Comprehensive Study Notes on Hypermetropia: Etiology, Clinical Manifestations, and Optical Correction

Definition and Classification of Hypermetropia

Hypermetropia, often referred to as farsightedness, is a spherical refractive error of the eye characteristically defined by the fact that the focal point of the image (the image focus) is formed behind the retina when the eye is in a relaxed state. This prevents a clear image from being focused directly on the retinal surface without the aid of accommodation or corrective lenses.

Hypermetropia is classified into three primary categories based on the anatomical and optical properties of the eye. The first is Axial Hypermetropia (Osová), where the optical system of the eye possesses a standard refractive power similar to an emmetropic eye, typically valued at $\phi = 58.64\,D$, but the physical length of the eye ($d_O$) is shorter than the standard emmetropic length, measuring less than $24\,mm$.

The second category is Systemic Hypermetropia (Systémová). In this case, the axial length of the eye remains at the standard $24\,mm$, but the optical system itself is less refractive, possessing a power of $\phi < 58.64\,D$. Systemic hypermetropia is further divided into Radius Hypermetropia (rádiusová), where the radius of curvature of individual optical surfaces in the eye is larger, resulting in a less powerful lens system ($r_{MY} > r_{EM}$), and Index Hypermetropia (indexová), where one or more media within the eye has a lower refractive index, leading to reduced total refractive power ($n_{MY} < n_{EM}$). The third category is Combined Hypermetropia (Kombinovaná), which presents as a mixture of both axial and systemic factors.

Optical-Anatomical Symptoms and the Role of Accommodation

Several specific optical-anatomical symptoms are associated with hypermetropia. The far point ($R$) of the eye is located at a finite distance behind the eye. The location of the near point ($P$) is dynamic and depends on the relationship between the magnitude of the accommodation width ($AŠ$) and the eye's axial refraction ($AR$). Specifically, if the accommodation width is greater than the axial refraction ($AŠ > AR$), the near point is located at a finite distance in front of the eye. As accommodation decreases, specifically when $AŠ = AR$, the near point moves to infinity. If a hypermetrope cannot focus at a distance or at near because their accommodation width is less than the axial refraction ($AŠ < AR$), the near point is located at a finite distance behind the eye, always further away than the far point.

Hypermetropes typically have an accommodation interval ($\Delta a$) that is situated further in front of the eye compared to an emmetrope. A defining characteristic of hypermetropia is the constant effort to correct the refractive error through active accommodation. This excessive use of the ciliary muscles leads to asthenopic complaints, which include symptoms such as burning, itching of the eyes, and headaches. These complaints are most prevalent during prolonged, maximum accommodation for near-vision tasks. To alleviate these symptoms, excessive accommodation must be replaced by optical correction using a convex (plus) lens.

Classification Based on Accommodation and Clinical Signs

Hypermetropia is clinically subdivided based on how the eye interacts with its accommodation. Latent Hypermetropia ($HYP_{LA}$) is a hidden form that represents the degree of refractive error permanently compensated by the individual's physiological tonus of the ciliary muscle (m. ciliaris) within the ciliary body. To diagnose latent hypermetropia, it is necessary to administer cycloplegic drops to paralyze the accommodation. Manifest Hypermetropia ($HYP_{MA}$) is the apparent form that occurs when the eye's accommodation is insufficient to compensate for the error, leading to visible asthenopic complaints and difficulty with near vision. The sum of these two constitutes Total Hypermetropia ($HYP_{TO} = HYP_{LA} + HYP_{MA}$).

Clinical signs of hypermetropia often include a smaller pupil diameter and a physically smaller eye, sometimes manifesting as enophthalmos. The ciliary muscle is frequently heavily developed due to constant use. In children, hypermetropia can lead to nasal squinting (esotropia) when looking into the distance because the act of accommodating to see clearly triggers a linked convergence reflex. A child without correction will use the "better" eye to look at infinity while the other eye deviates toward the nose. This can cause double vision (diplopia), which the brain manages by suppressing the image from one eye (supression). If left untreated, the suppressed eye becomes amblyopic (lazy eye/tupozrakost), a condition that cannot be corrected later in life. Treatment, such as occlusion therapy, must begin at a preschool age. Determining the total hypermetropia requires disabling the ciliary muscle with atropine (cycloplegia).

Correction and Vertex Power Relationships

To correct hypermetropia for distance, the image focus of the corrective lens must coincide with the far point of the eye ($F'_B = R$). The error is corrected using a convex (plus) lens to make the light rays entering the eye convergent so that the image forms correctly on the retina. The clinical goal is to provide the strongest plus lens with which the patient achieves the best visual acuity (vízus). For distance correction, lenses are centered horizontally based on the pupillary distance (PDD) for the right and left eye, and vertically based on the primary line of sight (VSOO) for a perpendicular gaze.

When calculating the relationship between the vertex power of the spectacle lens ($S'_B$) and the axial refraction of the eye ($AR$), the following formulas are used:

$S'_B = −\frac{AR}{1 + d \times AR}$

$AR = \frac{S'_B}{1 - d \times S'_B}$

where $d$ represents the distance of the lens from the eye. The vertex power required changes based on distance: the closer the convex lens is to the eye, the greater its vertex power must be (S'_{B2} = \frac{S'_{B1}}{1 - (\Delta d) \times S'_{B1}}). Overcorrection (providing too high a plus value) turns the patient into a pseudomyope, creating a sharp image in front of the retina and reducing visual acuity, requiring a reduction in lens power. Undercorrection leaves the patient hypermetropic, resulting in continued accommodation effort and asthenopic symptoms, requiring an increase in plus power.

Image Size and Refractive Examination

In an uncorrected axial hypermetropic eye, the image formed on the retina is smaller than that of an emmetropic eye. With correction, the image size increases. Moving the corrective lens closer to the eye in a corrected hypermetrope causes the retinal image size to decrease. In clinical practice, if the hypermetropia exceeds $+4\,D$, the medical prescription should always include the vertex distance (the distance of the lens from the corneal apex). The change in image size is governed by the factor \beta = 1 - (\Delta d) \times S'_B.

When determining refraction, the approach for hypermetropia differs from myopia. For hypermetropia, the practitioner uses the strongest plus lens that improves or maintains the best visual acuity to relax the patient's excessive accommodation. For myopia, the weakest minus lens (rozptylka) is used to avoid over-correcting the patient into a pseudohypermetrope. These examinations must be performed by a qualified optometrist or ophthalmologist. Refraction determination is divided into objective methods (using an autorefractometer, where the patient does not need to communicate) and subjective methods (using a trial frame and lenses where the patient provides feedback).

Axi
al Refraction and Ocular Length Calculations

Axial refraction ($AR$) is a function of the eye's axial length ($d_O$) and its refractive power (phi). It can be broken down into axial ($AR_O$) and systemic ($AR_S$) components ($AR = AR_O + AR_S$). Systemic axial refraction is defined as $AR_S = 58.64\,D - \phi_O$. When $AR_S < 0$, the eye is myopic; when $AR_S > 0$, it is hypermetropic. If $AR_S = 0$, then $AR = AR_O$.

The length of the eye ($d_O$) is the sum of the distance of the far point image ($a'_R$) and the distance between the anterior corneal surface and the image principal plane of the eye ($1.602\,mm$), expressed as $d_O = a'_R + 1.602$. Using the lens formula and refractive indices ($n' = n_O$ and $n = n_{VZ}$), the relationship is derived as follows:

$\frac{n'}{x'} - \frac{n}{x} = \phi$

$\frac{n_O}{a'_R} - \frac{n}{a_R} = \phi_O$

$\frac{n_O}{a'_R} = \phi_O + \frac{1}{a_R}$

$\frac{n_O}{a'_R} = AR + \phi_O$

$a'_R = \frac{n_O}{AR + \phi_O}$

Substituting this into the ocular length formula ($d_O = a'R + 1.602 \times 10^{-3}\,m$):

$d_O = \frac{n_O}{AR + \phi_O} + 1.602 \times 10^{-3}$

$d_O = \frac{n_O}{(AR_O + AR_S) + \phi_O} + 1.602 \times 10^{-3}$

$d_O = \frac{n_O}{AR_O + 58.64 - \phi_O + \phi_O} + 1.602 \times 10^{-3}$

$d_O = \frac{n_O}{AR_O + 58.64} + 1.602 \times 10^{-3}$

From these derivations, the formulas for the axial component and the total axial refraction are:

$AR_O = \frac{n_O}{d_O - 1.602 \times 10^{-3}} - 58.64$

$AR = \frac{n_O}{d_O - 1.602 \times 10^{-3}} - \phi_O$