Abstract

A three-dimensional model of corneal thermal response to CO2 laser radiation is constructed and numerical solutions for temperature rise are computed. Power distribution in the laser beam and a conducting air–cornea interface are considered explicitly. It is found that the radial distribution of temperature increases produced by a gaussian beam is also gaussian, for brief exposures. The corneal damage threshold is examined in terms of this result.

© 1970 Optical Society of America

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References

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  1. N. A. Peppers, A. Vassiliadis, K. G. Dedrick, H. Chang, R. R. Peabody, H. Rose, H. C. Zweng, Appl. Opt. 8, 377 (1969).
    [CrossRef] [PubMed]
  2. J. H. Prince, The Rabbit in Eye Research (Charles C Thomas, Springfield, 1964), p. 86.
  3. D. W. Peaceman, H. H. Rachford, J. Soc. Indust. Appl. Math. 3, 28 (1955).
    [CrossRef]
  4. M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, Bull. Math. Biophysics32 (1970), to be published.
    [CrossRef]
  5. H. C. Chang, K. G. Dedrick, Appl. Opt. 8, 826 (1969).
    [CrossRef] [PubMed]
  6. A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
    [CrossRef] [PubMed]
  7. A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).
  8. W. L. Derksen, T. I. Monahan, G. P. DeLhery, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, Ed. (Reinhold Publishing Corp., New York, 1963) Vol. 3, Part 3, pp. 171–175.
  9. A. R. Moritz, F. C. Henriques, Arch. Pathol. 43, 695 (1947).

1969 (3)

1966 (1)

A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).

1955 (1)

D. W. Peaceman, H. H. Rachford, J. Soc. Indust. Appl. Math. 3, 28 (1955).
[CrossRef]

1947 (1)

A. R. Moritz, F. C. Henriques, Arch. Pathol. 43, 695 (1947).

Chang, H.

Chang, H. C.

Clarke, A. M.

A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
[CrossRef] [PubMed]

Dedrick, K. G.

DeLhery, G. P.

W. L. Derksen, T. I. Monahan, G. P. DeLhery, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, Ed. (Reinhold Publishing Corp., New York, 1963) Vol. 3, Part 3, pp. 171–175.

Derksen, W. L.

W. L. Derksen, T. I. Monahan, G. P. DeLhery, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, Ed. (Reinhold Publishing Corp., New York, 1963) Vol. 3, Part 3, pp. 171–175.

Geeraets, W. J.

A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
[CrossRef] [PubMed]

Ham, W. T.

A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
[CrossRef] [PubMed]

Henriques, F. C.

A. R. Moritz, F. C. Henriques, Arch. Pathol. 43, 695 (1947).

Kohtiao, A.

A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).

Mainster, M. A.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, Bull. Math. Biophysics32 (1970), to be published.
[CrossRef]

Monahan, T. I.

W. L. Derksen, T. I. Monahan, G. P. DeLhery, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, Ed. (Reinhold Publishing Corp., New York, 1963) Vol. 3, Part 3, pp. 171–175.

Moritz, A. R.

A. R. Moritz, F. C. Henriques, Arch. Pathol. 43, 695 (1947).

Mueller, H. A.

A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
[CrossRef] [PubMed]

Newton, J.

A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).

Peabody, R. R.

Peaceman, D. W.

D. W. Peaceman, H. H. Rachford, J. Soc. Indust. Appl. Math. 3, 28 (1955).
[CrossRef]

Peppers, N. A.

Prince, J. H.

J. H. Prince, The Rabbit in Eye Research (Charles C Thomas, Springfield, 1964), p. 86.

Rachford, H. H.

D. W. Peaceman, H. H. Rachford, J. Soc. Indust. Appl. Math. 3, 28 (1955).
[CrossRef]

Resnick, I.

A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).

Rose, H.

Schwell, H.

A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).

Tips, J. H.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, Bull. Math. Biophysics32 (1970), to be published.
[CrossRef]

Vassiliadis, A.

White, T. J.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, Bull. Math. Biophysics32 (1970), to be published.
[CrossRef]

Williams, R. C.

A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
[CrossRef] [PubMed]

Wilson, P. W.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, Bull. Math. Biophysics32 (1970), to be published.
[CrossRef]

Zweng, H. C.

Amer. J. Ophthalmol. (1)

A. Kohtiao, I. Resnick, J. Newton, H. Schwell, Amer. J. Ophthalmol. 62, 524 (1966).

Appl. Opt. (2)

Arch. Environ. Health (1)

A. M. Clarke, W. T. Ham, W. J. Geeraets, R. C. Williams, H. A. Mueller, Arch. Environ. Health 18, 424 (1969).
[CrossRef] [PubMed]

Arch. Pathol. (1)

A. R. Moritz, F. C. Henriques, Arch. Pathol. 43, 695 (1947).

J. Soc. Indust. Appl. Math. (1)

D. W. Peaceman, H. H. Rachford, J. Soc. Indust. Appl. Math. 3, 28 (1955).
[CrossRef]

Other (3)

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, Bull. Math. Biophysics32 (1970), to be published.
[CrossRef]

J. H. Prince, The Rabbit in Eye Research (Charles C Thomas, Springfield, 1964), p. 86.

W. L. Derksen, T. I. Monahan, G. P. DeLhery, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, Ed. (Reinhold Publishing Corp., New York, 1963) Vol. 3, Part 3, pp. 171–175.

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Figures (3)

Fig. 1
Fig. 1

Geometry of the corneal heat conduction model.

Fig. 2
Fig. 2

υ(r, 7μ, T)/H0 with r0 = 2 mm for T = 10−5, 10−4, 10−3, 3.5 × 10−3, 10−2, 5.5 × 10−2, and 10−1. Solutions from the numerical model and from Eq. (3) are represented by solid and broken lines, respectively, when differences exist.

Fig. 3
Fig. 3

υ(r, 7μ, T)/H0 with T = 10 msec for r0 = 1 mm, 2 mm, and 3 mm. Solutions from the numerical model and from Eq. (3) are represented by solid and broken lines, respectively, when differences exist.

Tables (1)

Tables Icon

Table I v(r,7μ, T)/H0 for r0 = 1, 2 and 3 mm. The Units of v/H0 are °C(w/cm2)−1

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ρ c υ t = A + K r υ r + r ( K υ r ) + z ( K υ z ) ,
A = H / z = α H 0 exp [ α z ( r / r 0 ) 2 ] ,
υ ( r , z , 0 ) = 0 ° C , υ ( d , z , t ) = 0 ° C ,
υ ( r , ± d , t ) = 0 ° C .
H 0 ( t ) = { 0 ( t < 0 ) H 0 ( 0 t T ) 0 ( t > T ) .
υ ( r , 7 μ , T ) = υ ( 0,7 μ , T ) exp [ ( r / r 0 ) 2 ] .
υ ( r , z , T ) A ( r , z , T ) T / ρ c .
υ ( r , z , T ) A ( 0,0 , T ) ( 2 ρ c ) 1 exp [ ( r / r 0 ) 2 ] T S ( z , t ) = A ( 0,0 , T ) ( 2 ρ c ) 1 exp [ ( r / r 0 ) 2 ] T 2 e α z = A ( r , z , T ) T / ρ c ,

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