but use different implementations and beam models. A valid comparison must inform the product, version, machine and process of commissioning, without assuming that all these engines coexist or occur in the same way in any installation.

The table below summarizes the conceptual differences relevant to clinical practice.

Characteristic	Pencil Beam	Collapsed Cone	GPUMCD (Monte Carlo)
Electron transport	Implicit, pre-calculated kernel	Implicit, kernel in water	Explicit, condensed history
Heterogeneities	1D correction (WWTP/Batho)	Limited 3D correction	Explicit transport in the real environment
Lung dose	Frequently overestimates	Improvement in relation to PB	Documented improvement; validates locally
Small fields (<2×2 cm)	Often underestimates fluency	Kernel dependent	More complete physical modeling
Calculation time (VMAT)	Seconds	Minutes	Minutes (GPU); hours (CPU)
Output magnitude	Depends on implementation	Depends on implementation	Depends on product and version
Statistical uncertainty	None (deterministic)	None (deterministic)	User controllable

Monaco’s collapsed cone differs from its namesakes in other systems (such as Oncentra or Eclipse/AAA) by implementation details kernel. There is no single standardized “collapsed cone” — each vendor implements the technique with specific approximations that affect behavior at interfaces and in non-coplanar beams. Direct comparisons of accuracy between systems should be made with local measurement data, not just benchmarks published on different hardware configurations.

---

Dose to medium and dose to water in the Elekta ecosystem

The distinction between D_m and D_w is one of the most debated issues in modern radiotherapy dosimetry. D_m is the energy absorbed per unit mass of the real environment (bone tissue, lung, etc.), calculated directly in the MC simulation. D_w is the energy absorbed per unit mass of water, under equivalent conditions of energy flow, obtained by conversion via the ratio of braking powers (stopping power ratios, SPR):

D_w ≈ D_m × (S/ρ)_{w,m}

where (S/ρ)_{w,m} is the water-medium stopping power ratio, which can differ significantly from the unity in cortical bone and lung.

Monaco’s AAPM’s TG-186 (Beaulieu et al., 2012) was the first consensus document to formalize this distinction for brachytherapy and low-energy external radiotherapy. For MV bundles, the difference between D_m and D_w in soft tissue is relatively small, but may be more relevant in cortical bone, where the elemental composition differs substantially from water. Siebers et al. (2000) analyzed this conversion in the context of high-energy photon beams and discuss the magnitude of the differences as a function of tissue and energy.

You should not generalize a single output convention for all GPUMCD integrations. The 2016 publication on a research version of Monaco does not establish a universal D_m or D_w rule; The 2026 study by Elekta One Planning explicitly states that the calculations were recorded as a dose in water. Before comparing DVHs or tolerances, the service must confirm the magnitude reported by the local version and document it.

The following table summarizes the implications of choosing D_m or D_w in different anatomical regions according to the available literature.

Region	Relationship D_m vs. D_w (MV beams)	Potential clinical impact	Reference
Soft tissue (muscle, fat)	Typically small difference	Not very relevant in routine	TG-186
Cortical bone	D_m < D_w; difference depends on energy	Relevant in bone SBRT; consistency with historical tolerances	Siebers et al., 2000
Lung (low density)	Transport and lack of electronic balance dominate many differences	Validate algorithm, grid and beam model	Ahmad et al., 2016
Air-tissue interfaces	Sharp gradients; both quantities have limitations	Be careful with steep gradient verification dosimetry	Hissoiny et al., 2011

The choice of which quantity to use for plan approval must be documented in the local protocol and be consistent between planning and dosimetric verification. Mixing D_m in planning with historically established tolerance thresholds with D_w, without conscious conversion, is a potential source of systematic error.

---

Results in lung, bone, interfaces and small fields

The accuracy of GPUMCD has been evaluated in heterogeneous geometries in the literature. Ahmad et al. (2016) compared GPUMCD, XVMC and collapsed cone in heterogeneous phantoms with measurements. This study is useful for discussing low-density transport and interfaces, but did not present a clinical series of SBRT or a comparison of patient DVHs; its results should not be extrapolated as a direct clinical outcome.

In bone, the difference between D_m and D_w becomes more pronounced, and the clinical impact must be evaluated in relation to locally adopted tolerance protocols — which were historically established with water dosimetry. For plans for spinal irradiation or bone metastases, this point must be explained in the commissioning and in the plan approval protocol.

At tissue-air interfaces (cavities, paranasal sinuses, bronchi), explicit MC transport resolves dose gradients more correctly than kernel algorithms, which often smooth the dose profile across the interface. On the other hand, verification dosimetry in these regions is technically difficult: point detectors and films have their own limitations in high-gradient regions, which makes experimental validation challenging regardless of the algorithm.

For small fields — equivalent diameter below approximately 2×2 cm, used in SBRT and radiosurgery — the GPUMCD represents an improvement over the pencil beam and, in many cases, the collapsed cone. The physics of compromised lateral electronic equilibrium in these fields is best captured by explicit electron transport. However, the quality of the beam model in the Monaco — which describes the throttle exit fluency — directly influences the accuracy even with perfect MC. An inadequate beam model will produce systematic errors regardless of the transport engine.

---

Commissioning on the Monaco and the Elekta One

Monaco’s commissioning of the GPUMCD involves two distinct steps that are often confused: the commissioning of the beam model and the validation of the transport engine.

Monaco’s beam model mathematically describes the beam of photons leaving the accelerator: the energy distribution (spectrum), the source geometry, the lateral fluence and the modulating filters. This model is adjusted to open field measurements, dose profiles, PDD (percent deep dose) and, for small fields, to field factors (output factors). The MC engine uses this model as input to propagate particles into the patient’s geometry.

Validation of the MC engine itself — separate from beam model — involves comparing the calculated dose with measurements in homogeneous and heterogeneous phantoms (slab phantoms with synthetic lung and bone inserts). Published protocols such as TRS-430 from IAEA provide frameworks for this validation.

In the study of Rusu et al. (2026), Elekta One Planning version 6.2.3 was commissioned for a Versa HD accelerator via an adaptation of MPPG 5.b. Elekta One Planning is planning software, not an accelerator with an image integrated into the same gantry. The work described the need for new beam models for GPUMCD and found a reduction in calculation time in relation to XVMC in the studied environment, without transforming this speed ratio into a guarantee for other configurations.

Critical points of commissioning that require special attention:

• HU-density calibration: The HU→ρ conversion table must be derived from clinically used CT scanners, not from the TPS standard table. Errors in this calibration propagate directly to the voxel density and to the simulated mean free path.
• Small fields: output factors for fields below 2×2 cm require high resolution detectors (microchambers, diodes or synthetic diamond detectors) with protocol compatible with IAEA TRS-483.
• Reference statistical uncertainty: the protocol must specify the MC uncertainty threshold accepted for approval of plans, documenting the trade-off with calculation time.
• High-density materials: metal implants and prostheses fall outside the range covered by standard segmentation tables; Defining the procedure for these cases before clinical initiation avoids surprises.

---

How to choose calculation parameters without masking uncertainty

Monaco gives the user control over the target statistical uncertainty of the MC calculation. This setting is critically important: high uncertainty per voxel, although quick to calculate, can mask real dose gradients and introduce visual artifacts (“MC noise”) that make plan interpretation difficult and can falsely inflate the fail rate in gamma index-based QA.

Guidelines based on physics and literature guide the choices, but each center must define its goals in commissioning:

1. Routine clinical planning (IMRT/VMAT): the uncertainty target must be defined in commissioning and tested with the hardware and clinical version. A universal number is not a substitute for evaluating noise, time, and impact on plan metrics.

2. Pulmonary and spinal SBRT: given the sensitivity of these techniques to dose accuracy — and the frequent presence of severe heterogeneities —, smaller uncertainties are justifiable, especially when the target volume is in a region of high density gradient.

3. Second-check: When using GPUMCD as an independent second-check calculation, using the same uncertainty setting as the main calculation allows direct comparison of DVHs.

4. High modulation planes: If the MC calculation participates in the optimization process, statistical noise may affect convergence. Consult documentation and validate the flow for the specific version before clinical use.

Another frequently underestimated parameter is the calculation voxel size. The resolution must be chosen depending on the field size, gradient, anatomy and limits of the commissioned version. An overly coarse grid can attenuate gradients and produce partial volume; a finer grid increases cost and does not correct beam model errors.

The choice between D_m and D_w, in turn, must be documented and consistent. There is no single international consensus on which magnitude to use for plan approval in external radiotherapy MV beams. The key point is that normal tissue tolerances derived from historical studies (such as data compiled by QUANTEC) have been established with water-based dosimetry; When adopting D_m, this translation must be explicitly considered and documented in the local protocol.

---

Frequently asked questions

Is GPUMCD more accurate than Acuros XB of Eclipse?

Acuros XB numerically solves the linear Boltzmann transport equation, while GPUMCD uses stochastic sampling. Both can represent heterogeneities more faithfully than simplified methods, but there is no universal superiority: beam model, grid, materials, version and test scenario matter. Ahmad et al. (2016) did not compare Acuros XB; therefore, this article does not support a direct equivalence between the two engines. Clinical decision requires local validation and specific comparative studies.

Should I use D_m or D_w to approve clinical plans?

There is no single, binding international recommendation for external radiotherapy MV beams. TG-186 discusses the fundamentals with a focus on brachytherapy and low-energy radiotherapy. For MV beams in soft tissue, the numerical difference is small. In bone or lung, the choice affects DVHs in a measurable way. The most important thing is to document the choice in the local protocol and maintain consistency between planning, dosimetric verification and the tolerance thresholds adopted.

What is the impact of the HU-density table on the MC result?

Significant. GPUMCD uses the HU→density conversion table to assign the mass of each CT voxel. An incorrect table—for example, derived from a different scanner than that used clinically—produces systematic errors in particle transport, more severe in regions of cortical bone or lung than in soft tissue. The calibration of this table is an essential part of commissioning and must be checked periodically or after maintenance on the CT. The practice of using generic vendor tables without local validation is a relatively common and underappreciated point of failure.

Can MC statistical noise compromise QA?

Yes. QA systems based on dose map comparison (ArcCheck, MapCHECK, Delta4) measure point-to-point differences or by gamma index. MC noise in the planned distribution can artificially inflate the failure rate in the gamma index, especially in regions of low gradient but with high residual statistical uncertainty. The solution is to calculate with sufficiently low uncertainty before exporting to QA — the commissioning protocol should establish this threshold before clinical initiation, not after unexplained failures emerge.

Does GPUMCD work for protons or only for photons?

The original GPUMCD article describes coupled transport of photons and electrons in the energy range studied. This does not mean that the same clinical implementation calculates therapeutic proton beams. Proton therapy requires its own physics, beam models and validation; availability must be confirmed on the specific product and version.

---

References

• Hissoiny S, Ozell B, Bouchard H, Després P. GPUMCD: A new GPU-oriented Monte Carlo dose calculation platform. Med Phys. 2011;38(2):754–764.
• Ahmad SB, Sarfehnia A, Paudel MR, et al. Experimental evaluation of a commercial Monte Carlo dose calculation algorithm in heterogeneous phantoms. J Appl Clin Med Phys. 2016;17(6).
• Rusu SD, et al. Commissioning and validation of Elekta One Planning with GPUMCD for a Versa HD linear accelerator. J Appl Clin Med Phys. 2026.
• Beaulieu L, Tedgren ÅC, Carrier JF, et al. Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism. Med Phys. 2012;39(10):6208–6236.
• Siebers JV, Keall PJ, Nahum AE, Mohan R. Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dosimetry. Phys Med Biol. 2000;45(4):983–995.
• IAEA TRS-483. Dosimetry of Small Static Fields Used in External Beam Radiotherapy. Vienna: IAEA; 2017.
• IAEA TRS-430. Commissioning and Quality Assurance of Computerized Planning Systems for Radiation Treatment of Cancer. Vienna: IAEA; 2004.