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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Estimating Radiation Exposure through Ray Tracing Simulation</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Elisa Foderaro</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Rosanna Greco</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Giorgio De Magistris</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer, Control, and Management Engineering of Sapienza University of Rome</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <fpage>35</fpage>
      <lpage>42</lpage>
      <abstract>
        <p>Radiation plays a critical role in modern medical diagnostics and treatments but poses significant risks to healthcare personnel. Traditional dose estimation methods, primarily based on dosimeters placed on selected body parts, neglect the varying radiosensitivity of diferent organs. In this work, we present a system that models efective radiation dose by simulating threedimensional (3D) environments including radiation sources, shielding objects, and human models segmented by MeshCNN. We employed a ray tracing algorithm to simulate radiation behavior, considering both spatial attenuation (via inverse square law) and material shielding (via the Lambert-Beer law). Our approach allows for detailed analysis of organ-specific exposures and the impact of environmental shielding. Results demonstrate the feasibility of using 3D simulation and ray tracing to achieve a more comprehensive and accurate estimation of efective radiation dose in medical environments.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;ray tracing</kwd>
        <kwd>radiation dosimetry</kwd>
        <kwd>medical imaging</kwd>
        <kwd>mesh segmentation</kwd>
        <kwd>Monte Carlo methods</kwd>
        <kwd>3D modeling</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <sec id="sec-1-1">
        <title>Sievert, Sv) applies a radiation weighting factor. Further,</title>
        <p>the efective dose incorporates tissue weighting factors,
Radiation is widely utilized in the medical field for both providing a measure of the overall risk by considering
diagnostic and therapeutic purposes. Despite its clinical the varying sensitivity of diferent organs.
benefits, radiation exposure poses significant health risks Exposure to ionizing radiation carries both
determinto medical personnel, especially those working in envi- istic and stochastic risks. Deterministic efects, such as
ronments where frequent or prolonged exposure occurs. skin burns or cataracts, occur above a threshold dose.
Efective radiation protection strategies are thus essential Stochastic efects, including cancer, have no threshold
to mitigate these risks. and their probability increases with dose. The
Interna</p>
        <p>Radiation can be classified into particle radiation (e.g., tional Commission on Radiological Protection (ICRP)
recalpha and beta particles) and electromagnetic radiation ommends dose limits to protect workers and the general
(e.g., gamma rays and X-rays). While alpha and beta par- public, emphasizing the ALARA (As Low As Reasonably
ticles have limited penetration abilities, gamma rays and Achievable) principle.</p>
        <p>X-rays can deeply penetrate tissues, potentially damag- This work proposes a novel method to estimate the
ing sensitive organs. Consequently, understanding the efective dose absorbed by a human body placed in a
radibehavior of radiation in complex environments and its ation environment. We designed and implemented a
siminteraction with the human body is crucial for accurate ulation framework that combines 3D modeling, human
risk assessment and protection. body segmentation, and ray tracing to simulate radiation</p>
        <p>In current practice, radiation exposure is typically mon- propagation and interaction within complex scenes.
Usitored using personal dosimeters, devices worn on spe- ing this framework, we can analyze radiation exposure
cific body parts to record cumulative doses. However, on a per-organ basis, taking into account shielding by
this method has limitations: it does not account for the environmental objects and self-shielding by body
strucvarying radiosensitivity of diferent organs, the shielding tures.
efects of surrounding objects, or the spatial distribution Our methodology provides a step toward more detailed
of absorbed dose across the body. Moreover, improper and realistic radiation exposure assessments, with
potenusage, calibration issues, and body self-shielding efects tial applications in healthcare facilities and radiological
can lead to inaccurate estimations. safety evaluations.</p>
        <p>The absorbed dose, expressed in Gray (Gy), measures
the energy deposited per unit mass of tissue but does not
reflect the biological impact of diferent radiation types. 2. Related works
To account for this, the equivalent dose (measured in</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>3. Segmenting Human Models with MeshCNN</title>
      <p>
        of the methods used are based on Monte Carlo (MC)
simulation(s), a method extensively used in medical physics
applications [
        <xref ref-type="bibr" rid="ref6 ref7 ref8 ref9">6, 7, 8, 9</xref>
        ] and considered the gold standard
thanks to its capability of calculating statistical behavior. MeshCNN [22] is a convolutional neural network
archiIn addition to radiation dose estimation, MC techniques tecture specifically designed for analyzing 3D
trianguare also used for radiotherapy device development [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] lar meshes. Unlike traditional CNNs operating on
gridand treatment planning [
        <xref ref-type="bibr" rid="ref11 ref12 ref13">11, 12, 13</xref>
        ]. structured data, MeshCNN applies convolution and
pool
      </p>
      <p>
        However, the ability to model full particle transport ing directly to mesh edges, making it particularly suited
yields high computational complexity which makes MC for tasks such as segmentation and classification on
irsimulations prohibited for daily clinical practice. To over- regular 3D geometries.
come this problem and achieve a fast dose calculation,
several Deep Learning frameworks have been developed,
e.g. [
        <xref ref-type="bibr" rid="ref14 ref15 ref16">14, 15, 16</xref>
        ]. Figure 1: Edge-collapse operation in MeshCNN
      </p>
      <p>Although this type of research is interesting, it does
not correspond exactly to the objectives of this work.</p>
      <p>Indeed, we are more interested in the estimation of the
efective dose for radiation workers.</p>
      <p>
        The report [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] is better suited for this purpose.
However, due to the insuficient data provided by the
countries, many of the estimated values are subject to a
considerable degree of uncertainty.
      </p>
      <p>
        Indeed, the current trend is to monitor a person’s
exposure doses using devices called dosimeters. They rely
on numerous physical efects and can be of several types
[
        <xref ref-type="bibr" rid="ref18">18</xref>
        ]. The most significant for our purposes are:
• Personal dosimeters, used to assess the radiation
dose received by an individual who is wearing
the device. These are usually small devices worn
on the body itself, usually on the torso. While
passive dosimeters have traditionally been used,
the trend in radiation protection is increasingly
toward the use of active personal dosimeters [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ]; Edges are characterized by geometric features
includ• Area-monitoring dosimeters, used to detect radi- ing the dihedral angle between adjacent faces, internal
ations in a selected area. face angles, and normalized edge lengths. Mesh
convolutions operate on an edge and its neighboring edges across
      </p>
      <p>
        Although the use of dosimeters in estimation is very adjacent triangles, extracting local geometric patterns.
widespread, it leads to some problems. First, surveys have Downsampling is achieved via edge collapse operations,
shown that dosimeters are not always properly used [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ] reducing mesh complexity while preserving important
or well-calibrated [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ]. Moreover, even when properly features. Unpooling layers restore the original resolution
used, these devices do not cover the entire body and are for segmentation tasks, as illustrated in Figure 1.
therefore subject to phenomena that may reduce their For our purposes, we leveraged pre-trained weights
efectiveness. For example, the estimation provided by made available by the MeshCNN authors, trained on
personal dosimeters is subject to the self-shielding efect human body meshes segmented into eight anatomical
of the body, especially when the rays come from behind. regions [23]. The training dataset comprises 370 human
On the other hand, estimation methods based on area models from the SCAPE [24], FAUST [25], and MIT [26]
monitoring usually assume that a person remains in place, datasets, segmented according to the conventions in [27].
which of course is not always the case for people in a Our dataset consisted of two human models — one
working environment. male1 and one female2 — processed via Blender3 to match
      </p>
      <p>Finally, it should be noted that all dosimeters register the required number of edges (approximately 2250) for
cumulative doses, which may correspond to a high expo- MeshCNN input compatibility. The segmentation results
sure over a short period of time or a low exposure over a
longer period of time, but these have diferent efects on
the body.</p>
      <sec id="sec-2-1">
        <title>1https://free3d.com/3d-model/base-mesh-ready-to-be-rigged-15483.</title>
        <p>html
2https://sketchfab.com/3d-models/
study-human-female-sculpt-854fbf358991477aab518e07556da906
3https://www.blender.org/</p>
        <sec id="sec-2-1-1">
          <title>5.2. Radiation Intensity Attenuation</title>
        </sec>
      </sec>
      <sec id="sec-2-2">
        <title>The radiation energy carried by each ray diminishes due to two mechanisms: are depicted in Figure 2, with each anatomical region labeled and color-coded accordingly.</title>
        <p>This segmentation enables the calculation of
organspecific efective doses based on which body parts are
impacted by radiation in the simulation.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>4. Creating 3D Scenes</title>
      <sec id="sec-3-1">
        <title>The first step in our system involves constructing realistic</title>
        <p>3D scenes that represent potential radiation exposure
environments. For this purpose, we used the trimesh
Python library [28], which provides eficient tools for
manipulating and rendering triangular meshes.</p>
        <p>Each scene is composed of three primary elements:
Figure 3 shows examples of two constructed scenes. In
the first (a), a single massive pillar stands between the
radiation source and the human figure, while the
second (b) depicts a more complex setting involving a table
assembled from multiple primitives.</p>
        <p>Scene complexity can significantly influence radiation
propagation, with factors such as object shape, size,
material composition, and spatial arrangement playing key
roles. Therefore, our framework allows flexible scene
generation to evaluate a wide range of shielding
scenarios and their efects on radiation dose distribution.
(a)
(b)</p>
      </sec>
      <sec id="sec-3-2">
        <title>In the subsequent simulations, diferent human positions and environmental objects were systematically varied to study their impact on efective dose estimation.</title>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>5. Modeling Radiation Exposure</title>
      <p>To simulate the propagation of radiation within the
constructed scenes, we developed a ray tracing algorithm
tailored to radiological modeling. Unlike traditional ray
tracing used in computer graphics for visual rendering,
our method focuses on modeling energy deposition and
attenuation due to interaction with materials.</p>
      <sec id="sec-4-1">
        <title>5.1. Ray Tracing Methodology</title>
        <p>The radiation source emits a large number of rays
uniformly distributed in space. Each ray propagates until
it either exits the scene or is absorbed by an object. For
• Radiation Source: Modeled as a point source each ray, intersections with scene elements are detected
with configurable position and emitted intensity. using trimesh ray-mesh intersection routines.
• Human Model: Selected from the segmented If a ray strikes the human mesh, the intersected
trimale or female meshes described previously, angle is identified, allowing assignment of the absorbed
placed at a user-defined location within the scene. dose to a specific anatomical region. If a ray encounters
• Environmental Objects: A configurable set of an object, the radiation intensity is attenuated according
objects such as pillars, tables, or shields, each to the material properties before continuing propagation.
characterized by its position, size, and material For simplicity, scattering phenomena were neglected in
properties (e.g., attenuation coeficients). this implementation. Figure 4 illustrates an example of
rays propagating through a scene with a human model
and environmental objects.
5.2.1. Distance Decay
The intensity decreases with the square of the distance
from the source, following the inverse square law:
 =
0
2
where 0 is the source intensity and  is the distance
traveled.
5.2.2. Material Attenuation
When a ray passes through an object, its intensity is
reduced according to the Lambert–Beer law:</p>
        <p>= 0 · − 
where  is the linear attenuation coeficient of the
material and  is the thickness traversed. Attenuation
coefifcients were obtained from the NIST database [ 29] for
relevant materials.</p>
      </sec>
      <sec id="sec-4-2">
        <title>5.3. Calculating the Efective Dose</title>
        <p>To compute the efective dose:
1. For each human body part, the energy deposited
by rays intersecting that region is accumulated.
2. The absorbed dose (in Gy) is computed based on
deposited energy and local mass.
3. A radiation weighting factor ( = 1) is applied,
appropriate for gamma and X-ray radiation.</p>
        <p>Tissue
Bone-marrow (red), colon,
lung, stomach, breast</p>
        <p>Gonads
Bladder, oesophagus,</p>
        <p>liver, thyroid
Bone surface, brain,
salivary glands, skin</p>
        <p>Tissue weighting factor</p>
        <sec id="sec-4-2-1">
          <title>4. Tissue weighting factors ( ) specified by ICRP</title>
          <p>103 [31] are used to adjust contributions from
diferent body regions, reflecting their varying
radiosensitivity (see Table 1).</p>
        </sec>
        <sec id="sec-4-2-2">
          <title>For tissues such as bone marrow, bone surface, and</title>
          <p>skin that are distributed across multiple anatomical parts,
weighting adjustments are made based on
literaturereported fractional distributions [32, 30, 33] (see Tables 2,
3, and 4).</p>
          <p>Thus, the final efective dose is a weighted sum of
contributions from all body regions, accurately reflecting
both spatial and biological factors influencing radiation
risk.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>6. Results</title>
      <sec id="sec-5-1">
        <title>To validate our system, we designed a series of 3D scenes</title>
        <p>involving diferent human models (male and female),
shielding objects, and materials. Radiation propagation
and efective dose were computed for each
configuration, allowing analysis of shielding efectiveness and the
impact of spatial arrangement.</p>
        <p>For all experiments, we used three common materials
with known linear attenuation coeficients, summarized
in Table 5.</p>
        <sec id="sec-5-1-1">
          <title>6.1. Efect of Diferent Shielding Materials</title>
        </sec>
      </sec>
      <sec id="sec-5-2">
        <title>We first evaluated the efectiveness of diferent materials</title>
        <p>in shielding radiation. In these experiments, a cubic
object was placed in front of the torso of the human model.</p>
        <p>Figures 5a–f visualize the absorbed dose distribution for
each configuration.</p>
        <p>The numerical results, reported in Tables 6, 7, and 8, 6.2. Self-Shielding and Body Orientation
show that: Efects</p>
        <p>In all cases, unprotected regions such as the head and
arms still absorb considerable radiation, highlighting the
importance of whole-body analysis.</p>
        <p>• Plexiglass provides limited shielding, resulting in Next, we investigated how body orientation relative
high total absorbed doses. to the radiation source afects exposure through
self• Particleboard achieves moderate reduction in ab- shielding mechanisms. In one configuration, the human
sorbed dose. model faced the source directly; in the other, it was turned
• Concrete demonstrates superior shielding, reduc- sideways.</p>
        <p>ing the absorbed dose to approximately one-third Figures 6a–d depict the absorbed dose distributions for
of that without any shielding. these two configurations. Numerical results are shown
in Tables 9 and 10.</p>
        <p>As expected, the torso absorbed the highest dose when
facing the source. In the side-facing configuration,
total absorbed dose was reduced by approximately 50%,
demonstrating the significant protective efect of body</p>
        <sec id="sec-5-2-1">
          <title>6.3. Shielding by Complex Objects</title>
          <p>Finally, we evaluated scenarios involving more complex
shielding, such as a dining table modeled using multiple
primitives. Figure 7 illustrates this setup.</p>
          <p>The results (Table 11) demonstrate how lower limbs
and parts of the torso were partially shielded,
significantly altering the absorbed dose distribution compared
to the unshielded case.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>7. Conclusion and Future Work</title>
      <p>In this work, we developed a system for estimating
effective radiation dose absorbed by a human body placed
within a 3D environment containing a radioactive source
and various shielding objects. By integrating ray tracing
techniques with 3D modeling and human body
segmentation via MeshCNN, our method allows for spatially
resolved and organ-specific dose calculations, taking into
account both distance-based attenuation and
materialdependent shielding efects.</p>
      <p>Experimental results demonstrate the ability of the
system to capture important phenomena such as
selfshielding, diferential material absorption, and the
influence of complex object geometries on dose distribution.
Comparative analyses across diferent shielding
materials and body orientations underline the importance of
detailed scene modeling for accurate radiation protection
assessments. Overall, this work represents a step toward
more comprehensive, flexible, and accurate tools for
radiation exposure assessment, with potential applications
in healthcare worker protection, medical imaging facility
design, and radiological emergency response planning.</p>
    </sec>
    <sec id="sec-7">
      <title>Declaration on Generative AI</title>
      <sec id="sec-7-1">
        <title>During the preparation of this work, the authors</title>
        <p>used ChatGPT, Grammarly in order to: Grammar and
spelling check, Paraphrase and reword. After using this
tool/service, the authors reviewed and edited the content
as needed and take full responsibility for the publication’s
content.
35–42</p>
      </sec>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>United</given-names>
            <surname>Nations Scientific</surname>
          </string-name>
          <article-title>Committee on the Efects of Atomic Radiation</article-title>
          ,
          <string-name>
            <surname>UNSCEAR</surname>
          </string-name>
          <year>2020</year>
          /2021 Report Volume I:
          <article-title>"Sources, efects and risks of ionizing radiation"; Annex A: "Evaluation of medical exposure to ionizing radiation"</article-title>
          , https://www.unscear.org/ unscear/en/publications/2020_2021_
          <article-title>1</article-title>
          .html,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>F. A.</given-names>
            <surname>Mettler</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Mahesh</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Bhargavan-Chatfield</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C. E.</given-names>
            <surname>Chambers</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. G.</given-names>
            <surname>Elee</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. P.</given-names>
            <surname>Frush</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. L.</given-names>
            <surname>Miller</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H. D.</given-names>
            <surname>Royal</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. T.</given-names>
            <surname>Milano</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. C.</given-names>
            <surname>Spelic</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. J.</given-names>
            <surname>Ansari</surname>
          </string-name>
          ,
          <string-name>
            <given-names>W. E.</given-names>
            <surname>Bolch</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G. M.</given-names>
            <surname>Guebert</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. H.</given-names>
            <surname>Sherrier</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. M.</given-names>
            <surname>Smith</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. J.</given-names>
            <surname>Vetter</surname>
          </string-name>
          ,
          <article-title>Patient exposure from radiologic and nuclear medicine procedures in the united states: Procedure volume and efective dose for the period 2006-2016</article-title>
          , Radiology
          <volume>295</volume>
          (
          <year>2020</year>
          )
          <fpage>418</fpage>
          -
          <lpage>427</lpage>
          . doi:
          <volume>10</volume>
          .1148/radiol.2020192256, pMID:
          <fpage>32181730</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>J.</given-names>
            <surname>Hausleiter</surname>
          </string-name>
          , T. Meyer, F. Hermann,
          <string-name>
            <given-names>M.</given-names>
            <surname>Hadamitzky</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Krebs</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T. C.</given-names>
            <surname>Gerber</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>McCollough</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Martinof</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Kastrati</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Schömig</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Achenbach</surname>
          </string-name>
          ,
          <article-title>Estimated Radiation Dose Associated With Cardiac CT Angiography</article-title>
          , JAMA
          <volume>301</volume>
          (
          <year>2009</year>
          )
          <fpage>500</fpage>
          -
          <lpage>507</lpage>
          . URL: https:// doi.org/10.1001/jama.
          <year>2009</year>
          .
          <volume>54</volume>
          . doi:
          <volume>10</volume>
          .1001/jama.
          <year>2009</year>
          .
          <volume>54</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>M.</given-names>
            <surname>Woźniak</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Połap</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. K.</given-names>
            <surname>Nowicki</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Pappalardo</surname>
          </string-name>
          , E. Tramontana,
          <article-title>Novel approach toward medical signals classifier</article-title>
          ,
          <source>in: Proceedings of the International Joint Conference on Neural Networks</source>
          , volume
          <volume>2015</volume>
          <source>-September</source>
          ,
          <year>2015</year>
          . doi:
          <volume>10</volume>
          . 1109/IJCNN.
          <year>2015</year>
          .
          <volume>7280556</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>M.</given-names>
            <surname>Wozniak</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Polap</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Kosmider</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Tramontana</surname>
          </string-name>
          ,
          <article-title>A novel approach toward x-ray images classifier</article-title>
          ,
          <source>in: Proceedings - 2015 IEEE Symposium Series on Computational Intelligence</source>
          ,
          <string-name>
            <surname>SSCI</surname>
          </string-name>
          <year>2015</year>
          ,
          <year>2015</year>
          , p.
          <fpage>1635</fpage>
          -
          <lpage>1641</lpage>
          . doi:
          <volume>10</volume>
          .1109/SSCI.
          <year>2015</year>
          .
          <volume>230</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>P.</given-names>
            <surname>Andreo</surname>
          </string-name>
          ,
          <article-title>Monte carlo techniques in medical radiation physics</article-title>
          ,
          <source>Physics in Medicine &amp; Biology</source>
          <volume>36</volume>
          (
          <year>1991</year>
          )
          <article-title>861</article-title>
          . URL: https://dx.doi.org/10.1088/
          <fpage>0031</fpage>
          -9155/36/7/001. doi:
          <volume>10</volume>
          .1088/
          <fpage>0031</fpage>
          -9155/36/7/001.
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Ponzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Puglisi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Russo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>I. E.</given-names>
            <surname>Tibermacine</surname>
          </string-name>
          ,
          <article-title>Exploiting robots as healthcare resources for epidemics management and support caregivers</article-title>
          ,
          <source>in: CEUR Workshop Proceedings</source>
          , volume
          <volume>3686</volume>
          ,
          <year>2024</year>
          , p.
          <fpage>1</fpage>
          -
          <lpage>10</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>A. L.</given-names>
            <surname>Fielding</surname>
          </string-name>
          ,
          <article-title>Monte-carlo techniques for radiotherapy applications i: introduction and overview of the diferent monte-carlo codes</article-title>
          ,
          <source>Journal of Radiotherapy in Practice</source>
          <volume>22</volume>
          (
          <year>2023</year>
          )
          <article-title>e80</article-title>
          . doi:
          <volume>10</volume>
          .1017/ S1460396923000079.
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>N.</given-names>
            <surname>Boutarfaia</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Russo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Tibermacine</surname>
          </string-name>
          ,
          <string-name>
            <given-names>I. E.</given-names>
            <surname>Tibermacine</surname>
          </string-name>
          ,
          <article-title>Deep learning for eeg-based motor imagery classification: Towards enhanced human-machine interaction and assistive robotics</article-title>
          ,
          <source>in: CEUR Workshop Proceedings</source>
          , volume
          <volume>3695</volume>
          ,
          <year>2023</year>
          , p.
          <fpage>68</fpage>
          -
          <lpage>74</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>H.</given-names>
            <surname>Park</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Paganetti</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Schuemann</surname>
          </string-name>
          ,
          <string-name>
            <given-names>X.</given-names>
            <surname>Jia</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C. H.</given-names>
            <surname>Min</surname>
          </string-name>
          ,
          <article-title>Monte carlo methods for device simulations in radiation therapy</article-title>
          ,
          <source>Physics in Medicine &amp; Biology</source>
          <volume>66</volume>
          (
          <year>2021</year>
          )
          <article-title>18TR01</article-title>
          . URL: https://dx. doi.org/10.1088/
          <fpage>1361</fpage>
          -6560/ac1d1f . doi:
          <volume>10</volume>
          .1088/
          <fpage>1361</fpage>
          -6560/ac1d1f.
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <surname>C. M. C. Ma</surname>
            ,
            <given-names>I. J.</given-names>
          </string-name>
          <string-name>
            <surname>Chetty</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Deng</surname>
            ,
            <given-names>B.</given-names>
          </string-name>
          <string-name>
            <surname>Faddegon</surname>
            ,
            <given-names>S. B.</given-names>
          </string-name>
          <string-name>
            <surname>Jiang</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Li</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Seuntjens</surname>
            ,
            <given-names>J. V.</given-names>
          </string-name>
          <string-name>
            <surname>Siebers</surname>
          </string-name>
          , E. Traneus,
          <article-title>Beam modeling and beam model commissioning for monte carlo dose calculation-based radiation therapy treatment planning:</article-title>
          <source>Report of aapm task group 157, Medical Physics</source>
          <volume>47</volume>
          (
          <year>2020</year>
          )
          <fpage>e1</fpage>
          -
          <lpage>e18</lpage>
          . doi:https://doi.org/10.1002/mp.13898.
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>S.</given-names>
            <surname>Russo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>I. E.</given-names>
            <surname>Tibermacine</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Tibermacine</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Chebana</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Nahili</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Starczewscki</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          ,
          <article-title>Analyzing eeg patterns in young adults exposed to diferent acrophobia levels: a vr study</article-title>
          ,
          <source>Frontiers in Human Neuroscience</source>
          <volume>18</volume>
          (
          <year>2024</year>
          ). doi:
          <volume>10</volume>
          .3389/ fnhum.
          <year>2024</year>
          .
          <volume>1348154</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>S.</given-names>
            <surname>Russo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          , A comprehensive solution for doi:
          <volume>10</volume>
          .1088/
          <fpage>1361</fpage>
          -6498/aabce1.
          <article-title>psychological treatment and therapeutic</article-title>
          path plan- [22]
          <string-name>
            <given-names>R.</given-names>
            <surname>Hanocka</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Hertz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Fish</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Giryes</surname>
          </string-name>
          ,
          <string-name>
            <surname>S.</surname>
          </string-name>
          <article-title>Fleishning based on knowledge base and expertise shar- man,</article-title>
          <string-name>
            <surname>D.</surname>
          </string-name>
          Cohen-Or,
          <article-title>Meshcnn: A network with an ing</article-title>
          ,
          <source>in: CEUR Workshop Proceedings</source>
          , volume
          <volume>2472</volume>
          , edge,
          <source>ACM Transactions on Graphics (TOG) 38</source>
          <year>2019</year>
          , p.
          <fpage>41</fpage>
          -
          <lpage>47</lpage>
          . (
          <year>2019</year>
          )
          <volume>90</volume>
          :
          <fpage>1</fpage>
          -
          <lpage>90</lpage>
          :
          <fpage>12</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>C.</given-names>
            <surname>Kontaxis</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G. H.</given-names>
            <surname>Bol</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. J. W.</given-names>
            <surname>Lagendijk</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B. W.</given-names>
            <surname>Raay-</surname>
          </string-name>
          [23]
          <string-name>
            <given-names>H.</given-names>
            <surname>Maron</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Galun</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Aigerman</surname>
          </string-name>
          , M. Trope, makers, Deepdose:
          <article-title>Towards a fast dose calculation N</article-title>
          .
          <string-name>
            <surname>Dym</surname>
            ,
            <given-names>E.</given-names>
          </string-name>
          <string-name>
            <surname>Yumer</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          <string-name>
            <surname>Kim</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          <string-name>
            <surname>Lipman</surname>
          </string-name>
          ,
          <article-title>Convoengine for radiation therapy using deep learning</article-title>
          ,
          <source>lutional neural networks on surfaces via seamPhysics in Medicine &amp; Biology</source>
          <volume>65</volume>
          (
          <year>2020</year>
          )
          <article-title>075013</article-title>
          . less toric covers
          <volume>36</volume>
          (
          <year>2017</year>
          ). doi:
          <volume>10</volume>
          .1145/3072959. URL: https://dx.doi.org/10.1088/
          <fpage>1361</fpage>
          -6560/
          <year>ab7630</year>
          . 3073616,
          <string-name>
            <surname>publisher</surname>
            <given-names>Copyright</given-names>
          </string-name>
          : ©
          <year>2017</year>
          ACM.; ACM doi:
          <volume>10</volume>
          .1088/
          <fpage>1361</fpage>
          -6560/ab7630. SIGGRAPH 2017 ; Conference date:
          <fpage>30</fpage>
          -
          <lpage>07</lpage>
          -2017
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>N.</given-names>
            <surname>Brandizzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Fanti</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Gallotta</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Russo</surname>
          </string-name>
          , L. Ioc- Through 03-
          <fpage>08</fpage>
          -2017. chi, D. Nardi,
          <string-name>
            <given-names>C.</given-names>
            <surname>Napoli</surname>
          </string-name>
          , Unsupervised pose es- [24]
          <string-name>
            <given-names>D.</given-names>
            <surname>Anguelov</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Srinivasan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Koller</surname>
          </string-name>
          ,
          <string-name>
            <surname>S.</surname>
          </string-name>
          <article-title>Thrun, timation by means of an innovative vision trans- J.</article-title>
          <string-name>
            <surname>Rodgers</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Davis</surname>
          </string-name>
          ,
          <article-title>Scape: Shape completion former</article-title>
          ,
          <source>in: Lecture Notes in Computer Science and animation of people, ACM Transactions on (including subseries Lecture Notes in Artificial In- Graphics (TOG) 24</source>
          (
          <year>2005</year>
          )
          <fpage>408</fpage>
          -
          <lpage>416</lpage>
          .
          <source>doi:10.1145/ telligence and Lecture Notes in Bioinformatics)</source>
          , vol-
          <volume>1073204</volume>
          .1073207. ume 13589 LNAI,
          <year>2023</year>
          , p.
          <fpage>3</fpage>
          -
          <lpage>20</lpage>
          . doi:
          <volume>10</volume>
          .1007/ [25]
          <string-name>
            <given-names>F.</given-names>
            <surname>Bogo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Romero</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Loper</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. J.</given-names>
            <surname>Black</surname>
          </string-name>
          , FAUST:
          <fpage>978</fpage>
          -3-
          <fpage>031</fpage>
          -23480-
          <issue>4</issue>
          _
          <fpage>1</fpage>
          .
          <article-title>Dataset and evaluation for 3D mesh registration</article-title>
          , in:
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>T. I.</given-names>
            <surname>Götz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Schmidkonz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Chen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Al-Baddai</surname>
          </string-name>
          ,
          <source>Proceedings IEEE Conf. on Computer Vision</source>
          and T.
          <string-name>
            <surname>Kuwert</surname>
            ,
            <given-names>E. W.</given-names>
          </string-name>
          <string-name>
            <surname>Lang</surname>
          </string-name>
          ,
          <article-title>A deep learning approach Pattern Recognition (CVPR), Columbus</article-title>
          , Ohio, USA, to radiation dose estimation,
          <source>Physics in Medicine</source>
          <year>2014</year>
          , pp.
          <fpage>3794</fpage>
          -
          <lpage>3801</lpage>
          . doi:
          <volume>10</volume>
          .1109/CVPR.
          <year>2014</year>
          . &amp;
          <article-title>Biology 65 (</article-title>
          <year>2020</year>
          )
          <article-title>035007</article-title>
          . URL: https://dx. 491. doi.org/10.1088/
          <fpage>1361</fpage>
          -6560/ab65dc. doi:
          <volume>10</volume>
          .1088/ [26]
          <string-name>
            <given-names>D.</given-names>
            <surname>Vlasic</surname>
          </string-name>
          , I. Baran,
          <string-name>
            <given-names>W.</given-names>
            <surname>Matusik</surname>
          </string-name>
          , J. Popović,
          <fpage>Ar1361</fpage>
          -6560/ab65dc.
          <article-title>ticulated mesh animation from multi-view silhou-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <article-title>United Nations Scientific Committee on the ettes</article-title>
          ,
          <source>ACM Trans. Graph</source>
          .
          <volume>27</volume>
          (
          <year>2008</year>
          )
          <fpage>1</fpage>
          -
          <lpage>9</lpage>
          . URL: https: Efects of Atomic Radiation,
          <string-name>
            <surname>UNSCEAR</surname>
          </string-name>
          <year>2020</year>
          /
          <year>2021</year>
          //doi.org/10.1145/1360612.1360696.
          <source>doi:10.1145/ Report Volume I: "Sources, efects and risks 1360612</source>
          .1360696.
          <article-title>of ionizing radiation"; Annex D: "</article-title>
          <source>Evaluation</source>
          [27]
          <string-name>
            <given-names>E.</given-names>
            <surname>Kalogerakis</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Hertzmann</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Singh</surname>
          </string-name>
          ,
          <article-title>Learning of occupational exposure to ionizing radia- 3d mesh segmentation</article-title>
          and labeling
          <volume>29</volume>
          (
          <year>2010</year>
          ).
          <source>tion"</source>
          , https://www.unscear.org/unscear/en/ URL: https://doi.org/10.1145/1778765.1778839. publications/
          <year>2020</year>
          _2021_
          <article-title>4</article-title>
          .html,
          <year>2021</year>
          . doi:
          <volume>10</volume>
          .1145/1778765.1778839.
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <given-names>A.</given-names>
            <surname>Abaza</surname>
          </string-name>
          , New trend in radiation dosimeters, [
          <volume>28</volume>
          ]
          <string-name>
            <surname>Dawson-Haggerty</surname>
          </string-name>
          et al.,
          <source>trimesh (version 3.2.0)</source>
          ,
          <source>American Journal of Modern Physics</source>
          <volume>7</volume>
          (
          <year>2018</year>
          )
          <fpage>21</fpage>
          .
          <year>2019</year>
          . doi:
          <volume>10</volume>
          .11648/j.ajmp.
          <volume>20180701</volume>
          .13. [29]
          <string-name>
            <given-names>J.</given-names>
            <surname>Hubbell</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Seltzer</surname>
          </string-name>
          ,
          <article-title>Tables of x-ray mass attenu-</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <given-names>T.</given-names>
            <surname>Bolognese-Milsztajn</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Ginjaume</surname>
          </string-name>
          ,
          <string-name>
            <surname>F.</surname>
          </string-name>
          <article-title>Vanha- ation coeficients and mass energy-absorption covere, Active Methods &amp; Instruments for Personal eficients 1 kev to 20 mev for elements z = 1 to 92 Dosimetry of External Radiation: Present Situa- and 48 additional substances of dosimetric interest, tion in Europe and Future Needs</article-title>
          ,
          <source>EDP Sciences</source>
          ,
          <year>1995</year>
          . Les Ulis,
          <year>2004</year>
          , pp.
          <fpage>65</fpage>
          -
          <lpage>82</lpage>
          . URL: https://doi.org/10. [30]
          <string-name>
            <surname>ICRP</surname>
          </string-name>
          ,
          <string-name>
            <surname>Basic</surname>
            <given-names>anatomical</given-names>
          </string-name>
          <source>and physiological data 1051/978-2-7598-0117-6</source>
          .c008. doi:doi:10.1051/ for use in
          <source>radiological protection reference values, 978-2-7598-0117-6.c008. ICRP Publication 89. Ann. ICRP</source>
          <volume>32</volume>
          (
          <year>2002</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <surname>R. M. Sánchez</surname>
            ,
            <given-names>E.</given-names>
          </string-name>
          <string-name>
            <surname>Vano</surname>
            ,
            <given-names>J. M.</given-names>
          </string-name>
          <string-name>
            <surname>Fernández</surname>
          </string-name>
          , F. Ros- [31]
          <string-name>
            <surname>ICRP</surname>
          </string-name>
          ,
          <article-title>The 2007 recommendations of the internaales</article-title>
          , J.
          <string-name>
            <surname>Sotil</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          <string-name>
            <surname>Carrera</surname>
            ,
            <given-names>M. A.</given-names>
          </string-name>
          <string-name>
            <surname>García</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          <article-title>M. tional commission on radiological protection, ICRP Soler</article-title>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Hernández-Armas</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L. C.</given-names>
            <surname>Martínez</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. F.</given-names>
            <surname>Publication</surname>
          </string-name>
          <article-title>103</article-title>
          . Ann. ICRP
          <volume>37</volume>
          (
          <year>2007</year>
          ). Verdú, Staf doses in interventional radiol- [32]
          <string-name>
            <given-names>M.</given-names>
            <surname>Cristy</surname>
          </string-name>
          ,
          <article-title>Active bone marrow distribution as a ogy: A national survey</article-title>
          ,
          <source>Journal of Vascu- function of age in humans., Physics in medicine lar and Interventional Radiology</source>
          <volume>23</volume>
          (
          <year>2012</year>
          )
          <fpage>1496</fpage>
          - and
          <source>biology 26</source>
          <volume>3</volume>
          (
          <year>1981</year>
          )
          <fpage>389</fpage>
          -
          <lpage>400</lpage>
          . 1501. URL: https://www.sciencedirect.com/science/ [33]
          <string-name>
            <given-names>C. C.</given-names>
            <surname>Lund</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N. C.</given-names>
            <surname>Browder</surname>
          </string-name>
          ,
          <article-title>The estimation of areas article/pii/S105104431200591X</article-title>
          . doi:https://doi. of burns,
          <source>Surg Gynecol Obste</source>
          <volume>79</volume>
          (
          <year>1944</year>
          )
          <fpage>352</fpage>
          -
          <lpage>358</lpage>
          . org/10.1016/j.jvir.
          <year>2012</year>
          .
          <volume>05</volume>
          .056.
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <given-names>O.</given-names>
            <surname>Ciraj-Bjelac</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Carinou</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Vanhavere</surname>
          </string-name>
          ,
          <article-title>Use of active personal dosimeters in hospitals: Eurados survey</article-title>
          ,
          <source>Journal of Radiological Protection</source>
          <volume>38</volume>
          (
          <year>2018</year>
          )
          <article-title>702</article-title>
          . URL: https://dx.doi.org/10.1088/
          <fpage>1361</fpage>
          -6498/aabce1.
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>