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PreprintCited by 12Orbital Angular Momentum in OpticsDigital Holography and MicroscopyMicrofluidic and Bio-sensing Technologies

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Modelling red blood cell optical trapping by machine learning improved geometrical optics calculations

Open access
Tognato, R., Ciriza, D. Bronte, Maragò, O. M., Jones, P. H.·2023·Biomedical Optics Express
DOI 10.1101/2023.02.25.530023PMC PMC10368044

Preprint — published as 10.1364/boe.488931 · Paper page

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Abstract

Optically trapping red blood cells allows to explore their biophysical properties, which are affected in many diseases. However, because of their nonspherical shape, the numerical calculation of the optical forces is slow, limiting the range of situations that can be explored. Here we train a neural network that improves both the accuracy and the speed of the calculation and we employ it to simulate the motion of a red blood cell under different beam configurations. We found that by fixing two beams and controlling the position of a third, it is possible to control the tilting of the cell. We anticipate this work to be a promising approach to study the trapping of complex shaped and inhomogeneous biological materials, where the possible photodamage imposes restrictions in the beam power.

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Figures

Fig. 1. a) Definition of particle (yellow) and laboratory (white) reference frames and rotation angles (α, β, γ) of the cell around the laboratory reference frame; b) schematic depiction of the neural network. The input layer contains six neurons describing the cell position and orientation, and the output layer has six neurons describing the components of force and torque acting on the cell. In between are seven hidden layers (i=7), each of them with 256 neurons (j=256). c-d) Density plots comparing the magnitude of the total force (Ftot^NN) and torque (Ttot^NN) predicted with NN with those calculated with the GO method (Ftot^GO) and (Ttot^GO). Regression lines are shown in red. e) Log-Log plot of the normalised root mean squared error (NRMSE) between Ftot^NN and Ftot^GO, and Ttot^NN and Ttot^GO as a function of the number of rays used in the GO calculation. For each data point, the NN employed remains the same (trained with 4×10² rays).
Fig. 1. a) Definition of particle (yellow) and laboratory (white) reference frames and rotation angles (α, β, γ) of the cell around the laboratory reference frame; b) schematic depiction of the neural network. The input layer contains six neurons describing the cell position and orientation, and the output layer has six neurons describing the components of force and torque acting on the cell. In between are seven hidden layers (i=7), each of them with 256 neurons (j=256). c-d) Density plots comparing the magnitude of the total force (Ftot^NN) and torque (Ttot^NN) predicted with NN with those calculated with the GO method (Ftot^GO) and (Ttot^GO). Regression lines are shown in red. e) Log-Log plot of the normalised root mean squared error (NRMSE) between Ftot^NN and Ftot^GO, and Ttot^NN and Ttot^GO as a function of the number of rays used in the GO calculation. For each data point, the NN employed remains the same (trained with 4×10² rays).CC BY · PubMed Central
Fig. 2. a) Schematic depiction of an RBC trapped by a double-beam OT. b-c) Comparison between the GO calculation and the NN prediction for the b) torque-rotation curve for rotation around the x-axis and c) force-displacement curve along the x-direction. (d) Comparison of the probability distribution obtained with the GO calculation and with the NN prediction for a RBC in a DBOT. (e) Cell orientations in the numerical simulation for both GO and NN.
Fig. 2. a) Schematic depiction of an RBC trapped by a double-beam OT. b-c) Comparison between the GO calculation and the NN prediction for the b) torque-rotation curve for rotation around the x-axis and c) force-displacement curve along the x-direction. (d) Comparison of the probability distribution obtained with the GO calculation and with the NN prediction for a RBC in a DBOT. (e) Cell orientations in the numerical simulation for both GO and NN.CC BY · PubMed Central
Fig. 3. a) Translational autocorrelation function. The solid lines are exponential fits. Cxx(t), Czz(t), decay as single exponential while Cyy(t) as double exponential. b) y−α correlation shown as density plot. c) Normalised cross-correlation function between the rotation around the x-axis (α) and the y-displacement (red line exponential fit). Both Fy(α) d) and Tx(y) e) reveal unstable equilibrium when the cell is tilted of 90^(∘) around the x-axis (i.e. RBC in its folded position)
Fig. 3. a) Translational autocorrelation function. The solid lines are exponential fits. Cxx(t), Czz(t), decay as single exponential while Cyy(t) as double exponential. b) y−α correlation shown as density plot. c) Normalised cross-correlation function between the rotation around the x-axis (α) and the y-displacement (red line exponential fit). Both Fy(α) d) and Tx(y) e) reveal unstable equilibrium when the cell is tilted of 90^(∘) around the x-axis (i.e. RBC in its folded position)CC BY · PubMed Central
Fig. 4. a) Schematic depiction of the triple-beam optical trap and the polar co-ordinates system used to identify the position of the moving beam, and respective beam definition as beam 1, 2 and 3. (b) Force-field acting on the RBC located on a grid of coordinates in the x-y plane for ζ=45^(∘). The color scale indicates the magnitude of the total force acting on the x-y plane, while the grey arrows indicate the direction of the force. (c) Three-dimensional trajectories of the cell centre of mass over a simulation time of 10 s for different ζ, and the average values for the last second of simulation. d) Polar (ϕ) and e) azimuthal (θ) orientation of the RBC as a function of the simulation time. Average orientations are measured over the last second of the simulation. The error bar represents the standard deviation. f,g) Final equilibrium configuration for a RBC in the reconfigurable triple beam optical trap for ζ=15^(∘) and 90^(∘) respectively. The blue dot indicates the center of mass of the RBC while the red stars indicates the beams’ foci. The numbers indicate the position of each of the beams.
Fig. 4. a) Schematic depiction of the triple-beam optical trap and the polar co-ordinates system used to identify the position of the moving beam, and respective beam definition as beam 1, 2 and 3. (b) Force-field acting on the RBC located on a grid of coordinates in the x-y plane for ζ=45^(∘). The color scale indicates the magnitude of the total force acting on the x-y plane, while the grey arrows indicate the direction of the force. (c) Three-dimensional trajectories of the cell centre of mass over a simulation time of 10 s for different ζ, and the average values for the last second of simulation. d) Polar (ϕ) and e) azimuthal (θ) orientation of the RBC as a function of the simulation time. Average orientations are measured over the last second of the simulation. The error bar represents the standard deviation. f,g) Final equilibrium configuration for a RBC in the reconfigurable triple beam optical trap for ζ=15^(∘) and 90^(∘) respectively. The blue dot indicates the center of mass of the RBC while the red stars indicates the beams’ foci. The numbers indicate the position of each of the beams.CC BY · PubMed Central

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Citations

Cites

Show all 1 references

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Metadata

Authors
Tognato, R., Ciriza, D. B., Maragò, O. M., & Jones, P. H.
Affiliations
  • University College London (GB)
  • Institute for Chemical and Physical Processes (IT)
Corresponding author
Jones, P. H.
ORCID
Venue
Biomedical Optics Express
Publisher
openRxiv
Published
2023-02-26
Volume
14
Issue
7
Pages
3748-3748
ISSN
2156-7085 (ISSN-L)
DOI
10.1101/2023.02.25.530023
PMC
PMC10368044
OpenAlex
W4381429421
Cited by
12
References
1
Citations by year
2026: 7 · 2025: 2 · 2024: 3
FWCI
1.39
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Biomedical Optics Express (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • UCL Discovery (University College London) (submittedVersion, cc-by)
Funders
  • European Commission (SAMOTHRACE (ECS00000022)., PE0000023-NQSTI)
  • Göteborgs Universitet
  • H2020 Marie Skłodowska-Curie Actions (812780)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Digital Holography and Microscopy
  • Physical Sciences › Engineering › Biomedical Engineering › Microfluidic and Bio-sensing Technologies
Keywords
optical trapping, erythrocytes, optical forces, neural network surrogate model, geometrical optics, non-spherical particles, beam arrangement, photodamage, biophysical properties

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Tognato, R., Ciriza, D. B., Maragò, O. M., & Jones, P. H. (2023). Modelling red blood cell optical trapping by machine learning improved geometrical optics calculations. Biomedical Optics Express. https://doi.org/10.1101/2023.02.25.530023

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