MD869Z - Method for optical capture of mobile particles in biological tissues - Google Patents

Abstract

The invention relates to methods of optical capture of mobile particles in biological tissues with the optical tweezers and can be used to study the structural, biophysical, morphological and optical properties of the particles of a biological tissue in vivo and their interactions with the environment for particle retention. a particular place in biological tissue or manipulation with them. The method of optical capture of mobile particles in biological tissues consists in determining the depth of localization of the mobile particle, forming a parallel beam of coherent laser light with an optimum irradiation wavelength selected depending on the value of the depth of location of the moving particle, the irradiation of the tissue with this beam and the capture of the moving particle.

Description

The invention relates to methods for optically capturing mobile particles in biological tissues with optical tweezers and can be used to study the structural, biophysical, morphological and optical properties of particles of a biological tissue in vivo and their interactions with the environment for retaining particles in a specific location in the biological tissue or manipulating them.

When changing the density of the light field flux I along an arbitrary axis x, a force of electromagnetic origin (Fgrad) appears, which acts on the moving dielectric particles located in the spatial region of the flux change. The absolute value of the force Fgrad depends on the gradient dI/dx - along the x-axis, as well as on the optical and structural parameters of the moving particles and the environment in which they are located. The force Fgrad, called the gradient force, is used in optical traps (laser tweezers) to capture, move and perform other contactless transactions with small moving particles [1].

A method of trapping dielectric particles in an optical trap is known, created by the light pressure Fp generated by one or more laser sources. The force acts in the direction of propagation, and their absolute value is equal to

,\tab(1)

where A - the light reflection coefficient for the particle [2].

The disadvantages of these methods are that they produce weak forces and cannot be used to capture particles in tissues because of the need to use high power density (E0) irradiations of the tissue surface to create the necessary force. Increasing E0 causes excessive heating of the tissues and can cause injury or death.

Also known is the method in which the gradient of the light flux density is created by the interference of two beams from single-mode lasers with a wavelength of λ = 632.8 nm. These beams are directed towards the particle, which, due to the action of gradient forces, is captured near the maxima (bright portions) of the interference image [3].

The disadvantage of this method is the impossibility of its application under in vivo conditions, since light with a wavelength of 632.8 nm does not exert the necessary force Fgrad at a wide range of tissue depths z, where the particle can be captured. In addition, due to light dissipation in the tissue, the interference image formed in the depth of the medium is usually very blurred in space, which leads to a considerable reduction in the flux density gradient, and, consequently, the gradient force Fgrad.

The closest solution is a method of capturing biological particles in an optical trap created by infrared laser light of a fixed wavelength in the range 800…1800 nm. The laser light falls on a converging lens with a short focal length, and at the focus point (beam constriction) a large gradient of the light field and the corresponding force Fgrad are formed. The converging laser beam is directed into an area containing a particle, which is captured near the focal point of the converging lens [4].

The disadvantage of this method is the impossibility of its use in in vivo tissue, since the infrared wavelength range does not provide the desired magnitude of the force Fgrad at a wide range of tissue depths z, where the particle can be captured. In addition, due to the strong light dissipation in the tissue, the region of beam constriction is usually spatially blurred, which leads to a considerable reduction in the flux density gradient and, consequently, the force Fgrad. Also, the method does not answer the question, what wavelength of laser radiation is optimal for capturing the particle at a certain depth z in the tissue from the point of view of ensuring the maximum particle capture power.

The problem solved by the invention consists in developing a method for capturing a mobile particle in a wide range of tissue depths, forming a maximum capture force of the mobile particle, with minimal heating of the tissue.

The method, according to the invention, eliminates the disadvantages mentioned above by determining the depth z of localization of the mobile particle, forming a parallel beam of coherent laser light with an optimal irradiation wavelength λ*, selected depending on the value z, which:

for z < 0.1 mm it is λ* = 450 nm and

for z ≥ 0.1 mm it is λ* ={1250[1 - exp(-z/1.35)]} nm,

irradiating the tissue with this beam and capturing the mobile particle.

The invention is explained by the drawings in Fig. 1-3, which represent:

– Fig. 1, radial structure of the flux density I(r) in soft tissue for the dermis of the skin at wavelength λ = 600 nm (continuous curves) and 700 nm (dotted curves) with blood oxygenation degree S = 0.5 (Fig. a, c) and 0.97 (Fig. b, d) with blood volume density Cb = 0.04 (Fig. a, b) and 0.02 (Fig. c, d) and melanin volume concentration Cm = 0.08, z = 1 mm, E0 = 1 W/cm2;

– Fig. 2, dependence of the force gradient F, generated by the laser light beam at a depth z = 0.16 (curve 1), 0.2 (curve 2), 0.5 (curve 3), 1 (curve 4), 2 (curve 5), 4 (curve 6) and 8 mm (curve 7), upon skin irradiation at different wavelengths λ = 400…1800 nm;

– Fig. 3, the calculated dependence (continuous curve) and after approximation (dotted curve) of the irradiation wavelength λ*, which ensures a maximum force gradient Fmax, depending on the depth z of the particles captured in the dermis of the skin.

The dispersion of the coherent radiation beam in biological tissues leads to the formation of a speckle structure of the light field inside the tissue. The speckle structure is the result of the interference of light scattered at small angles to the direction of incidence of the light [Ivanov A. P., Katsev I. L. On the speckle structure of the light field in a dispersed medium illuminated by a laser beam, Quantum Electronics, 2005, Vol. 35, No. 7, pp. 670 - 674]. In the radial plane or in the plane perpendicular to this direction, the structure presents bright and dark regions, called speckles. This change in the flux density I causes the formation of Fgrad, which can be calculated by the formula

,(2)

where c = cm/s - speed of light in the medium,

n - absolute value of the refractive index of the medium,

- the specific polarizability of the particle,

m = np/n - relative refractive index of the particle,

np - absolute value of the refractive index of the particles,

R - radius of the sphere of the same volume as the particle,

dI/dx - gradient of light flux density (W/cm3),

B - a constant of proportionality depending on the parameters of the particle (np and R) and the environment (n) in which it is located.

From (2) it follows that the force Fgrad is directed along the x-axis in the direction of increasing (if m>1) or decreasing (if m <1) the luminous flux density. For mobile tissue particles usually m≈1.05.

The characteristic radius L of the speckles, which depends on the wavelength λ and the depth z, can be defined by the formula [Иванов А. P., Katsev I. L. On the speckle-structure of the light field in a dispersed medium illuminated by a laser beam, Quantum Electronics. 2005, T. 35, No. 7, p. 670 - 674; Абрамович Н. D., Barun V. V., Dik С. К., Терех А. С. Analytical methodology for estimating the contrast of the speckle-structure of the light field scattered by soft biotkans // 5th Troitskaya conference «Medical physics and innovations in medicine», Collection of materials. 2012, T. 1, c. 212 - 214]:

,(3)

where - the dispersion of the angular distribution of light intensity, which propagates at small angles to the direction of surface irradiation.

The total density of the luminous flux at the depth z in the radial plane can be calculated by the formula [Абрамович Н. D., Barun V. V., Dik С. К., Терех А. С. Analytical methodology for estimating the contrast of the speckle-structure of the light field scattered by soft biotkans // 5th Trinity conference "Medical physics and innovations in medicine". Collection of materials. 2012, T. 1, c. 212 - 214]:

,\tab(4)

where E0 - illumination of the material surface,

r - distance measured from the beam axis,

ф - random phase.

On the right side of formula (4), the first term gives the field component of the light, which depends on r, and the second - the incoherent background, which is independent of r. Therefore, only the first term contributes to the formation of gradient forces in the depth of the medium.

Fig. 1 shows the radial structure of the density I(λ, z, r), calculated by the authors using formula (4), for two wavelengths λ = 600 and 700 nm, at a depth z = 1 mm.

Human skin serves as an example of tissue. The structural and optical parameters are presented in [Барун В. V., Ivanov A. П., Волотовская А. V., Ulaschik V. С. Absorption spectra and depth of light penetration into normal and pathologically altered human skin // Journal of applied spectroscopy. 2007, T. 74, № 3, c. 387 - 394], and the method of calculating the characteristics in [Иванов А. P., Katsev I. L. On the speckle-structure of the light field in a dispersed medium illuminated by a laser beam. Квантовая электроника, 2005, T. 35, No. 7, p. 670 - 674; Абрамович Н. D., Barun V. V., Dik С. К., Терех А. С. Analytical methodology for estimating the contrast of the speckle-structure of the light field, scattered by soft biotkans // 5th Troitskaya Conference "Medical Physics and Innovations in Medicine". Сборник материов, 2012, Т. 1, c. 212 - 214; Barun V. V., Ivanov A. P. Absorption of light by blood during low-intensity laser irradiation of skin // Kvantovaya elektronika, 2010, T. 40, № 4, c. 371 - 376]. Typical values of the structural and biophysical parameters of the skin were selected. Here, the degree of blood oxygenation S = 0.5 (Fig. a, c) and 0.97 (Fig. b, d), the volume concentration of blood Cb = 0.04 (a, b) and 0.02 (c, d), the volume concentration of melanin Cm = 0.08, the thickness of the stratum corneum of the epidermis is 20 µm and 100 µm. The authors performed calculations for other values of these skin parameters. It turned out that the variable component r (the first term on the right side of formula (4)) depends weakly on these changes and is determined mainly by the values of λ and z.

From formula (4) we find the density gradient dI/dr, which creates the force Fgrad, which acts on the moving particle at depth z:

. \tab(5)

The "minus" sign indicates the direction of the force - in the direction of decreasing or increasing r. As can be seen from (1) and (5), Fgrad in the radial plane receives the largest absolute value, which corresponds to the equality . From (1) and (5) it also follows that the maximum absolute value of the force Fgrad:

(6)

depends on z and λ of the speckle characteristics and . We compare the maximum values of the gradient force (6) and the light pressure, at the same surface irradiance power density. For this purpose, we take as an example a moving particle with R=3 µm and evaluate the equation:

,

where the index max indicates the maximum value of the corresponding quantities. For example, A = 1. Calculations have shown that this ratio is in the range 150…800 at z < 2 cm. So, the maximum gradient force is about 2…3 orders of magnitude greater than the pressure force, so the latter can be ignored.

Similar calculations have shown that, due to the small value compared to , it is possible to ignore the density gradient in the z-axis direction, in the direction of light propagation.

Fig. 2 shows the values of the force Fgrad (in newtons), created by a parallel laser beam of light with E0 = 1 W/cm2 at a depth z = 0.16 (curve 1), 0.2 (curve 2), 0.5 (curve 3), 1 (curve 4), 2 (curve 5), 4 (curve 6) and 8 mm (curve 7) when irradiating the tissue surface with different wavelengths λ = 400…1800 nm. In the calculations, the typical parameters for soft tissues n = 1.33, m = 1.05 and R = 3 µm were used. As can be seen, with increasing z, to obtain the maximum force Fmax, the wavelength λ* must be increased. Thus, at the level of the upper dermis of z ≈ 0.12 mm, the highest value of Fmax is at λ* ≈ 450 nm, z ≈ 0.5 mm - λ* ≈ 700 nm, z ≈ 1 mm - λ* ≈ 850 nm, etc. The peculiarities of the dependence of the force F on the wavelength λ are presented in Fig. 2, and the maximum value for λ =λ* is due to the behavior of the spectral characteristics of absorption and scattering of the components of soft tissues, primarily - derivatives of hemoglobin and water.

Using the data in Fig. 2, we compare the values of the force Fmax, which acts on mobile particles in the irradiated medium, λ = 800…1800 nm). We assume that the irradiation is carried out at the wavelength λ = 1000 nm. As can be seen from Fig. 2, in the upper layer of the tissue at z ≤ 0.5 mm (curves 1…3) and at a depth of z ≥ 4 mm (curves 6 and 7) the values of Fmax obtained, according to the method proposed in the invention, are approximately 2…4 times higher than the maximum force according to [US 4893886 A 1990.01.16] with the same power density E0. When z = 1…2 mm (curves 4 and 5), both methods give approximately the same maximum power. Similar conclusions can be made for other wavelengths of radiation in the range of 800…1800 nm, as proposed in the mentioned source. We emphasize that the results of calculations in Fig. 2 show the case of irradiation of the tissue surface with a parallel beam of light. If the beam is convergent, as in the mentioned source, then the value of Fmax calculated by the proposed method will be even higher than in the mentioned source in the wide range of depths z, because in this case the laser energy at о depth will be allocated to о larger surface.

In Fig. 3 is represented the method of determining the wavelength λ*, to obtain the maximum force Fmax at a certain depth z in the tissue. The calculated dependence λ* (z), obtained from the graph (Fig. 2, solid line) and its approximation (Fig. 2, dotted line) according to the formula λ* ={1250[1 - exp(-z/1.35)]}, where λ* is expressed in nm and z in mm, are presented. The difference in the values obtained between these curves of the maximum force Fmax is minor and does not exceed 5%.

Embodiment of the invention

Let us assume that it is necessary to capture red blood cells in a capillary, which is located at a depth z = 1 mm below the skin surface. According to the formula λ* ={1250[1 - exp(-z/1.35)]} we calculate λ* = 654 nm. Thus, for optical capture of the erythrocyte it is necessary to irradiate the skin surface with a parallel laser beam with a wavelength of 654 nm. The optical capture method includes the following steps:

Determination of the z-depth of localization of the mobile particle. In the case of erythrocytes, it is known that they are distributed throughout the entire thickness of the dermis and subcutaneous fat layer to a depth of 8…10 mm. In the case of other mobile particles, we can track them non-invasively, using optical coherence tomography.

Selecting the laser that emits radiation at a calculated wavelength.

Formation of the parallel light beam, using the selected laser.

Irradiation of the tissue surface with a parallel beam of laser light.

Thus, the proposed method allows generating the maximum force Fmax of capturing the mobile particle in a wide range of depths z in soft tissues due to the choice of the optimal wavelength of irradiation of the tissue surface. The force obtained is 2 or more times higher than that calculated according to the closest solution.

1. Yavorskiy B.M., Detlaf A. A. Справочник по физике, Москва, Наука, 3rd edition, 1965, p. 347 - 348

2. US 3710279 A 1973.01.09

3. Afanasyev A. A., Katarkevych V. M., Rubinov A. N., Efendiev T. Sh. Modulation of particle concentrations in the interference field of laser radiation, Zhurn. acc. spektrosk. 2002, T. 69, No. 5, p. 675 - 679

4. US 4893886 A 1990.01.16

Claims (1)

Method for optical capture of mobile particles in biological tissues, which consists of determining the depth z of localization of the mobile particle, forming a parallel beam of coherent laser light with an optimal irradiation wavelength λ*, selected depending on the value z, which: for z < 0.1 mm it is λ* = 450 nm and for z ≥ 0.1 mm it is λ* ={1250[1 - exp(-z/1.35)]} nm, irradiating the tissue with this beam and capturing the mobile particle.