INNOVATION

New insights into blindness; mechanical fatigue of optic nerve head in glaucomatous optic neuropathy Amir Norouzpour*1 and Alireza Mehdizadeh2 1

Eye Research Center, Khatam-Al-Anbia Eye Hospital, Mashhad University of Medical Sciences (MUMS), Mashhad, Iran and 2Department of Medical Physics, Shiraz University of Medical Sciences (SUMS), Shiraz, Iran Abstract

Keywords

A common cause of blindness worldwide is glaucoma. It is characterized by visual field loss which is caused by optic nerve damage leading to glaucomatous optic neuropathy (GON). Modelling of GON development may be helpful for designing strategies to decelerate the rate of GON progression and prevent GON development at early stages. Attempts to complete the modelling of GON development continue. In this paper, it was speculated that the modelling could be more completed through a biomechanical point of view. GON may result from the mechanical fatigue effects of radial tensile stress (TS), caused by intra-ocular pressure (IOP), on the optic nerve head (ONH). The mechanical fatigue rate is influenced by patient’s age, the maximum and minimum magnitude of IOP, the amplitude of IOP and TS fluctuations, the ONH geometry, scleral thickness and biomechanical properties of the sclera, particularly the peripapillary part, and the axial length of the globe. Based on this model, more efficient strategies can be developed to augment the ONH and decelerate the progression of glaucomatous optic nerve damage, and even screen high-risk individuals at early stages.

Glaucoma, mechanical fatigue, optic neuropathy, tensile stress

1. Introduction A leading cause of blindness worldwide is glaucoma [1–3]. It is characterized by visual field loss which is caused by optic nerve damage leading to glaucomatous optic neuropathy (GON). Early diagnosis of high-risk individuals and appropriate interventions at early stages may delay the onset of primary glaucoma before any detectable nerve fibre damage and visual field loss occur. In addition, attempts to decelerate the rate of GON progression continue. Modelling of GON development may be helpful for designing strategies to prevent nerve fibre damage and slow the GON progression. Besides increased intraocular pressure (IOP), other factors which are independently associated with an increased risk of GON development include decreased central corneal thickness (CCT), advanced age and high cup-disc ratio [4]. Attempts to explain the roles of known risk factors in GON development have been continuing for many years. Two major hypotheses have emerged to explain the mechanism of GON development including mechanical and ischaemic theories [5–7]. The mechanical theory explains this phenomenon through the direct mechanical compression of the nerve fibres resulting in the death of retinal ganglion cells at the level of the optic nerve head (ONH). The ischaemic theory focuses on the potential development of intra-neural ischaemia resulting from decreased optic nerve perfusion. However, the exact *Corresponding author. Email: [email protected]

History Received 24 January 2014 Revised 27 July 2014 Accepted 27 July 2014

mechanism whereby known risk factors damage the ONH has not been fully elucidated and the proposed hypotheses remain to be proven. 1.1 The proposed model Another mechanism which may explain the process of GON development, as well as the role of known risk factors in the ONH damage, is the mechanical fatigue of the ONH. 1.2 Mechanical fatigue in materials Fatigue, in materials science, is the progressive and localized structural damage that occurs when a material is subjected to a fluctuating load. In this repetitive loading condition, with damage accumulation, fatigue failure (i.e. breakage) eventually occurs when stress levels are even much lower than those needed to produce failure following a single maximal load (i.e. the maximum stress values are less than the ultimate strength) [8]. Fatigue life is considered to be the number of fluctuations before a material fails (i.e. it breaks) and is dependent on different factors such as the geometry of materials and the magnitude of fluctuating and residual stress. Engineers had developed empirical means of quantifying the fatigue process. Perhaps the most important concept is the S-N diagram, such as those shown in Figure 1, in which a constant cyclic stress (D) applied to a material and the number of loading cycles (N) until the material fails is determined. Millions of cycles might be required to cause

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J Med Eng Technol, 2014; 38(7): 367–371

500

Δσ, MPa

400 300 200 100 0 3

4

5

6 log N

7

8

9

Figure 1. A typical S–N curve shows the inverse relationship between the amplitude of cyclic stress (D) and the number of cycles to failure.

failure at lower loading levels, so the horizontal axis is usually plotted logarithmically. A very substantial amount of testing is required to obtain an SN curve for a material that withstands a fully reversed loading and it will usually be impractical to determine whole families of curves for every combination of mean and alternating stress. In addition, when the cyclic load level varies during the fatigue process, a cumulative damage model is often used. To illustrate, the lifetime was taken to be N1 cycles at a stress level 1 and N2 at 2. If damage is assumed to accumulate at a constant rate during fatigue and a number of cycles n1 is applied at stress 1, where n15N1, then the fraction of lifetime consumed will be n1/N1. To determine how many additional cycles the material withstands at stress 2, an additional fraction of life will be available such that the sum of the two fractions equals one: n1 n2 þ ¼1 N1 N2 The generalization of this approach is called Miner’s Law and can be expressed as: X ni ¼1 ð1Þ Ni where ni is the number of cycles applied at a load corresponding to a lifetime of Ni. The concept of fatigue failure is applied to the design, manufacture and maintenance of aircrafts, bridges, machinery and other objects exposed to fluctuating loads. Moreover, in medicine, this concept has formed a field of study in skeletal [9], cardiovascular [10] and ophthalmologic sciences [11].

The major mechanical stresses applied on the ONH include radial tensile stress (TS) on a conceptual plane tangential to the lamina cribrosa and compressive stress perpendicular to the lamina cribrosa (Figure 2). TS is defined as the force acting in a unit area of a section of the ONH. It is presented by the Greek letter and expressed as dyn cm2 or mmHg m2. TS can be modelled on the basis of the Law of Laplace [12,13] as: Pr 2t

where, in this case, is TS, P is IOP, r is the radius of the globe and t is the thickness of the ONH. Axial length (AL) of the globe can be assumed as AL¼2r Therefore, the equation can be expressed as ¼

ð2Þ

P AL 4t

Any increases in IOP as well as the axial length of the globe or any decreases in the thickness of the ONH lead to increases in TS on the ONH. For the sake of simplicity, we consider some assumptions and draw the relationships on the basis of the assumptions. The relationship between the axial length of the globe and the thickness of the ONH is not clear clinically. Our first assumption is that the ONH thickness remains constant, despite changes in the axial length of the globe. We show graphically the TS as a percentage change compared to an eye with an AL of 24 mm, where the TS is taken to be 100% (Figure 3). This was calculated for the assumption of constant ONH thickness in different AL. The formula used for this calculation was ¼

1.3 Mechanical stress on ONH

¼

Figure 2. The major biomechanical stresses applied on the optic nerve head by intraocular pressure. The radial tensile stress, which is applied tangentially to the lamina cribrosa, and the compressive stress, which is applied perpendicularly to the lamina cribrosa, have been shown.

P AL 4

Our second assumption is that there may be a consistent change in the ONH thickness as a function of AL. We may assume a relationship in which the ONH thickness is reduced by 12.5% for every additional 10 mm of AL. Therefore, the ONH thickness of an eye with AL of 34 mm may be 87.5% of that of an eye with AL of 24 mm, and the ONH thickness of an eye with AL of 14 mm may be 114% of an eye with AL of 24 mm. Furthermore, the relationship may also be assumed as the ONH thickness is reduced by 25% for every additional 10 mm of AL. Through this assumption, the ONH thickness of eyes with AL of 14 mm and 34 mm may be 133% and 75%

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DOI: 10.3109/03091902.2014.950435

200 Tensile stress, mm Hg/m2

0.3

180 160 Tensile stress, mm Hg/m2,% of 24-mm eye

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140 120 100

0.25 0.2 0.15 0.1 0.05 0 6

11

16

21

26

31

36

IOP, mm Hg

80

Figure 4. The relationship between IOP and tensile stress for the assumption of constant ONH thickness in different axial length (AL ¼ 14 mm, ˙; 24 mm, ; 34 mm, g).

60 40

0.35 20

0.014

0.024

0.034

0.044

Axial length, m

Figure 3. The relationship between axial length and tensile stress for the assumption of the constant ONH thickness (˙) or the assumption of a reduction in the ONH thickness by 12.5% () or 25% (g) for every additional 10 mm of AL. IOP is assumed to be constant.

Tensile stress, mm Hg/m2

0.3 0 0.004

0.25 0.2 0.15 0.1 0.05 0

of that of an eye with AL of 24 mm, respectively. Therefore, the formula can be expressed as

6

11

16

21

26

31

36

IOP, mm Hg

AL

P AL C ð0:00124Þ 4

If the ONH thickness is reduced by 12.5% for every additional 10 mm of AL, C would be 1.14. If the ONH thickness is reduced by 25%, C would be 1.33. AL If C is considered to be 1.14, the parameter 1:14ð0:00124Þ represents an increase in the TS by a power of 1.14 for a reduction in the ONH thickness of 12.5%. If C is 1.33, the AL parameter 1:33ð0:00124Þ represents an increase in the TS by a power of 1.33 for a reduction in the ONH thickness of 25%. We present graphically the TS with the assumption of a consistent change in the ONH thickness as a function of AL, using the above formula (Figure 3). This is of course an assumption and it needs to be measured clinically. We also calculated the effect of changes in IOP on TS in eyes with an AL of 14 mm, 24 mm and 34 mm (Figure 4). This calculation was done once for the assumption of constant ONH thickness (Figure 4), and once for the assumption of a reduction in ONH thickness by 12.5% (Figure 5) and 25% (Figure 6) for every additional 10 mm of AL. 1.4 Mechanical fatigue of ONH IOP has a fluctuating pattern which applies a fluctuating radial TS on the globe wall and the ONH as well (Figure 7). Therefore, the fluctuating TS may have mechanical fatigue effects on the ONH leading to nerve fibre damage at the level of the ONH and eventually GON development. Although experimental data required us to supply a complete numerical solution, the mechanical fatigue effect of

Figure 5. The relationship between tensile stress and IOP for the assumption of a reduction in the ONH thickness by 12.5% for every additional 10 mm of AL (AL ¼ 14 mm, ˙; 24 mm, ; 34 mm, g). 0.4 0.35 Tensile stress, mm Hg/m2

¼

0.3 0.25 0.2 0.15 0.1 0.05 0 6

11

16

21

26

31

36

IOP, mm Hg

Figure 6. The relationship between tensile stress and IOP for the assumption of a reduction in the ONH thickness by 25% for every additional 10 mm of Al (AL ¼ 14 mm, ˙; 24 mm, ; 34 mm, g). The interval between two marked horizontal lines shows a 0.06 mmHg m2 increase in tensile stress in response to a 10 mmHg increase in IOP (see text and Figure 7).

fluctuating TS on the ONH may be analysed considering some assumptions. As shown in typical S-N curves, the amplitude of cyclic stress (D or S) is inversely related to the lifetime. Saðlog NÞ1 or log NS1

A. Norouzpour and A. Mehdizadeh

Δτ, mmHg/m2

0.012 0.009

A

τm τmin

0.006 0.003 0 me

Figure 7. A typical sort of cyclic stress applies a mean stress m on which a sinusoidal cycle is superimposed. Fluctuating IOP may apply a similar pattern of tensile stress on the ONH. In practice, the measured IOP is the mean IOP which correlates to m, and little attention is paid to the cyclic stress (D ¼ max min). Graph (b), with higher amplitude of cyclic stress may apply higher fatigue affects than graph (a) (see text).

When the stress value (S) is equal to the ultimate tensile strength of the ONH (f), one cycle is needed to break the ONH (log N ¼ 0). It can expressed as S log N 1 f Considering the S–N curve for a tissue may help us to complete the above relationship. Now, for the sake of simplicity, we may assume that S log N ¼ K 1 ð3Þ f where K is a constant coefficient. Consider a hypothetical tissue in which the S–N curve is linear. We assume that the tissue was subjected to n1 ¼ 106 stress cycles at a level S1 ¼ 0.2f. We wish to estimate how many cycles n2 the tissue can withstand if we raise the TS to S2 ¼ 0.3f. From the S–N curve and equation (3), if we assume K ¼ 10, we know the lifetime at S1 ¼ 0.2f would be N1 ¼ 108, and the lifetime at S2 ¼ 0.3f would be N2 ¼ 107. Now applying equation (1): n1 n2 106 n2 þ ¼ 8þ 7¼1 N1 N2 10 10 Thus n2 ¼ 99 105 Therefore, the tissue fails after applying 106 stress cycles at a level of 0.2f and 99 105 stress cycles at a level of 0.3f. The fatigue effects of TS on the ONH may be influenced by the maximum and minimum magnitude of IOP, the amplitude of IOP fluctuations, patient’s age, scleral thickness and biomechanical properties of the sclera, particularly the peripapillary sclera, the geometry of the ONH, and the axial length of the globe. Therefore, the rate of fatigue damage accumulation is not constant during a lifetime. It can be correlated with the cyclic variation in the stress intensity factor: da ¼ ADK m ð4Þ dN where da/dN is the rate of fatigue damage accumulation per cycle, DK ¼ Kmax Kmin is the stress intensity factor range

0 −2 −4 −6 −8

Rapid ONH damage

τmax

Slow ONH damage

B

No ONH damage

0.015

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log (rate of damage accumulaon, m/cycles)

370

−10 −12 0

20

40

60

80

100

stress intensity factor range ΔK, MPa√m

Figure 8. A typical graph showing the Paris law for the rate of fatigue damage accumulation on the ONH. Note that the vertical axis is plotted logarithmically.

during the cycle, and A and m are parameters that depend on the material, environment, frequency, temperature and stress ratio. This is sometimes known as the ‘Paris law’ and leads to plots similar to that shown in Figure 8. Of course, experimental data are needed to supply a complete numerical solution.

2. Discussion Mechanical fatigue of the ONH may be influenced by several factors. An important factor is the magnitude of TS applied on the ONH, which depends on the magnitude of IOP. Diurnal IOP fluctuations [14], as well as fluctuations in response to respiratory and cardiac cycles, cause a fluctuating TS to apply on the ONH. In this model, either maximum or minimum magnitude of IOP can independently influence the mechanical fatigue effects of TS on the ONH. An increase in either maximum or minimum magnitude of IOP is associated with an increase in the peak or trough magnitude of the fluctuating TS on the ONH, respectively, leading to more rapid GON development. Furthermore, in this model, an increase in the amplitude of TS fluctuations can enhance the fatigue effects of TS on the ONH (Figures 1 and 7), even when the maximum magnitude of IOP is within the normal range of the general population (Figure 6). The amplitude of TS fluctuation may increase in eyes with either higher amplitude of IOP fluctuation or higher axial length in a given amplitude of IOP fluctuation (Figure 6). The sclera is the main load-bearing tissue within the eye and, therefore, plays an important role in maintaining the biomechanical integrity of the eye. The stiffness of the ONH tissues is lower than that of the sclera, therefore they tend to be deformed whenever the surrounding sclera is deformed (e.g. in response to IOP fluctuations) [15]. Thus, any changes in the biomechanical properties of the sclera, particularly the peripapillary sclera, greatly influence the ONH biomechanical properties [15]. These findings suggest that the scleral biomechanical properties may influence the fatigue life of the ONH and the biomechanics of GON. In addition, clinical surveys showed that CCT is an independent risk factor for

Glaucoma and mechanical fatigue

DOI: 10.3109/03091902.2014.950435

GON development [4]. CCT may be a surrogate measurement for some biomechanical properties of the sclera. However, further investigations are needed to explain how a thin cornea, independent of corrected IOP, may increase the risk of GON development. Additionally, in this model, ONH geometry can influence the distribution of TS on the ONH. The points which undergo higher mechanical TS than their neighbouring points are more susceptible to be influenced by the fatigue effects of the fluctuating TS. Different ONH geometries including different cup–disc ratios and narrowing or notching or undermining of the neuroretinal rim and different scleral canal geometries may independently influence the ONH susceptibility for the GON development in a given IOP [16]. Another risk factor which can be predicted by this model is the high axial length of the globe. In a given IOP and scleral thickness, when the axial length of the globe increases, TS applied on the ONH increases (Figure 3). Therefore, it is predictable that individuals with a higher axial length are at a higher risk for the development of GON. However, clinical surveys showed that the potential risk of high axial myopia remains controversial [4,17,18]. The conflict may arise from this fact that the diagnosis of GON and visual field loss attributed to glaucomatous damage is difficult in these cases. ONH evaluation is complicated in the presence of myopic fundus changes, such as tilting the disc, which may make an assessment of cupping difficult. Moreover, the magnification of the disc associated with the myopic refractive error interferes with ONH evaluation. In addition, myopic fundus changes can cause visual field abnormalities, apart from any glaucomatous defects. High myopic refractive error may also make it difficult to perform accurate perimetric measurement and to interpret visual field defects. Therefore, further prospective clinical studies are needed to evaluate the potential risk of high axial length on the development of GON.

3. Conclusion Glaucomatous optic neuropathy may result from the mechanical fatigue effects of the fluctuating TS on the ONH, which are influenced by patient’s age, the maximum and minimum magnitude of IOP, the amplitude of IOP and TS fluctuations, scleral thickness and biomechanical properties of sclera, particularly the peripapillary sclera, the ONH geometry and the axial length of the globe. 3.1 Clinical implications Computational and experimental studies are needed to be designed to evaluate the relative risks of each factor in GON development, leading to a better understanding of determinants of GON development. Based on these ongoing studies, more efficient strategies can be developed to decelerate GON progression in the affected individuals, and even screen highrisk individuals at early stages before any glaucomatous nerve fibre damage and visual field loss occur.

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Acknowledgements The authors would like to thank Dr Zeinab Farhoudi for her help with preparing the manuscript.

Declaration of interest The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

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