ac / a ratios ( convergence change driven by a change in blur ) are commonly used to explain many characteristics of strabismus , but clinicians may be unaware of significant limitations of clinically measured ratios . for example , 3.0 d of blur is often assumed to drive 3.0 d of accommodation , and so the change in angle per diopter is calculated by dividing by 3a stimulus ( clinical ) ac / a ratio . in figure  1 the upper line ( in meter angles ( ma ) and diopters ) represents this  perfect  response ( on the y - axis ) to the blur produced by near fixation or minus lenses ( x - axis ) . 1 ma is required to fix at 1 meter and 3 ma are required at 33 cm . they are a useful theoretical measure because they are independent of interpupillary distance ( ipd ) . an infant with an ipd of 45 mm needs 4.5 at 1 m , whereas a large adult with a 70 mm ipd will converge 7 but both will converge 1 ma to fix bifoveally . they are also a useful because ma can be plotted on the same scale as diopters . 3 d of accommodation accompanies 3 ma of convergence , leading to response gains of 1.0 and an ac / a ratio of 1 ma to 1 d ( 6 to 1 d in an adult with an ipd of 60 mm ) figure  1 shows two hypothetical cases , reflecting the range of actual responses we see experimentally . example 2 ( still typical of many normal people ) has lower accommodation and vergence responses to the same blur but still accommodates more than converges . the stimulus ac / a ratio ( convergence change in relation to the blur stimulus given ; using 3.0 d as the divisor ) will be higher in example 1 because they converge more . the response ratios ( convergence change in relation to accommodation response and the measure that most vision scientists consider the  true in example 1 the divisor is 2.4 d , but in example 2 it is only 0.6 d ; therefore , both stimulus ratios are lower than the response ratios , but much lower for example 2 response ratios tell us the true convergence/ accommodation relationship , but not necessarily how either relate to the stimulus . in both examples , each has an identical  normal  response ac / a ratio of 0.75 ma to 1 d ( approximately 4.5 to 1 d in an adult ) , despite very different responses to the change in blur . both stimulus and response ratios are missing detail about how we use blur as a cue . the rarely considered ca / c ratio describes accommodation associated with convergence driven by disparity ( rather than vergence to blur above ) and is similarly problematical . high ac / a accompanies low ca / c ; if blur drives a large amount of convergence , then disparity drives less accommodation . in our laboratory , higher ca / c than ac / we predicted how different biases toward blur and disparity , in combination with anatomical factors , such as position of rest and refractive error , would result in specific diagnoses and treatment responses . our dataset was collected from a wide range of normal controls and patients in the course of other published and unpublished studies . subjects fulfilled accepted diagnostic criteria of normality , heterophoria , or intermittent heterotropia , for example , as set out by ansons and davis . all were healthy , 4 - 42 years of age , with normal binocular vision and stereopsis of at least 120 arcsec at at least one fixation distance ; none were amblyopic . we selected the cases by clinical diagnosis , and all cases tested in the laboratory within any diagnosis were included in the analysis ; that is , none were rejected because they did not fit our model . laboratory data were collected using a remote haploscopic photorefractor to present images moving in depth between distances of 0.33 m to 2 m , described in detail elsewhere and in e - supplement 1 ( available at jaapos.org ) . simultaneous , objective , vergence position and accommodation were calculated from eye position and refraction data collected by a plusoptix s04 powerrefii photorefractor ( plusoptix gmbh , nuremberg ) . we calculated convergence angle in mas and accommodation in d at each fixation distance after correcting for ipd , angle lambda ( representing the offset of the corneal reflection from the pupil center , equivalent to angle kappa ) , and spectacle magnification . different target manipulations allowed us to assess responses to blur , disparity , and proximity separately as the target moved in space . by allowing binocular viewing or by remotely occluding one eye we could present or eliminate disparity . by presenting a detailed clown cartoon or a gabor patch target we could present or minimize blur cues , and proximal ( size / motion / looming ) cues could be retained if the same size picture was visible during motion or could be minimized by obscuring target motion and scaling the target for target distance . by varying these conditions , our discussion concentrates on the three targets most pertinent to our argument : ( 1 ) a naturalistic all - cue ( bdp ; blur [ b ] , disparity [ d ] , and proximal [ p ] ) target ( detailed clown , viewed binocularly and unscaled for distance ) ; a blur - only ( b ) target ( detailed clown , viewed monocularly , scaled - for - distance ) ; disparity only ( d ) target ( binocular gabor patch , also scaled - for - distance ) . we calculated response ac / a ratios using the gains in the b condition ( convergence gain / accommodation gain ) and response ca / c ratios using accommodation gain / convergence gain in the d condition . as we argue that the ratios are insufficient , we also needed a measure of bias toward better responses to disparity or blur , independent of the ac / a and ca / c ratios . we averaged vergence and accommodation gains ( [ accommodation gain + vergence gain]/2 ) to the b target , and those to the d target , then subtracted the b target gains from the d target gains to form a disparity bias index ( dbi ) . if blur and disparity responses are equal , the dbi is zero ; a larger positive number indicates a stronger disparity bias , whereas a smaller or negative number indicates more blur bias . we present six hypothetical patterns:normal / classical  ac / a and ca / c ( figure  2a , b ) : blur driving more accommodation than vergence and disparity driving more vergence than accommodation.high ac / a and low ca / c ( figure  2c , d ) : vergence response gains always greater than accommodation.low ac / a and high ca / c ( figure  2e , f ) : accommodation response gains always better than convergence .  normal / classical  ac / a and ca / c ( figure  2a , b ) : blur driving more accommodation than vergence and disparity driving more vergence than accommodation . high ac / a and low ca / c ( figure  2c , d ) : vergence response gains always greater than accommodation . low ac / a and high ca / c ( figure  2e , f ) : accommodation response gains always better than convergence . the ac / a and ca / c ratios are identical in each pair , but with different blur and disparity biases . the upper tables under the pairs of charts show the responses used to calculate ac / a and ca / c ratios as well as the disparity bias index ( dbi ) . the lower tables show how changing blur or disparity has different effects on the angle of deviation and/or the accommodation depending on the pattern . responses to the naturalistic ( bdp ) cue show that overall responses stay within normal limits , but responses to blur and disparity within this stimulus can be very different . we then present real examples drawn from our laboratory dataset ( with 95% confidence intervals and statistical tests quoted where large enough numbers permit meaningful analyses ) . patterns a and b show classical normal responses in the naturalistic ( bdp ) condition , with perfect vergence and slight accommodation lag for near ( vergence gain , 1.00 ; accommodation gain , 0.9 ) . both have identical and normal response ac / a and ca / c ratios , but pattern a 's normal responses are stronger to disparity than blur , whereas pattern b 's responses to blur and disparity are more equal . most normal people are disparity - biased , with more bias in adults ( adult ( n = 56 ) dbi 0.43 vs child ( n = 24 ) dbi 0.20 , t ( 78 ) = 3.52 ; p = 0.001 ) response ac / a ratios are within normal ranges ( approximately 5 to 1 d in both groups ) . the weaker response to blur explains why spectacles rarely change heterophoria much in nonstrabismic individuals . disparity is the main drive , so changing blur makes little difference if disparity remains available . however , researchers who use naive participants ( as opposed to  visual experts ,  such as vision scientists and optometry students ) , consistently find that disruption of binocularity causes a significant drop in accommodation as well as major inaccuracies of convergence that occur in strabismus . similar findings have been reported in primates . as additional lenses or change in refractive error rarely change angles of deviation in nonstrabismic children and adults , our hypothesis was that disparity bias is normal , whereas accommodative strabismus , where lenses change angles of deviation , would show blur - biased pattern b. as predicted , classic accommodative esotropias ( similar near / distance angles ; n = 3 ) followed pattern b ( figure  4 ) , with a low dbi of 0.03 , below the lower 95% confidence interval of normal children . ten further children had higher ac / a accommodative esotropia ( near esodeviation more than 10 greater than distance while still retaining control with spectacles ) . these 10 fell between this group and pattern d below , with a dbi of 0.01 and ac / a ratio of 1.7 ma to 1 d. the vergence and accommodation of pattern a are more disrupted by occlusion or suppression disrupting disparity cues but less disrupted by lenses or developing refractive error changing blur . pattern b is more affected by blur change but less disrupted by disparity change . because the ac / a and ca / c ratios are normal , blur change drives more accommodation than convergence and disparity change drives more convergence than accommodation . there are also disparity - biased vs blur - biased alternatives possible for the high ac / a and low ca / c ( convergence exceeds accommodation ) and the low ac / a and high ca / c ( accommodation exceeds convergence ) scenarios , each pair with similar ratios ( patterns c and d ) . disparity - biased pattern c shows a higher dbi . despite the high ac / a ratio , blur stimuli should not lead to overconvergence because blur is a weak cue ; underaccommodation occurs , but overconvergence does not . the vergence response to disparity ( low ca / c ratio ) might not drive sufficient accommodation in the case of orthophoria where there is normal convergence demand , but in exophoria , the additional convergence required to overcome the deviation would not result in overaccommodation . the weak accommodation of early presbyopia ( figure  5a ) by necessity means more convergence associated with each unit of accommodation , but overconvergence on attempted near fixation does not occur because disparity , not blur , drives responses . many well - controlled basic exodeviations , controlling with good accommodation , also fall into this category . in blur - biased pattern d the high ac / a ratio causes excessive convergence in response to blur ; individuals with this pattern are at risk of convergence excess accommodative esotropia . as predicted , high ac / a ratio convergence excess esotropias ( n = 8) fit pattern d , with a negative dbi of 0.31 , significantly lower than normal children ( t = 2.86 ; p = 0.008 ) . some naturalistic bdp responses in the figure show hypoaccommodation , suggesting that some try to control their deviation , but at the expense of clear near vision . patterns e and f in figure  2 show that these low ac / a and high ca / c individuals accommodate with relatively little convergence , but when they converge they overaccommodate ( also reflected in the slight accommodation lead in the bdp condition ) . disparity - driven pattern e subjects do not accommodate well to increasing blur targets , and do even less convergence , leading to near exophoria . poor blur response might be found in straight - eyed hyperopic ametropic amblyopia . reducing disparity cues by dissociation , prisms or surgery , however , significantly reduces accommodation , while the need to control a large exodeviation , for example , might result in overaccommodation . our near exophoric subjects were in a subclinical , asymptomatic group of young adults with small deviations ( but with > 6 larger near angle ) and were in fact recruited as normal controls ( figure  6 ) . they had significantly lower ac / a ratios ( t   = 2.27 ; p  =  0.028 ) than normal and accommodated more than the normal adults while responding to the d target ( 2.98 d vs 2.45 d ( t   = 3.34 ) ; p = 0.001 ) . although the high ca / c ratio means that accommodation exceeds convergence , the weakness of disparity - driven responses does not result in over - accommodation . we predict that hyperopic children who manage to accommodate over their refractive error without becoming strabismic would fit this group . our dataset did not include any individuals in pattern f. our patient participants were drawn from a hospital population , referred for poor visual acuity , so this  silent  group of hyperopic children with good vision is difficult to detect because they pass screening . we predict that subjects with the combination of convergence insufficiency but good accommodation will fit into this group . patterns a and b show classical normal responses in the naturalistic ( bdp ) condition , with perfect vergence and slight accommodation lag for near ( vergence gain , 1.00 ; accommodation gain , 0.9 ) . both have identical and normal response ac / a and ca / c ratios , but pattern a 's normal responses are stronger to disparity than blur , whereas pattern b 's responses to blur and disparity are more equal . most normal people are disparity - biased , with more bias in adults ( adult ( n = 56 ) dbi 0.43 vs child ( n = 24 ) dbi 0.20 , t ( 78 ) = 3.52 ; p = 0.001 ) response ac / a ratios are within normal ranges ( approximately 5 to 1 d in both groups ) . the weaker response to blur explains why spectacles rarely change heterophoria much in nonstrabismic individuals . disparity is the main drive , so changing blur makes little difference if disparity remains available . however , researchers who use naive participants ( as opposed to  visual experts ,  such as vision scientists and optometry students ) , consistently find that disruption of binocularity causes a significant drop in accommodation as well as major inaccuracies of convergence that occur in strabismus . as additional lenses or change in refractive error rarely change angles of deviation in nonstrabismic children and adults , our hypothesis was that disparity bias is normal , whereas accommodative strabismus , where lenses change angles of deviation , would show blur - biased pattern b. as predicted , classic accommodative esotropias ( similar near / distance angles ; n = 3 ) followed pattern b ( figure  4 ) , with a low dbi of 0.03 , below the lower 95% confidence interval of normal children . ten further children had higher ac / a accommodative esotropia ( near esodeviation more than 10 greater than distance while still retaining control with spectacles ) . these 10 fell between this group and pattern d below , with a dbi of 0.01 and ac / a ratio of 1.7 ma to 1 d. the vergence and accommodation of pattern a are more disrupted by occlusion or suppression disrupting disparity cues but less disrupted by lenses or developing refractive error changing blur . pattern b is more affected by blur change but less disrupted by disparity change . because the ac / a and ca / c ratios are normal , blur change drives more accommodation than convergence and disparity change drives more convergence than accommodation . there are also disparity - biased vs blur - biased alternatives possible for the high ac / a and low ca / c ( convergence exceeds accommodation ) and the low ac / a and high ca / c ( accommodation exceeds convergence ) scenarios , each pair with similar ratios ( patterns c and d ) . disparity - biased pattern c shows a higher dbi . despite the high ac / a ratio , blur stimuli should not lead to overconvergence because blur is a weak cue ; underaccommodation occurs , but overconvergence does not . the vergence response to disparity ( low ca / c ratio ) might not drive sufficient accommodation in the case of orthophoria where there is normal convergence demand , but in exophoria , the additional convergence required to overcome the deviation would not result in overaccommodation . the weak accommodation of early presbyopia ( figure  5a ) by necessity means more convergence associated with each unit of accommodation , but overconvergence on attempted near fixation does not occur because disparity , not blur , drives responses . many well - controlled basic exodeviations , controlling with good accommodation , also fall into this category . in blur - biased pattern d the high ac / a ratio causes excessive convergence in response to blur ; individuals with this pattern are at risk of convergence excess accommodative esotropia . as predicted , high ac / a ratio convergence excess esotropias ( n = 8) fit pattern d , with a negative dbi of 0.31 , significantly lower than normal children ( t = 2.86 ; p = 0.008 ) . see figure  5b . some naturalistic bdp responses in the figure show hypoaccommodation , suggesting that some try to control their deviation , but at the expense of clear near vision . patterns e and f in figure  2 show that these low ac / a and high ca / c individuals accommodate with relatively little convergence , but when they converge they overaccommodate ( also reflected in the slight accommodation lead in the bdp condition ) . disparity - driven pattern e subjects do not accommodate well to increasing blur targets , and do even less convergence , leading to near exophoria . poor blur response might be found in straight - eyed hyperopic ametropic amblyopia . reducing disparity cues by dissociation , prisms or surgery , however , significantly reduces accommodation , while the need to control a large exodeviation , for example , might result in overaccommodation . our near exophoric subjects were in a subclinical , asymptomatic group of young adults with small deviations ( but with > 6 larger near angle ) and were in fact recruited as normal controls ( figure  6 ) . they had significantly lower ac / a ratios ( t   = 2.27 ; p  =  0.028 ) than normal and accommodated more than the normal adults while responding to the d target ( 2.98 d vs 2.45 d ( t   = 3.34 ) ; p = 0.001 ) . although the high ca / c ratio means that accommodation exceeds convergence , the weakness of disparity - driven responses does not result in over - accommodation . we predict that hyperopic children who manage to accommodate over their refractive error without becoming strabismic would fit this group . our dataset did not include any individuals in pattern f. our patient participants were drawn from a hospital population , referred for poor visual acuity , so this  silent  group of hyperopic children with good vision is difficult to detect because they pass screening . we predict that subjects with the combination of convergence insufficiency but good accommodation will fit into this group . we readily accept other theoretical models based on complex feedback loops , engineering - type modeling , ac / a and ca / c cross - links , and slow tonic versus rapid step adaptive mechanisms , but these models are mainly concerned with subtleties and control of normal behavior . we suggest that consideration of how people use visual cues provides a useful conceptual model for clinicians , who deal with more severe problems outside the envelope of normality . different blur and disparity biases characterize clinical patterns despite identical ac / a and ca / c ratios . we suggest clinicians should first consider which aspect of the visual stimulus is mainly used to compute target depth . next , determine whether accommodation and convergence are strongly linked in the individual , assessing changes induced by lenses , prisms , or dissociation , whether the individual accommodates more than converges , or vice versa . ac / a and ca / c ratios help , but are only informative if an individual 's blur or disparity bias is also known . although there are many individual differences in cue use within asymptomatic normal individuals , inflexibility and excessive bias appear to characterize clinical groups and predict treatment responses . time or orthoptic exercises may alter biases , for example , teaching a blur - biased accommodative esotropic patient to pay closer attention to single vision while accepting some blur . disparity people , the majority , maintain binocularity by motor fusion and are less concerned with the effect on accommodation . lenses change angles little , but they may dissociate more on occlusion . if , as is usual , most of their accommodation is also driven by disparity , then dissociation , prisms or surgery will not only change the angle , but also influence accommodation . if most people are disparity - driven , why do we not see more accommodative problems ? binocular accommodation is better than monocular , monocular accommodation is rarely required , and blur is often tolerated . we found underaccommodation of > 1.0 d at 33 cm in 22% of normal adults , 12% of normal children , 22% of hyperopic subjects with glasses , and 100% of hyperopic subjects without glasses . even  accommodative targets  are rarely threshold , that is , smaller than 20/20 , or 0.0 logmar ; expert readers decode text from word shape rather than individual letters , while early readers use large print . are disparity people also more tolerant of blur and thus happy without their glasses , with suboptimal prescriptions , or with dirty glasses ? blur people will be more sensitive to changes in clarity and accommodate accordingly . these seem rare among the general population but do appear in our clinical caseload . even a normal , but especially a high , amount of vergence associated with the response to blur , risks accommodative esotropia in hyperopia as we know . if less vergence is associated with this accommodation ( low ac / a ) , hyperopes may be able to respond to blur without over - converging  an advantage in uncorrected hyperopia , but a disadvantage for the clinician hoping to change an angle with spectacles . blur - driven people 's sensitivity to disparity may be low , so changing an angle with prisms , dissociation or surgery will have less effect on their accommodation but weaker fusion might mean that binocularity is more easily lost . are these also the people who notice small changes of refractive prescription , be slow to settle into new glasses and insist on them being clean ? our examples are only illustrative and not comprehensive , but some more predictions from this model are summarized in table  1 . further laboratory and clinical research is necessary to test these speculations , but in the meantime it is probably clinically important to test clarity of a near target to threshold , to ask about image clarity at every swap of an occluder during a prism cover test and to measure accommodation objectively . remaining symptom free may depend on being able to use both blur or disparity to drive responses , and to be able accommodate and converge more independently (  positive and negative relative fusion  ) to compensate for  style  biases . our naturalistic paradigm repeatedly finds that responses are variable , accommodation and vergence do not always co - vary , and ratios  are rarely fixed or repeatable , so perhaps the two systems are , and need to be , less closely linked than we assume .
purposeto propose an alternative and practical model to conceptualize clinical patterns of concomitant intermittent strabismus , heterophoria , and convergence and accommodation anomalies.methodsdespite identical ratios , there can be a disparity- or blur - biased  style  in three hypothetical scenarios : normal ; high ratio of accommodative convergence to accommodation ( ac / a ) and low ratio of convergence accommodation to convergence ( ca / c ) ; low ac / a and high ca / c . we calculated disparity bias indices ( dbi ) to reflect these biases and provide early objective data from small illustrative clinical groups that fit these styles.resultsnormal adults ( n = 56 ) and children ( n = 24 ) showed disparity bias ( adult dbi 0.43 [ 95% ci , 0.50 - 0.36 ] , child dbi 0.20 [ 95% ci , 0.31 - 0.07 ] ; p = 0.001 ) . 
 accommodative esotropia ( n = 3 ) showed less disparity - bias ( dbi 0.03 ) . in the high ac / a  low ca / c scenario , early presbyopia ( n = 22 ) showed mean dbi of 0.17 ( 95% ci , 0.28 - 0.06 ) , compared to dbi of 0.31 in convergence excess esotropia ( n=8 ) . in the low ac / a  high ca / c scenario near exotropia ( n = 17 ) showed mean dbi of 0.27 . 
 dbi ranged between 1.25 and 1.67.conclusionsestablishing disparity or blur bias adds to ac / a and ca / c ratios to explain clinical patterns . excessive bias or inflexibility in near - cue use increases risk of clinical problems .