The Biologist
(Lima)
The Biologist (Lima), 2021, vol. 19 (1), 87-96.
ORIGINAL ARTICLE / ARTÍCULO ORIGINAL
198693, Germany Applied Nanophysics, Institute for Phyysics, Technical University of Ilmenau, Ilmenau
2Pontificia Universidad Católica del Perú, Mechatronic Master Program and Energy Laboratory, Lima 32, Peru
3Department of Protocol and Investigation National Hospital Guillermo Almenara, Perú.
4 Northern (Artic) Federal University named after MV Lomonosov, Arkhangelsk Russia.
*Corresponding author: alan.calderon.pucp.edu.pe
1,2,* 2 2 2,3
J. Alan Calderón Ch ; Julio Tafur Sotelo , Benjamín Barriga Gamarra ; Julio Guevara Guevara ;
2,4 2 2
John Lozano Jauregui ; Juan Lengua Arteaga ; Gonzalo Solano
ABSTRACT
Keywords: COVID-19 – 3D reconstruction – mathematical modelling
This research explains the applications of 3 dimensional (3D) reconstruction for COVID-19 families
images, to look for the correlation between the mathematical model “event by event” with antiviral effect
on the virus, furthermore, the mathematical model obtained from 3D reconstruction is correlated with “A
general mathematical modelling for immune responses”. Therefore, the designed algorithm, provides
support for medical doctors through a graphic analysis and predictions regarding “What happens with the
virus before applying anti-malaria drugs?”. Many Countries are trying to find the vaccine against COVID
19; however, many Countries only have statistical strategies achieved by population displacement
restrictions, which is not enough to avoid faster virus transmission. Hence, in this research is proposed a
mathematical analysis to deal with the virus by a predictive model based on 3D COVID 19 images
reconstruction, correlated with antiviral analysis applications. As a consequence of the model designed,
the medical doctor can predict responses of cells damaged by the virus after application of antivirals or
plasma. The algorithm is elaborated to be a support for COVID 19 treatment.
The Biologist (Lima)
ISSN Versión Impresa 1816-0719
ISSN Versión en linea 1994-9073 ISSN Versión CD ROM 1994-9081
doi:10.24039/rtb2021191884
87
EVENT RECONSTRUCTION ALGORITHM FOR CORONAVIRUS (COVID-19) 3D
RECONSTRUCTION, ACCORDING TO STUDY ITS REACTION THROUGH ANTIVIRAL
ANALYSIS TREATMENT
ALGORITMO DE RECONSTRUCCIÓN DE EVENTOS PARA LA RECONSTRUCCIÓN 3D DE
CORONAVIRUS (COVID-19), SEGÚN EL ESTUDIO DE SU REACCIÓN A TRAVÉS DEL
TRATAMIENTO DE ANÁLISIS ANTIVIRAL
https://orcid.org/0000-0002-6486-5105
D
The Biologist (Lima). Vol. 19, Nº1, jan - jun 2021
INTRODUCTION
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According to achieve the mathematical model of an
“event process” through 3D image reconstruction
to be a support for medical doctor understanding of
the virus damage over lungs, it was studied some
figures of the virus effect in mice lungs. The
permission of the figures was given by Lin et al.
(2004).
Notwithstanding, “the main task of this research is
to achieve the mathematical model of the
interaction/effect among COVID 19 with antiviral
treatment”.
Hence, it is necessary to process at least 2 figures
during different stage of the treatment due to get the
3D reconstruction.
Figure 1 depicts the scheme of the algorithm. For
which, “Tfi” represents the mathematical model of
the “interaction/effect virus and cells”. “Ui” is the
input variables matrix, that represents “viral
application, plasma application, chemical
component” all of them as the input excitation
signal. “Yi” is the output variables matrix, that
represents every answer of the cells under the
interaction/effect of the virus because of “Ui”. “Yi”
can give information (for a medical doctor)
regarding the geometrical dimension of cells (as a
consequence of some input variable applied as a
viral over cells in interaction with the virus), also, it
can give information of any kind of changes over
system composed by “cells and virus interaction”.
RESUMEN
Palabras clave: COVID-19 – recontrucción 3D – modelado matemático
Esta investigación explica las aplicaciones de reconstrucción tridimensional (3D) para las imágenes de las
familias COVID-19, según la búsqueda de la correlación entre el modelo matemático "evento por evento"
con efecto antiviral sobre el virus, además, el modelo matemático obtenido de la reconstrucción 3D está
correlacionado con "Un modelado matemático general para las respuestas inmunitarias". Por lo tanto, el
algoritmo diseñado, proporciona apoyo a los médicos a través de un análisis gráfico y predicciones con
respecto a "¿Qué sucede con el virus antes de aplicar una acción como los medicamentos contra la
malaria?". Muchos países están tratando de encontrar la vacuna contra COVID 19; sin embargo, muchos
países sólo tienen estrategias estadísticas dadas por las restricciones de desplazamiento de la población, lo
cual no es suficiente para evitar la rápida transmisión del virus. Por lo tanto, en esta investigación se
propone un análisis matemático para tratar el virus mediante un modelo predictivo basado en la
reconstrucción de imágenes 3D del COVID 19, correlacionada con aplicaciones de análisis antiviral.
Como consecuencia del modelo diseñado, el médico puede predecir las respuestas de las células dañadas
por el virus después de aplicar antivirales o plasma sobre ellas. El algoritmo proporcionado se elabora para
ser un soporte para el tratamiento del COVID 19.
Figure 1. Event reconstruction algorithm scheme.
Calderón-Chavarri et al.
89
Therefore, to improve real information that the
only doctor can verify or validate whether “Ui” has
real information (according to analyze predictions
or estimations), in that context, it is necessary
feedback by adaptation of a weights matrix “W”.
That is the reason, why, in the axis “Y” of figure 1,
it is depicted for every instance “i”, in which was
achieved an event “the response of the system after
every internal feedback adaptation”, all of them
executed during total time “T”. This research
explains the applications of 3 dimensional (3D)
reconstruction for COVID-19 families images,
according to look for the correlation between the
mathematical model “event by event” with
antiviral effect on the virus.
After to get the analysis of the 3D reconstruction
model, separated from every stage of the treatment
“virus and antiviral”, it is analyzed their curves
through “Set Evolution Functions”. Therefore, the
following equation takes the information of a curve
from the figure processed, which is stored (by
derivatives and divergences) its behaviour (their
parameters α). That is the reason, why the
dependence in position and time for level set
functions “g” and “φ” can be solved by many
models such as polynomial equations.
As it was described above, the treatment solutions
worked in this research are based on polynomial
models, like in equation (2). In that, the derivatives
“P” with maximal order “n” is applied for the
changes on time of the response function “y”,
internal functions “x” and excitation signal (that
causes changes in the system) “u”. Furthermore, its
error “e”, the treatment solution to follow is given
by “Modulating function analysis”.
MATERIALS AND METHODS
Where solution error analysis “e(t)” is the discrete
error, and “V” keeps the Fourier series coefficients
showed in equation (3).
Moreover, is the frequency parameter function in
the equation , and is the numerical (4) Ck-m
combination of the physical parameters “ ”.a
For which, the nonlinear model for error analysis is
given by equation . In that equation, “g” is the (5)
function for the parameters “ ”, “E and F” are the
specified functions for the input variables “u” and
responses “y”. Finally, “P” are the fixed
polynomials as dependence on derivatives
Therefore, the estimation matrix is given by the
following equation:
For which, the weighting matrix “W” was solved
by “Feasible Generalized Least Square (FGLS),
Cochrane Orcutt Procedure (COCR)”. It must be
known take values between -1 and 1:
That is the reason why the general solution is given
by the following equation:
The Biologist (Lima). Vol. 19, Nº1, jan - jun 2021
3D reconstruction for COVID-19
90
In figure 2, it is showing a Representative lung
histopathology” kindly provided by Yan et al.
(2013), in which is described the interaction
between virus H5N1 with the antiviral, that
sequence of figures is quite necessary to achieve
the 3D image reconstruction of the “interaction
stages between the virus and antiviral”, even
though “it is more necessary to apply this research
for COVID 19”. In the image provided is not
known the scale (only magnifications: 200x and
400x), hence, the equivalent scale in every 3D
reconstruction image (from figure 3 to figure 10) is
depicted by colours while growing up the size in
“Z” axis: blue, light blue, yellow, orange and red.
Figure 2. Representative lung histopathology provided by Yan et al. (2013).
The Biologist (Lima). Vol. 19, Nº1, jan - jun 2021
Calderón-Chavarri et al.
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Therefore, it was executed the algorithm designed
and described above owing to achieve 3D
reconstruction. The following figure shows the 3D
reconstruction of mice lung cells under PBS
(Phosphate Buffered Saline) control around 200x
magnification due to the original figure (cells
inside “C” curve [1] during the test day 4) was
under that magnification value. It means that “C1,
C2 and C3” achieved similar scale reconstruction,
these reconstructions give geometrical details of
the internal sizes (estimated) for the “PBS control”
applied.
Figure 3. Mice lung cells under PBS control (Yan et al., 2013), original magnification was 200x by the SEM and the 3D
reconstruction under that magnification (during the test day 4). C = circumference. C1, C2 and C3 = 3D reconstruction in SEM.
Moreover, the following figure shows the same
mice lung cells under PBS but infected by H5N1
(during day 4 after virus infection) in
magnification SEM of 400x (Yan et al., 2013)
inside the circumference “C”, also, “C1, C2 and
C3” show the 3D reconstruction at 400x in
magnification SEM (Figure 4). It is possible to
identify better view from “monocytes and
neutrophils of the infiltrating cells”.
Figure 4. 3D reconstruction at 400x magnification SEM of mice lung cells infected by H5N1 (during the test day 4). C =
circumference. C1, C2 and C3 = 3D reconstruction in SEM.
The following figure shows the 3D reconstruction
of mice lung cells under CQ (chloroquine) control
around 200x magnification due to the original
figure (cells inside C curve (Yan et al., 2013)) was
achieved under that magnification value, in both
contexts (SBS and CQ control) were analyzed for
the day 4 of infection. It means that “C1, C2 and
C3” achieved similar scale reconstruction, these
reconstructions give geometrical details of the
internal sizes (estimated) for the “CQ control”
applied (Figure 5). It is necessary to remind “CQ is
a highly effective therapeutic but not prophylactic
agent against avian influenza AH5N1 (Yan et al.,
2013)”.
The Biologist (Lima). Vol. 19, Nº1, jan - jun 2021
3D reconstruction for COVID-19
92
Furthermore, the following figure shows the same
mice lung cells under CQ but infected by H5N1
(during day 4 after virus infection) in
magnification SEM of 400x (Yan et al., 2013)
inside the circumference “C”, also, “C1, C2 and
C3” show the 3D reconstruction at 400x in
magnification SEM (Figure 6). It is possible to
identify a better view from “monocytes and
neutrophils of the infiltrating cells”. This
reconstruction can be used by a medical doctor to
evaluate the effects of CQ in mice lungs.
Figure 5. Mice lung cells under CQ control (Yan et al., 2013), original magnification was 200x by the SEM and the 3D
reconstruction under that magnification (during the test day 4). C = circumference. C1, C2 and C3 = 3D reconstruction in SEM.
Figure 6. 3D reconstruction at 400x magnification SEM of mice lung cells infected by H5N1 (during the
test day 4). C = circumference. C1, C2 and C3 = 3D reconstruction in SEM.
Therefore, it was executed the algorithm designed
and described above owing to achieve 3D
reconstruction. The following figure shows the 3D
reconstruction of mice lung cells under PBS
control around 200x magnification due to the
original figure (cells inside C curve (Yan et al.,
2013) during day 5 after virus infection) was
achieved under that magnification value. It means
that “C1, C2 and C3” achieved similar scale
reconstruction, these reconstructions give
geometrical details of the internal sizes (estimated)
for the “PBS control” applied (Figure 7).
The Biologist (Lima). Vol. 19, Nº1, jan - jun 2021
Calderón-Chavarri et al.
93
Figure 7. Mice lung cells under PBS control (Yan et al., 2013), original magnification was 200x by the SEM and the 3D
reconstruction under that magnification (during the test day 5). C = circumference. C1, C2 and C3 = 3D reconstruction in SEM.
Furthermore, the following figure shows the same
mice lung cells under PBS but infected by H5N1
(during day 5 after virus infection) in
magnification SEM of 400x (Yan et al., 2013)
inside the circumference “C”, also, “C1, C2 and
C3” show the 3D reconstruction at 400x in
magnification SEM (Figure 8). It is possible to
identify better view from “monocytes and
neutrophils of the infiltrating cells”.
Figure 8. 3D reconstruction at 400x magnification SEM of mice lung cells infected by H5N1 (during the test day 5). C =
circumference. C1, C2 and C3 = 3D reconstruction in SEM.
Therefore, it was executed the algorithm designed
and described above owing to achieve 3D
reconstruction. The following figure shows the 3D
reconstruction of mice lung cells under CQ control
around 200x magnification due to the original
figure (cells inside C curve (Yan et al., 2013)
during day 5 after virus infection) was achieved
under that magnification value. It means that “C1,
C2 and C3” achieved similar scale reconstruction,
these reconstructions give geometrical details of
the internal sizes (estimated) for the “CQ control”
applied (Figure 9).
Figure 9. Mice lung cells under PBS control (Yan et al., 2013), original magnification was 200x by the SEM and the 3D
reconstruction under that magnification (during the test day 5). C = circumference. C1, C2 and C3 = 3D reconstruction in SEM.
The Biologist (Lima). Vol. 19, Nº1, jan - jun 2021
3D reconstruction for COVID-19
It was designed an algorithm according to be a
support for medical doctors, who are dealing with
COVID 19 treatment in Peruvian hospitals
(Haeberle et al., 2016; Goldsmith & Miller, 2009;
Bhalla et al., 2020; Duan et al., 2020; İnandıklıoğlu
& Akkoc, 2020; Kaniyala-Melanthota et al., 2020).
At the time that was finished this research, the
world and Perú are losing many lives, even though
some countries are crossing this epidemic.
However, there are countries such as Perú in which
the epidemic makes that medical doctors need to
research new strategies as did colleagues from
other countries (Prompetchara et al., 2020; Shah et
al., 2020). Yan et al. (2013), who let to analyze their
images, researched responses from viral against
H5N1, and that results helped to this research
owing to make 3D reconstructions of that figures,
and getting a mathematical model in which
medical doctors can evaluate the different response
of different excitation signals (viral, plasma,
medicines) that are translated as input excitation
signals to the model, from which was elaborated
the algorithm. Therefore, every answer and
prediction of this research help to medical doctors
to accelerate reaction over patients, it is looking for
94
Furthermore, the following figure shows the same
mice lung cells under CQ but infected by H5N1
(during day 5 after virus infection) in
magnification SEM of 400x (Yan et al., 2013)
inside the circumference “C”, also, “C1, C2 and
C3” show the 3D reconstruction at 400x in
magnification SEM. It is possible to identify better
view from “monocytes and neutrophils of the
infiltrating cells” (Figure 10).
Figure 10. 3D reconstruction at 400x magnification SEM of mice lung cells infected by H5N1 (during the test day 5). C =
circumference. C1, C2 and C3 = 3D reconstruction in SEM.
RESULTS AND DISCUSSION a faster understanding of what can happen with the
patient under different excitation signal.
Furthermore, it is possible to analyze the behaviour
inside of the body, that means reaction from the
lung and cells damaged by the virus, because of
images help to validate information expected by
medical doctors, which are formalized by the
mathematical model, and that can warrant to find
different solutions to estimate the best response
that medical doctor can use according to enhance
treatment to deal with this virus. The performance
of this research is constantly corrected while there
is more and more database to adapt its parameters,
which depend on many conditions due to every
patient has different characteristics, even
similitude but the difference are modelled by the
coefficient of the polynomial that represents the
behaviour of the general immunity response,
supported by the image processed and excitation
signal response evaluated to find the more adapted
model.
It is expected to complement this research for
plasma analysis application. Hence, it waits that
this research could be a support to correlate
advanced predictive polynomial models to achieve
adaptive predictions, in the image analysis of
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figures achieved from cells damaged by COVID
19, and as consequence, the medical doctors could
get faster emulations to study better answers to
understand new treatments against this virus.
It is dedicated special gratitude to Hugo Medina
because of his teachings in “Science Physics” for
many generations of engineers, he did and makes
that “Physics laws” could be so easy necessities to
get understanding of nature and current life, such as
for this research, with a very good base of nature
laws, it was possible to obtain a fundamental to
correlate advanced mathematics for the formalism
that engineering applications always need. Even
though Perú was not prepared to face against a big
epidemic, but it was found the answer from many
researchers who supported with points of view,
suggestions and analysis discussions to finish this
research, which is waiting to be useful for the
responsible people who have the task to organize
priority of activities, again in Perú. However, with
much attention in physical parameters that humans
can return to solve tasks but caring much distance
separations, room temperature, room humidity,
airflow and airspeed between them. Therefore, it is
expressed deep warm thanks to Willy Gamboa,
Christian Gozar, Darío Huanca, Daniel Menacho,
Broni Huamaní, Alexánder Zutta, Leslie Vargas
and Lilian Gamarra. There is expressed deep
special thanks to the researchers: “Yiwu Yan, Zhen
Zou, Yang Sun, Xiao Li, Kai-Feng Xu, Yuquan
Wei, Ningyi Jin, Chengyu Jiang”, they are authors
of the article: “Anti-malaria drug chloroquine is
highly effective in treating avian influenza A H5N1
virus infection in an animal model”, and they
proportioned the figure 2 from their research, from
which was possible to test the algorithm designed
and explained in sections above. It is expressed
thankful to Medical Doctors from Health Center of
PUCP, it because of their time to give suggestions
in the development of this research. It is expressed
thankful to researchers Hui Dai, Bin Zhao, and
Lawrence J. Schoen due to their time to share
opinions and suggestion to this research. It is
expressed thankful to students of the lecture
Nanotechnology MTR609 PUCP because of their
opinions and suggestions to analyze the
consequence of this research.
ACKNOWLEDGMENT
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Received November 10, 2020.
Accepted January 11, 2021.
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