Cataract Incision Fluid Ingress, an Engineering Analysis

Cataract Incision Fluid Ingress, an Engineering Analysis

David S.C. Pao, M.D.

Kristina Y. Pao, B.S.

Erik A. Cheever, Ph.D.

Cory Schroeder, B.S.

David S.C. Pao, M.D.

Kristina Y. Pao, B.S.

Erik A. Cheever, Ph.D.

Cory Schroeder, B.S.

Medicare data shows an increase in the incidence of endophthalmitis from 1994 to 2001. The only significant change in cataract surgery over this period is the sutureless clear corneal incision. Ingress of fluids through the incision is the etiology. From various studies two mechanisms are postulated:

1. Prolonged hypotony results in loss of wound architecture with wound gape.

2. Ingress of fluids due to pressure gradient with normal and increased intraocular pressure (IOP) without loss of wound architecture.

The second mechanism is described using engineering analysis.

Medicare data shows an increase in the incidence of endophthalmitis from 1994 to 2001. The only significant change in cataract surgery over this period is the sutureless clear corneal incision. Ingress of fluids through the incision is the etiology. From various studies two mechanisms are postulated:

1. Prolonged hypotony results in loss of wound architecture with wound gape.

2. Ingress of fluids due to pressure gradient with normal and increased intraocular pressure (IOP) without loss of wound architecture.

The second mechanism is described using engineering analysis.

..

Figure 1. The eye is an elastic globe. When force is applied, there is no egress of fluid, since the wound construction will withstand high pressures produced by an outside force. The corneal wound serves as a one-way valve in which fluid can ingress, but fluid cannot egress. An outside force distorts the globe, but the volume remains the same. The syringe represents the elasticity of the globe accepting the displaced volume. When the force is no longer applied, the elasticity of the syringe refills the globe configuration. At this point there is an instantaneous pressure gradient that provides ingress of fluid through the wound.

Figure 1. The eye is an elastic globe. When force is applied, there is no egress of fluid, since the wound construction will withstand high pressures produced by an outside force. The corneal wound serves as a one-way valve in which fluid can ingress, but fluid cannot egress. An outside force distorts the globe, but the volume remains the same. The syringe represents the elasticity of the globe accepting the displaced volume. When the force is no longer applied, the elasticity of the syringe refills the globe configuration. At this point there is an instantaneous pressure gradient that provides ingress of fluid through the wound.

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Figure 2. Mechanical analog. A force applied on the external eye at point a results in point a moving left causing an increase in IOP. This is indicated by compression of the spring. Note that positive displacement (x) is to the left. If the force is suddenly released, point a will begin to move to the right. When point a reaches its initial equilibrium position, the force on the spring is zero. If point a moves beyond the equilibrium position, the spring exerts a force to the left. This creates the pressure gradient (relative vacuum) with ingress of fluid through an incompetent wound. This gradient exists even without a wound. Assume the moving parts have a mass (M), and loss of force due to friction and damping is represented by a damper (B).

Figure 2. Mechanical analog. A force applied on the external eye at point a results in point a moving left causing an increase in IOP. This is indicated by compression of the spring. Note that positive displacement (x) is to the left. If the force is suddenly released, point a will begin to move to the right. When point a reaches its initial equilibrium position, the force on the spring is zero. If point a moves beyond the equilibrium position, the spring exerts a force to the left. This creates the pressure gradient (relative vacuum) with ingress of fluid through an incompetent wound. This gradient exists even without a wound. Assume the moving parts have a mass (M), and loss of force due to friction and damping is represented by a damper (B).

A force balance equation yields the mathematical formula and response curves that is represented in the form of a standard second order system. This is represented by the following:

A force balance equation yields the mathematical formula and response curves that is represented in the form of a standard second order system. This is represented by the following:

2

2

2

2

22

n n2

Forces 0

Ma Bv kx 0

d x dxM B kx 0

dtdt

d x B dx kx 0

M dt Mdt

d x dx2 x 0

dtdt

n

n

n

kwhere :

M

B k2 2

M MB B

2M 2 kM

Response CurvesUnder Damped, Critically Damped,

Over Damped

Response CurvesUnder Damped, Critically Damped,

Over Damped

Goal: ≥ 1 0 < < 1: system will oscillate with negative pressure gradient

resulting in ingress of fluids k and M not controlled by surgical techniques

k: spring constant; includes elastic modulus of sclera and cornea

M: mass of the eye; variable (i.e. myopia, hyperopia) B: damping coefficient

Tissue damping of cornea and scleraViscous damping of the vitreousFrictional damping is controlled by surgical technique:

Area of cornea incision (width and length) and IOP

Goal: ≥ 1 0 < < 1: system will oscillate with negative pressure gradient

resulting in ingress of fluids k and M not controlled by surgical techniques

k: spring constant; includes elastic modulus of sclera and cornea

M: mass of the eye; variable (i.e. myopia, hyperopia) B: damping coefficient

Tissue damping of cornea and scleraViscous damping of the vitreousFrictional damping is controlled by surgical technique:

Area of cornea incision (width and length) and IOP

n

B B

2M 2 kM

must be greater than 1. From the formula the spring constant (k), M, and much of B is not under surgeon control. Only the wound friction component and IOP is under surgeon control. Wound construction is thus the main criteria for surgical safety.

must be greater than 1. From the formula the spring constant (k), M, and much of B is not under surgeon control. Only the wound friction component and IOP is under surgeon control. Wound construction is thus the main criteria for surgical safety.

The average IOP was 38 mmHg at the conclusion of cataract surgery with the eye hyper inflated. 25 minutes later it was in the low 20’s.Rhee, D., Deramo,V., Connolly, B., Blecher, M., Intraocular Pressure Trends After Supranormal Pressurizaton to Aid Closure of Sutureless Cataract Wounds; J. Cataract Refractive Surgery, Vol. 25, April, 1999.

The average IOP was 38 mmHg at the conclusion of cataract surgery with the eye hyper inflated. 25 minutes later it was in the low 20’s.Rhee, D., Deramo,V., Connolly, B., Blecher, M., Intraocular Pressure Trends After Supranormal Pressurizaton to Aid Closure of Sutureless Cataract Wounds; J. Cataract Refractive Surgery, Vol. 25, April, 1999.

Clinical Observations

Recording of IOP over 70 mmHg on squeezing lids tight for approximately 2 seconds. On command to open the lids the IOP dropped pass the average of 17 mmHg to less than 10 mmHg and rebounded back to 17 mmHg.

Coleman, D. J., Trokel, S., Direct-Recorded Intraocular Pressure Variations in a

Human Subject. Arch. Ophthal.,Vol. 82, Nov, 1969.

Clinical Observations

Recording of IOP over 70 mmHg on squeezing lids tight for approximately 2 seconds. On command to open the lids the IOP dropped pass the average of 17 mmHg to less than 10 mmHg and rebounded back to 17 mmHg.

Coleman, D. J., Trokel, S., Direct-Recorded Intraocular Pressure Variations in a

Human Subject. Arch. Ophthal.,Vol. 82, Nov, 1969.

SummarySummary

Formula:Ma + Bv + kx = 0

Goal: keep ζ ≥ 1 0 < ζ < 1:

Results in ingress of fluid

Surgical control over: Incision width Incision length IOP at end of procedure

Formula:Ma + Bv + kx = 0

Goal: keep ζ ≥ 1 0 < ζ < 1:

Results in ingress of fluid

Surgical control over: Incision width Incision length IOP at end of procedure

n

B B

2M 2 kM

ConclusionConclusion

The engineering analysis provides ranges of the parameters (i.e. IOP, incision size, shape, length) that confirms our clinical observations and adds to further understanding of parameter limits. This allows increase safety and reduces the risk of endophthalmitis.

The engineering analysis provides ranges of the parameters (i.e. IOP, incision size, shape, length) that confirms our clinical observations and adds to further understanding of parameter limits. This allows increase safety and reduces the risk of endophthalmitis.