David A Rusling

Phillip A Rachwal

Tom Brown

Keith R Fox

The stability of triplex DNA is affected by the stability of the underlying duplex

Keywords: Triplex, nucleotide analogue, thermal melting

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Abstract

We have studied the formation of DNA triple helices in different sequence contexts and show that, for the most stable triplexes, their apparent stability is affected by the stability of the underlying duplex. For a 14-mer parallel triplex-forming oligonucleotide (generating C + .GC and T.AT triplets) at pH 5.0 the T m is more than 10 °C lower with an intermolecular 14-mer duplex target, than it is with an intramolecular duplex, or one which is flanked by 6 GC base pairs at either end. A similar effect is seen with triplex-forming oligonucleotides that contain stabilising analogues, for which the T m is higher for an intramolecular than an intermolecular duplex target. These results suggest that the use of simple intermolecular duplex targets may underestimate the triplex stabilisation that is produced by some nucleotide analogues.

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Introduction

Triple helical nucleic acids are formed by binding a third oligonucleotide strand within the major groove of duplex DNA, in which bases in the third strand make specific contacts with the exposed edges of the duplex base pairs [START_REF] Fox | Targeting DNA with triplexes[END_REF][START_REF] Kalish | Targeted genome modification via triple helix formation[END_REF][START_REF] Potaman | Applications of triple-stranded nucleic acid structures to DNA purification, detection and analysis[END_REF][START_REF] Rusling | Towards the targeted modulation of gene expression by modified triplex-forming oligonucleotides[END_REF][START_REF] Thuong | Sequence-specific recognition and modification of double-helical DNA by oligonucleotides[END_REF]. In the most commonly studied form the third strand is oriented parallel to the purine strand of the duplex generating T.AT and C + .GC triplets [START_REF] Asensio | Comparison of the solution structures of intramolecular DNA triple helices containing adjacent and non-adjacent CG.C + triplets[END_REF][START_REF] Moser | Sequence-specific cleavage of double helical DNA by triple helix formation[END_REF][START_REF] Radhakrishnan | Solution structure of a pyrimidine.purine.pyrimidine DNA triplex containing T.AT, C + .GC and G.TA Triplets[END_REF]. The three stranded structure is usually less stable than the underlying duplex, as a result of the repulsion between the three negatively charge strands. The formation of these complexes is also limited by the requirement for low pH (required for protonation of cytosine in the C + .GC triplet) and is usually restricted to oligopurine.oligopyrimidine tracts. A large number of nucleotide analogues have been devised in attempts to overcome these limitations [START_REF] Amosova | A search for base analogs to enhance third-strand binding to 'inverted' target base pairs of triplexes in the pyrimidine/parallel motif[END_REF][START_REF] Buchini | Recent improvements in antigene technology[END_REF][START_REF] Cassidy | Recognition of GC base pairs by triplex forming oligonucleotides containing nucleosides derived from 2-aminopyridine[END_REF][START_REF] Cuenoud | Dual recognition of double-stranded DNA by 2'aminoethoxy-modified oligonucleotides[END_REF][START_REF] Eritja | Modified oligonucleotides with triple-helix stabilization properties[END_REF][START_REF] Fox | An extra dimension in nucleic acid sequence recognition[END_REF][START_REF] Gowers | Towards mixed sequence recognition by triple helix formation[END_REF][START_REF] Hojland | LNA (locked nucleic acid) and analogs as triplex-forming oligonucleotides[END_REF][START_REF] Lacroix | Chemical modification of pyrimidine TFOs: Effect on i-motif and triple helix formation[END_REF][START_REF] Prévot | Evaluation of novel third-strand bases for the recognition of a CG base pair in the parallel DNA triple-helical binding motif[END_REF][START_REF] Rusling | Four base recognition by triplex-forming oligonucleotides at physiological pH[END_REF].

One of the most commonly used methods for assessing the stability of these triple helical complexes is to measure their thermal stability by either UV or fluorescence melting experiments [START_REF] Darby | High throughput measurement of duplex, triplex and quadruplex melting curves using molecular beacons and a LightCycler[END_REF]. These are usually performed with short synthetic duplex targets, which are of similar length to the third strand. In some experiments the duplex has been made longer than the triplex in order to separate the duplex and triplex melting transitions [START_REF] Gerrard | CG base pair recognition within DNA triple helices using N-methyl-3H-pyrrolo[2,3-d]pyrimidin-2(7H)one nucleoside analogues[END_REF][START_REF] Li | Triplex staples: DNA double-strand cross-linking at internal and terminal sites using psoralen-containing triplex-forming oligonucleotides[END_REF][START_REF] Rusling | DNA triplex formation with 5-dimethylaminopropargyl deoxyuridine[END_REF], while others have employed intramolecular duplexes in order to increase the stability of the target [START_REF] Renneberg | Exploring Hoogsteen and reversed-Hoogsteen duplex and triplex formation with tricyclo-DNA purine sequences[END_REF][START_REF] Bernal-Mendez | Stability and kinetics of nucleic acid triplexes with chimaeric DNA/RNA third strands[END_REF][START_REF] Bijapur | 5-(1propargylamino)-2 '-deoxyuridine (U-P): a novel thymidine analogue for generating DNA triplexes with increased stability[END_REF]. In contrast in most footprinting experiments and for in vivo applications the duplexes in which the target sequences are located will be much longer than the third strand [START_REF] Rusling | Four base recognition by triplex-forming oligonucleotides at physiological pH[END_REF][START_REF] Sollogoub | Stable DNA triple helix formation using oligonucleotides containing 2'-aminoethoxy,5propargylamino-U[END_REF][START_REF] Rusling | Combining nucleoside analogues to achieve recognition of oligopurine tracts by triplex-forming oligonucleotides at physiological pH[END_REF].

As a result of progress in the design and synthesis of modified nucleotides it is now possible to generate triplexes that are as stable as the underlying duplex and the entire complex melts in a single transition. We were therefore concerned that for some very stable triplexes the apparent affinity of the third strand will be limited by the stability of the underlying duplex, since melting of the duplex will probably cause the third strand to dissociate from its Hoogsteen partner. We have therefore examined how the stability of the duplex target affects triplex melting. We have done this by comparing the interaction of one oligonucleotide (TFO1, Fig. 1a) with its duplex target when this is placed in a variety of different duplex contexts. This TFO is suited to this analysis as at low pHs, and on incorporation of stabilising nucleotides, the melting of this triplex overlaps with that of the simple intermolecular duplex. For

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these studies we have used duplexes that are stabilised by adding GC-or AT-tails to either end, or by joining the two strands to generate an intramolecular duplex.

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Materials and Methods

Oligonucleotides

The sequences of the oligonucleotides used in these studies are shown in Fig. 1. These were prepared as previously described [START_REF] Rusling | DNA triplex formation with 5-dimethylaminopropargyl deoxyuridine[END_REF]. For the experiments with unmodified triplex-forming oligonucleotides all the duplex targets contained the oligopurine tract AGAGAGAAGGAGGA, which was embedded within a variety of different sequence contexts. The 14-mer third strand oligonucleotide (TFO1) contained natural bases only (T and C). The oligonucleotides containing nucleotide analogues at a single central location in place of T (TFOs 2-7) were 18-mers and were targeted against the duplexes inter2 and intra2. The structures of the various nucleotide analogues are shown in Fig. 1b. In each case the purine strand of the duplex was labelled with fluorescein, which was either placed at the 5'-end or attached to the 5-position of a U located close to the 5'-end of the triplex target site (FAM-dU). The TFOs were labelled with dabcyl at the 5'-end. Phosphoramidites for 5'-fluorescein, FAM-dU and 5'-dabcyl were purchased from Glen Research.

Fluorescence melting

Triplex stability was assessed by fluorescence melting experiments as previously described [START_REF] Darby | High throughput measurement of duplex, triplex and quadruplex melting curves using molecular beacons and a LightCycler[END_REF]. In these experiments, triplex formation brings the fluorophore (fluorescein) and quencher (dabcyl) close together and the fluorescence is quenched.

When the triplex melts these reporter groups move apart and there is a large increase in the fluorescence signal. Unless otherwise stated the concentration of the fluorescein-labelled strand was 0.25 µM, while the dabcyl-labelled strand was 3 µM, as in previous work [START_REF] Rusling | Four base recognition by triplex-forming oligonucleotides at physiological pH[END_REF][START_REF] Rusling | DNA triple-helix formation at target sites containing duplex mismatches[END_REF][START_REF] Rusling | Kinetic studies on the formation of DNA triplexes containing the nucleoside analogue 2'-O-(2-aminoethyl)-5-(3-amino-1-propynyl)uridine[END_REF]. Melting curves were measured using a Roche

LightCycler with complexes prepared in 50 mM sodium acetate containing 200 mM NaCl at pH 5.0 or 5.8 (total volume 20 µL). The LightCycler has one excitation source (488 nm) and changes in fluorescence were measured at 520 nm. The midpoints of the melting transitions were estimated from the maximum of the first derivative, using the LightCycler software. Each experiment was repeated at least twice and melting temperatures are accurate to within 0.5 °C. Rates of temperature change of slower than 6 °C.min -1 were achieved by increasing the temperature in 1 °C steps, leaving the samples for a fixed time interval between each increase in temperature. The LightCycler is designed for real-time PCR in which heat is rapidly

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transferred to the glass capillary and it is compatible with very fast heating and cooling (up to 12 °C.min -1 in these experiments).

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Results

Comparison of different duplexes

We have examined how the stability of the duplex target affects the apparent triplex stability by studying the interaction of TFO1 (Fig. 1a) with its target site when this is placed in a variety of different duplex contexts. Each of these duplexes (shown in Fig. 1a) contains the same 14 base pair oligopurine.oligopyrimidine target sequence. Inter1 is a simple 14 base pair intermolecular duplex. This is flanked by 6

AT or 6 GC base pairs on either or both sides in sequences 3'ATATAT, 5'-ATATAT, 3'-GCGCGC, 5'-GCGCGC and 5'& 3'-GCGCGC. Intra1 is the same 14 base pair sequence in which the two strands are linked by hexaethylene glycol generating an intramolecular duplex. Representative melting profiles for the interaction of TFO1 with these different duplexes are shown in Fig. 2a at pH 5.0 for a rate of heating of 0.2 °C.min -1 . Under these conditions there is no hysteresis between the heating and cooling profiles, but the triplex melting profile is different for the various duplexes.

The triplex formed with inter1 melts at the lowest temperature, followed in turn by 3'-ATATAT, 3'-GCGCGC and intra1. The T m values for these and the other duplexes are summarised in Table 1. These data show that increasing the length of the duplex increases the triplex melting temperature and that GC tails produce more stable complexes than AT tails. There is no significant difference between 5'-ATATAT and 3'-ATATAT or between 3'-GCGCGC and 5'-GCGCGC. The most stable complexes are formed with the duplex that contains 6 GC pairs at both ends and the intramolecular duplex intra1.

When these experiments were repeated at pH 5.8, producing less stable triplexes as a result of the pH dependence of the C + .GC triplets, there was little difference between the various triplex to duplex melting transitions (Fig. 2b, Table 1).

The effect of duplex stability on triplex melting therefore appears to be greatest under conditions that generate triplexes that are more stable; this is exaggerated when using third strands that contain stabilising analogues (see below). In each of these profiles (as well as those shown in Fig. 2a) a decrease in fluoresence is often evident at higher temperatures subsequent to the triplex melting. This has been noted in our previous studies [START_REF] Darby | High throughput measurement of duplex, triplex and quadruplex melting curves using molecular beacons and a LightCycler[END_REF] and corresponds to melting of the underlying duplex, caused by unstacking of the fluorescein. The apparent melting temperatures of the duplexes

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alone are summarised in Supplementary material Table S1 and confirm that the addition of the tails stabilises the duplex and that GC is more effective than AT.

When these triplexes were heated and cooled at faster rates there was hysteresis between the melting and annealing profiles, as previously observed [START_REF] Rusling | DNA triplex formation with 5-dimethylaminopropargyl deoxyuridine[END_REF][START_REF] Rusling | Kinetic studies on the formation of DNA triplexes containing the nucleoside analogue 2'-O-(2-aminoethyl)-5-(3-amino-1-propynyl)uridine[END_REF],

indicating that one or more steps in the association or dissociation pathways are slow and that the system is not at thermodynamic equilibrium. Representative melting and annealing curves at a fast rate of temperature change (12 °C.min -1 ) are shown in Fig. 3, for the duplex targets inter1 and intra1. It can be seen that at pH 5.0 (Fig. 3a) there is considerable hysteresis (12.7 °C) with inter1, but very little with intra1 (1.4 °C).

The differences are much smaller at pH 5.8 (Fig. 3b). The T m values for these and the other target duplexes, determined at heating rates of 12 °C.min -1 , are presented in S2 andS3). At pH 5.0 the difference between the triplex T m s for heating and cooling is greatest for the less stable duplexes.

Comparison of different nucleoside analogues on intermolecular and intramolecular duplexes.

Triplex melting curves are commonly used to assess the stabilising effects of nucleotide substitutions [START_REF] Hojland | LNA (locked nucleic acid) and analogs as triplex-forming oligonucleotides[END_REF][START_REF] Rusling | Four base recognition by triplex-forming oligonucleotides at physiological pH[END_REF][START_REF] Rusling | DNA triplex formation with 5-dimethylaminopropargyl deoxyuridine[END_REF][START_REF] Rusling | Kinetic studies on the formation of DNA triplexes containing the nucleoside analogue 2'-O-(2-aminoethyl)-5-(3-amino-1-propynyl)uridine[END_REF][START_REF] Buchini | Stable and selective recognition of three base pairs in the parallel triple-helical DNA binding motif[END_REF][START_REF] Buchini | 2 '-O-aminoethyl oligoribonucleotides containing novel base analogues: Synthesis and triple-helix formation at pyrimidine/purine inversion sites[END_REF][START_REF] Hojland | Triplex-forming ability of modified oligonucleotides[END_REF][START_REF] Mayer | Pyrrolidino DNA with bases corresponding to the 2oxo deletion mutants of thymine and cytosine: Synthesis and triplex-forming properties[END_REF][START_REF] Osborne | Selectivity and affinity of triplex-forming oligonucleotides containing 2'aminoethoxy-5-(3-aminoprop-1-ynyl)uridine for recognizing AT base pairs in duplex DNA[END_REF]. Such modifications can produce complexes in which the triplex and duplex melts overlap, producing a single melting transition.

Under these circumstances it is possible that the apparent triplex stability is limited by the stability of the underlying duplex. This is suggested by the experiments described above, which demonstrates that as the triplex becomes more stable (by lowering the pH), so the melting temperatures become more dependent on the nature of the underlying duplex. We have therefore compared the melting transitions of triplexes that contain modified oligonucleotides, formed on inter and intramolecular duplexes.

In order to increase further the stability of these complexes the oligopurine.oligopyrimidine target site was extended to 18 base pairs, generating triplexes with the 18-mer TFOs 2-7 (Fig. 1b). Each of these TFOs contains a single nucleotide analogue in the centre that bears a positive charge on either the base (TFOs 3-5) or the base and the sugar (TFOs 6-7). The melting temperatures of these complexes, determined at the slowest rate of temperature change, at three different pHs, are presented in Table 2. Further values determined at faster rates of heating and

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cooling are presented in the Supplementary material (Table S4). As previously noted, each of these modifications increases triplex stability and the most stable complexes are generated with BAU and BGU, which possess amino groups on the 2'-and 5positions. At pH 6.0 there is no significant difference between the T m s determined with inter2 and intra2. When the pH is decreased to 5.5, although the unmodified TFO2 binds equally well to both duplexes, the most stabilising analogues show higher T m s with the intramolecular duplex. This effect is further exaggerated at pH 5.0; at this pH the unmodified TFO shows a higher T m with intra1 than inter1 and this difference is even greater for the modified TFOs.

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Discussion

The results presented in this paper demonstrate that the apparent stability of a triple helix can be affected by the length and sequence of the underlying duplex.

Duplexes with enhanced stability, produced by adding extra base pairs at either end or by generating an intramolecular complex, generate higher triplex T m s, even though the target site itself is unchanged. This effect is greatest at low pHs, at which the triplex is more stable and melts at a temperature that is closer to the duplex T m . Under these conditions of enhanced triplex stability the triplex to duplex and duplex to single strand transitions can occur at similar temperatures. It is then possible that the Watson-Crick duplex may melt before the third strand dissociates, leaving a Hoogsteen paired duplex between the TFO and the duplex purine strand. This is likely to be unstable, when removed from the context of the entire triplex, and so will also dissociate. The melting transition of the third strand will therefore be limited by the stability of the underlying duplex.

The limiting effect of duplex stability on triplex formation is especially important when comparing triplexes that have been generated with oligonucleotides that contain stabilising nucleotide analogues. T m determination is one of the simplest and most commonly used means for assessing improvements in triplex stability and these experiments are usually performed with intermolecular duplexes that are often no longer that the triplex target. Although this technique has successfully established the stabilising effects of many such analogues, the results presented in this paper suggest that these experiments may have underestimated the improvements in stability of the best nucleotide analogues.

The observation that there is little hysteresis for third strand melting from the most stable duplexes at low pH is at first sight puzzling. At pH 5.0, with a temperature change of 12 °C.min -1 there is a 12.6 °C difference between melting and annealing with duplex inter1, but only 1.4 °C for intra1. In contrast there is little difference in the hysteresis at these targets at pH 5.8. Hysteresis is caused by the slow association or dissociation of the third strand, such that at fast rates of temperature change, the reaction is not at thermodynamic equilibrium [START_REF] Bernal-Mendez | Stability and kinetics of nucleic acid triplexes with chimaeric DNA/RNA third strands[END_REF][START_REF] Rougée | Kinetics and thermodynamics of triple-helix formation -effects of ionic-strength and mismatches[END_REF]. It is well known that triplex formation is very slow (typically three orders of magnitude slower than duplex formation) [START_REF] Rougée | Kinetics and thermodynamics of triple-helix formation -effects of ionic-strength and mismatches[END_REF][START_REF] Maher | Kinetic-analysis of oligodeoxyribonucleotide-directed triple-helix formation on DNA[END_REF] and we would expect the fundamental rate constants for the reaction to be independent of the stability of the target. Our observations suggest that the apparent association and/or dissociation reactions are faster for the intra-than the

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inter-molecular duplex at pH 5.0. The differences largely arise from changes in the annealing (rather than the melting) temperature, which becomes much lower for the less stable duplexes, suggesting that the differences are caused by changes in the association reaction. A possible origin of this is the rate of end-fraying of double stranded DNA caused by ingress of water. In all DNA duplexes the base pairs at or

near the termini open and close much more rapidly than do the internal base pairs. This is especially true for AT base pairs. In contrast, the base pairs at the ends of hairpin loops (particularly at the "closed" end) are less prone to fraying. It is likely that the end fraying propagates well into the duplex, possibly as a wave of instability as the temperature is raised in a UV melting experiment. This will make the duplex an unstable, or structurally incorrect scaffold for attachment of a third strand, thus slowing the rate of triplex association. It is also possible that the Hoogsteen duplexes that are formed with the oligonucleotides containing stabilising analogues may be as stable as the normal Watson-Crick duplex target. However these parallel structures should be less stable than the entire triplex as they lack the stacking interactions with the duplex pyrimidine strand. Hairpin loop or cyclic duplexes will therefore be better model systems for studying triplex formation in genomic DNA.

A C C E P T E

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Table S4

T m values (°C) for the interaction of TFOs 2-7 with the duplexes inter2 and intra2, determined at various rates of heating and cooling. The values for annealing are shown in parentheses. The reactions were performed in 50 mM sodium acetate containing 200 mM NaCl, at pH 5.0, 5.5 or 6.0. The concentration the fluorescentlylabelled duplexes was 0.25 µM, while the TFO concentration was 3 µM. T m (°C) 0.2 °C.min -

Fig. 1 .

 1 Fig. 1. A) Sequences of the triplex forming oligonucleotides TFO1-7 and the various duplexes used in this work. H = hexaethyelene glycol; U = FAM-dU. B) Structures of the nucleotides analogues used for TFOs 2-7.

Fig. 2 .

 2 Fig. 2. Representative melting curves for the interaction of TFO1 with the intermolecular duplexes inter1, 3'-ATATAT, 3'-GCGCGC and intra1. In each case the concentration of the third strand was 3 µM and the duplex concentration was 0.25 µM. The rate of hearing was 0.2 °C. min -1 .The experiments were performed in 50 mM sodium acetate containing 200 mM NaCl pH 5.0 or 5.8. Dotted line, inter1; long dashes, 3'-ATATAT; short dashes 3'-GCGCGC; solid line, intra1. The inset shows the first derivatives of the melting profiles, for which the peak corresponds to the Tm.

Fig. 3 .

 3 Fig. 3. Representative melting curves for TFO1 with duplexes inter1 and intra1, performed at a fast rate of temperature change (12 °C.min -1 ). In each case the concentration of the third strand was 3 µM and the duplex concentration was 0.25 µM. The experiments were performed in 50 mM sodium acetate containing 200 mM NaCl pH 5.0 or 5.8. inter 1: anneal (open triangles), melt (filled triangles); intra1: anneal (open circles), melt (filled circles). In A) for inter1 the arrows indicate the direction of heating or cooling.

Table 1

 1 alongside those determined at 0.1 min -1 , while the values determined at intermediate rates of heating and cooling are presented in the Supplementary material (Tables

Table 1

 1 T m values (°C) for the interaction of TFO1 with the different duplexes, determined at a m values (°C) for the interaction of TFO1 with the different duplexes, determined at various rates of heating and cooling. The values for annealing are shown in parentheses. The reactions were performed in 50 mM sodium acetate pH 5.0 containing 200 mM NaCl. The concentration of each fluorescently-labelled strand was 0.25 µM (duplex or TFO), while the concentration of quencher-labelled strand was 3 µM.

	rate of heating of 0.2 °C.min -1 and 12 °C.min -1 . Values for annealing are shown in
	parenthesis. The reactions were performed in 50 mM sodium acetate containing 200
	mM NaCl. The concentration of each fluorescently-labelled strand was 0.25 µM
	(duplex or TFO), while the concentration of quencher-labelled strand was 3 µM.
			T m	°C
		0.2 °C.min -1	12 °C.min -1
	Target duplex	pH 5.0	pH 5.8	pH 5.0	pH 5.8
	Inter1	55.7 (55.6) 41.6 (41.5) 62.8 (50.1)	43.9 (40.5)
	Intra1	65.9 (66.2) 42.5 (42.6) 66.9 (65.5)	45.1 (41.3)
	3´-ATATAT	59.3 (59.6) 42.5 (42.6) 64.7 (55.5)	44.8 (41.3)
	5´-ATATAT	58.6 (58.4) 43.3 (43.4) 65.3 (52.6)	46.0 (42.5)
	3´-GCGCGC	64.0 (64.2) 41.9 (41.6) 65.1 (63.8)	43.9 (41.1)
	5´-GCGCGC	63.5 (64.0) 43.3 (43.3) 66.0 (63.7)	46.2 (42.2)
	3´&5´-GCGCGC 67.4 (67.6) 42.2 (42.4) 68.5 (67.3)	45.6 (42.3)

T

Table S3 T

 S3 m values (°C) for the interaction of TFO1 with the different duplexes, determined at various rates of heating and cooling. The values for annealing are shown in parentheses. The reactions were performed in 50 mM sodium acetate pH 5.8 containing 200 mM NaCl. The concentration of each fluorescently-labelled duplex was 0.25 µM, while the TFO concentration was 3 µM.

				T m (°C)
		12 °C.min -1	6 °C.min -1	3 °C.min -1	1 °C.min -1	0.2 °C.min -1
	inter1	43.9 (40.5)	43.5 (40.6)	42.4 (42.0)	41.6 (41.8)	41.6 (41.5)
	intra	45.1 (41.3)	44.3 (42.0)	43.1 (43.2)	42.5 (43.1)	42.5 (42.6)
	3´-ATATAT	44.8 (41.3)	44.1 (41.8)	43.0 (43.1)	42.6 (42.9)	42.5 (42.6)
	5´-ATATAT	46.0 (42.5)	45.2 (43.8)	44.2 (44.0)	43.5 (43.9)	43.3 (43.4)
	3´-GCGCGC	43.9 (41.1)	43.2 (41.0)	43.1 (42.0)	42.0 (42.1)	41.9 (41.6)
	5´-GCGCGC	46.2 (42.2)	45.1 (43.0)	43.5 (42.9)	43.5 (43.8)	43.3 (43.3)
	3´&5´-GCGCGC 45.6 (42.3)	44.6 (42.3)	43.2 (42.8)	42.5 (42.8)	42.2 (42.4)

  DMAPdU 67.0 (67.3) 62.4 (62.2) 67.3 (67.4) 63.5 (61.5) 68.7 (65.9) 67.6 (57.4) APdU 69.3 (69.2) 63.5 (62.9) 69.3 (69.6) 65.0 (62.4) 70.4 (68.4) 69.0 (58.2) GPdU 70.7 (70.9) 64.4 (63.7) 70.8 (71.1) 66.1 (62.7) 72.0 (70.0) 70.1 (58.8) BAU 73.5 (73.5) 66.6 (63.3) 73.0 (73.6) 68.9 (62.1) 74.5 (72.0) 73.4 (57.8) BGU 73.3 (73.4) 67.6 (63.6) 73.4 (73.6) 70.4 (61.9) 75.7 (71.4) 74.5 (57.1) pH 5.5 T 51.2 (51.3) 51.4 (51.5) 52.3 (51.4) 52.4 (51.4) 55.3 (48.6) 55.1 (48.7) DMAPdU 53.8 (53.7) 53.2 (53.4) 54.4 (54.5) 54.1 (53.8) 57.4 (52.7) 56.7 (51.2) APdU 56.1 (56.3) 55.3 (55.6) 56.6 (56.9) 55.8 (55.9) 59.2 (55.3) 58.7 (53.7) GPdU 57.4 (57.5) 56.5 (56.8) 58.1 (58.3) 57.1 (56.8) 60.4 (56.4) 59.7 (54.4) BAU 61.6 (61.7) 59.3 (59.2) 62.2 (62.5) 60.2 (59.2) 63.8 (61.2) 63.5 (55.6) BGU 60.6 (60.7) 58.8 (58.7) 61.5 (61.1) 60.2 (58.1) 64.3 (57.8) 63.7 (54.1) pH 6.0 T 39.4 (39.2) 39.8 (39.6) 40.8 (39.1) 41.0 (39.5) 44.6 (<35) 44.7 (<35) DMAPdU 41.3 (41.5) 41.8 (41.9) 42.5 (41.3) 42.8 (41.9) 46.1 (37.3) 46.3 (38.7)

			1	1 °C.min -1	6 °C.min -1
	pH 5.0	Intra	Inter	Intra	Inter	Intra	Inter
	T	65.1 (65.3) 61.0 (61.2) 64.8 (65.2) 61.9 (60.7) 66.5 (63.8) 65.6 (56.9)
	APdU	43.7 (43.9) 44.0 (44.1) 44.7 (43.8) 45.0 (44.1) 47.8 (40.5) 48.2 (41.1)
	GPdU	45.2 (45.4) 45.1 (45.3) 45.8 (45.5) 46.0 (45.5) 49.3 (42.6) 49.1 (42.6)
	BAU	48.1 (48.3) 48.4 (48.6) 49.2 (47.8) 49.5 (48.1) 52.6 (44.3) 53.0 (45.3)
	BGU	48.1 (48.0) 48.4 (48.3) 49.3 (47.6) 49.6 (47.9) 53.5 (42.1) 53.5 (42.9)

Acknowledgements

This work was supported by grants from the BBSRC

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Péter Kálmán

Tamás Keszthelyi

Dániel Kis

Boson induced nuclear fusion in crystalline solids

Keywords: 42, 55, -f Lasers -25, 60, Pj Fusion reactions -63, 90, +t Other topics in lattice dynamics -23, 20, Nx Internal conversion and extranuclear effects

In a calculation of demonstrative type collective, laser-like behavior of low energy nuclear fusion reaction of deuterons in crystalline environment is investigated. It is found that the reported extra 4 He production can be appropriately described with a model well known in quantum electronics in which the quantized boson ( 4 He) field interacts with an ensemble of two-level systems in a crystal resonator. The estimated life times of the two levels indicate that population inversion may be achieved. Thresholds of the deuteron number of the sample and of the electric current density of the pumping electrolysis are estimated in the calculation by analyzing the gain parameter and some other characteristics of the process.

An explanation for the experimentally observed threshold behavior of the electric current density is given. A loss of a special type, that is the degenerate parametric amplifier mechanism, is suggested to be responsible for the difference between the expected and observed energies of the outgoing charged particles.

Introduction

This paper is motivated by the two decade old announcement [1], that excess heat due to nuclear fusion reaction of deuterons can be observed at deuterized Pd cathodes during electrolysis at near room temperature. The phenomenon of low energy nuclear fusion (LENF) reactions, summarized in Refs. [2], [3], [4], and [5], is still doubted by most physicists due to the rather confused experimental situation. Recently, however, in a series of papers reproducible experimental evidence of LENF was reported [6].

In the first few years after the appearance of [1] a great number of efforts for the theoretical explanation of the ef-fect were made (these are well summarized in [7]) but its full theoretical explanation is still missing (see the Scientific Overview of ICCF15 [8]). Therefore, recently, we have also tried to explain some of the basic questions of LENF reactions in solids [9] on the base of phonon exchange induced attraction [10] and solid state internal conversion processes [11].

The phonon exchange induced attraction between like charges is a well known phenomenon in solid state physics and it gives the ground to the theoretical explanation of superconductivity [START_REF] Ziman | Principles of the Theory of Solids[END_REF]. Adapting the phonon exchange induced electron-electron interaction potential for two quasifree, heavy particles of like charges we obtained [10], [9] their interaction potential V ph (K,λ) due to phonon exchange in the λ-th branch in K space as

V ph (K,λ) = |g (K,λ)|
2 ω q,λ (D 1 (k 1 ) + D 2 (k 2 )) , (1) where g (K,λ) is the particle-phonon coupling function, ω q,λ is the energy of the exchanged phonon, q is the wave number vector in the first Brillouin zone (K = q+G outside the first Brillouin zone, where G is a vector of the reciprocal lattice), and

D j (k j ) = 1 ∆E j (k j , K) 2 -( ω q,λ ) 2 , (2)
for j = 1, 2 with ∆E j (k j , K) = E j (k j ) -E j (k j + K).

Here E j = 2 k 2 j / (2M j ) is the kinetic energy and M j is the rest mass of the quasi-free particle. (We can get back the phonon exchange induced electron-electron interaction potential substituting M j = m, with m as the rest mass of the electron, into E j .) As can be seen from ( 2) the interaction is attractive if |∆E j (k j , K)| < ω q,λ . Heavy particles, e.g. protons, deuterons and other light nuclei, have much larger rest mass than the electronic rest mass (M j m) therefore this inequality is fulfilled in a much larger range of K than for electrons. Consequently the attraction is expected to be much stronger than in the case of electrons resulting a much deeper interaction potential (after Fourier transformation) in the real space.

According to our calculations the attractive potential, that arises due to phonon exchange between two quasifree particles (that move in a crystalline material, such as e.g. Pd, which is partly filled in the interstitial lattice sites by deuterons), essentially compensates the effect of the Coulomb repulsion between them. It was found [9], [10], that the attraction heavily depends on the parameter u = n d /n ion , the deuteron over metal ion number density. It was also recognized that the Gamow factor [START_REF] Marmier | [END_REF],

that hinders nuclear reactions, e.g. nuclear fusion, between particles of like electric charge, strongly increases with increasing u and its hindering effect practically disappears at u = 2. (Our theory, according to the classification of [7], may be classified as a theory of barrier reduction due to lattice vibration.) As a conclusion, one can say that due to the phonon exchange generated attractive potential between fusionable particles their fusion reaction is possible at low, near room temperature. (Attraction due to phonons was already proposed by Schwinger in 1990 [14].)

It must be emphasized here that despite the strong at- Motivated by the experimental observations that ordinary fusion products are missing in low energy fusion reactions we looked for a process which may partly be responsible for this fact. It is standard in nuclear physics that isomers of long life time mainly decay by internal conversion process in which an electron takes off the energy of the nuclear transition instead of a γ photon [START_REF] Hamilton | Internal Conversion Processes[END_REF]. It was recognized that in a fusion of solid state internal conversion type [11], ordinary fusion products are missing, similarly to the normal internal conversion process, and charged particles help to get rid of the energy of the fusion reaction. In a solid, such as deuterized Pd, there are many possible particles that may take part in the solid state internal conversion process channel of the fusion reaction. The process was demonstrated through electron and deuteron assisted p + d → 3 He nuclear reactions. It was also shown that lattice effects can significantly increase the cross section of solid state internal conversion processes [START_REF] Kálmán | [END_REF]. (Extra heat production can be partly attributed to the solid state internal conversion process too [9].)

In what was said above, fusion mechanisms, that are thought to be responsible for low energy fusion reactions, were sought for among individual processes of fusion. However, if the particles, which take part in the individual processes, are bosons, as e.g. it is the case of normal d + d → 4 He and charged particle (e.g. electron) assisted d + d → 4 He reactions, then their collective behavior may also be essential. In other words, their initial and/or final states must be described as part of a multi-particle (quantized) boson field. On the other hand, if there is a resonator present too, in our case it can be the crystal, then due to the (quantized) boson field, induced emission can take place and laser-like processes may be expected. Our theoretical attempt is strongly motivated by the observation that in the electric current density of the electrolysis threshold appeared [4], [17], a fact that can indicate laser-like behavior.

We will focus our attention to the outgoing 4 He that has bosonic nature as its angular momentum/parity is 0 + .

In order to demonstrate the idea, we investigate here the In a demonstrative calculation it is shown that if LENF reactions of type (3) take place in a crystalline material then the behavior of the system is similar to that of a two-level atom ensemble coupled to the quantized field of a resonator. (Our model is similar in some aspect to the theory proposed in the early stage of cold fusion story [18] and it is closer to the one presented recently [START_REF] Hagelstein | Int. Conf. Cold Fusion 15 (ICCF15)[END_REF].) As was said above, the experimentally observed threshold in the electric current density of the electrolysis, that is considered to be the pumping mechanism, indicates laser-like behavior, therefore the condition of lasing is investigated and it is connected with the threshold of the gain of the boson field. Numerical results of the threshold number of the quasi-free (fusionable) deuterons, that must be present in the sample to start lasing, are determined and the threshold in the electric current density of the electrolysis is estimated. The problem of missing energetic charged fusion products is recognized and the degenerate parametric amplifier mechanism, a possible loss mechanism that may be responsible for this fact, is proposed. The importance of other BIF processes and their cross effects, furthermore the possible connection with an other cold fusion theory is also mentioned. onator can be written as

Ψ 1 (r) = 1 H 2 d j exp(ik j • r) cos (k ⊥j • r) (4)
and

Ψ 2 (r) = 1 H 2 d j exp(ik j • r) sin (k ⊥j • r) . ( 5
)
Here k j and k ⊥j are the components of the wave vector of 4 He parallel with and orthogonal to the j-th crystal plane, k = k j +k ⊥j , k j • k ⊥j = 0 . (The symbols and ⊥ refer to the components of any vector parallel with and orthogonal to the j-th crystal plane.) With this notation the Bragg law has the form

2 |k ⊥j | = n B |G j | , ( 6
)
where n B is a natural number, G j is a reciprocal lattice vector, and tensive when compared it with the cosine-like case. (The phenomenon is well-known in the case of x-rays as anomalous x-ray transmission [START_REF] Borrmann | [END_REF].)

|G j | = 2π/d j ,
The motion of the two deuterons and the electron, furthermore the motion of 4 He parallel with the resonator planes are treated quantum mechanically. A possible initial (upper) state of the two fusing deuterons and the initial electron with energy

E a = 2m d0 c 2 + E kin,1 + E kin,2 + E e,i , (7)
is

|a = |d 1 ⊗ |d 2 ⊗ |e i ⊗ |0 . ( 8
)
m d0 c 2 denotes
|b = |0 ⊗ |0 ⊗ |e f ⊗ |He (9)
with energy

E b = m He0 c 2 + E kin,He, + E e,f , (10)
that is the sum of energy of motion of The part of the 4 He (bosonic) motion orthogonal to the resonator planes is field quantized, whose energy eigenvalue is

E kin,He,⊥ (k ⊥j ) = 2 k 2 ⊥j 2m He0 . ( 12
)
The corresponding Hamiltonian is oscillator type, a + (k ⊥j ) and a(k ⊥j ) are the boson creation and annihilation operators in the mode with

[a(k ⊥i ), a + (k ⊥j )] = δ ij . ( 13
)
The orthogonal part of the state of 4 He can be described by number states |n(k ⊥j ) .

The interaction of an ensemble of the above two-level systems with the quantized boson field of state |n(k ⊥j )

describing the perpendicular motion can be treated in a way known in quantum electronics [START_REF] Nussenzveig | Introduction to Quantum Optics[END_REF]. The interaction Hamiltonian in the rotating wave approximation is

H I = k ⊥j ,l g l (k ⊥j )a + (k ⊥j )σ l + g * l (k ⊥j )a(k ⊥j )σ + l , (14)
with

σ l |a l = |b l , (15)
and

σ + l |b l = |a l . ( 16
)
The interaction Hamiltonian couples the k ⊥j -th mode of the boson field and the l-th two-level system, i.e. the direct

product states |A l = |a l ⊗ |n(k ⊥j ) and |B l = |b l ⊗ |n(k ⊥j ) + 1 . The coupling constant g l (k ⊥j ) = g 0 (k ⊥j ) exp (-G W /2) , ( 17
)
and exp (-G W ) is the Gamow-factor with

G W = 2π µR y m e |U 0 (0)| , ( 18
)
that has u dependence through U 0 (0), that is the depth of the optical phonon exchange induced attractive interaction potential between two quasi-free deuterons of the same kinetic energy E kin,1 = E kin,2 = E kin (see Fig. 2 of [9] and Fig. 5 of [10]). In (18) µ is the reduced mass of the two deuterons, m e is the rest mass of the electron and R y is the Rydberg energy. g 0 (k ⊥j ) is determined by the matrix element of the Coulomb interaction governing solid state assisted nuclear fusion reaction V ab as

V ab = g 0 (k ⊥j ) exp (-G W /2) . ( 19
)
The Gamow-factor increases with increasing the localized deuteron concentration (u) in Pd.

In this model the parallel component of the 4 He motion is present in the lower level (see Eq.( 9)). As a consequence there is a coupling between the parallel and perpendicular motions of 4 He. The transition |A l → |B l describes mainly nuclear fusion. It takes part in the buildup of the boson field. However, due to the coupling, in certain conditions, the induced emission through a laserlike process can increase the fusion rate.

The matrix element V ab is calculated in a model similar to the one used in [11] and it is

V ab = ϕ i (r, R) χ i (r 3 ) ϕ * f (r, R) χ * f (r 3 ) ( 20
)
× V Cb [R- 1 2 r -r 3 ] + V Cb [R+ 1 2 r -r 3 ] d 3 rd 3 Rd 3 r 3 .
Here V Cb is the Coulomb potential, and the r 1 , r 2 coordinates of the two deuterons are replaced by their relative r = r 1 -r 2 and center of mass R = r 1 /2 + r 2 /2 coordinates. With these coordinates the initial two deuteron state

ϕ i (r, R) = 1 √ V e ik i •R ψ 2d,i (r) , ( 21
)
where ψ 2d,i (r) is the initial state in the relative coordinates of the two deuterons that has the form

ψ 2d,i = (4π) -1/2 r -1 u n (r h )e -G W /2 (22)
in the r ≤ R 0 region, with R 0 as the radius of 4 He and r = |r|. The classical turning point r h is determined by the condition

e 2 r h + U 0 (r h ) = 0 (23)
(the lower root in Fig. 6 in [10]). u n (r) is the solution of the reduced Schrödinger equation

- 2 2µ d 2 u n (r) dr 2 + e 2 r + U 0 (r) u n (r) = E rel u n (r) ( 24
)
with energy eigenvalue |E rel | < ∆E/2 (for ∆E see later) valid for r > r h . An approximate solution of u n (r) of the form

u n (r) = β/ 2 n n! √ π e -β 2 (r-r0) 2 /2 H n [β(r -r 0 )] ( 25
)
can be obtained [START_REF] Cohen-Tannoudji | Quantum Mechanics[END_REF] approximating e 2 /r + U 0 (r) (see Fig. 6 in [10]) with an oscillator potential, whose minimum is fitted to the minimum of e 2 /r + U 0 (r) at r = r 0 . H n is an Hermite polynomial and β = µω/ with ω as the corresponding angular frequency of the oscillator. The initial electronic state is

χ i (r 3 ) = 1 √ V e ik e •r 3 ( 26
)
where V is the volume of normalization, k e and r 3 are the wave vector and coordinate of the electron.

The final state of 4 He is

ϕ f (r, R) = Φ He (r) 1 H e ik j •R 2 d j sin (k ⊥j • R) , ( 27
)
where Φ He (r) is the r dependent part of the 4 He wave function. For the function Φ He we apply the Weisskopf approximation, i.e. Φ He = 3/ (4πR 3 0 ) if r ≤ R 0 and

Φ He = 0 if r > R 0 .
The final electronic state is

χ f (r 3 ) = 1 √ V e ik3•r3 ( 28
)
where k 3 is the wave vector of the outgoing electron. Using

that |k i | ≈ |k e | |k 3
| and the dipole approximation in the integral over the relative nuclear coordinates we obtain

V ab = 64π 3 e 2 √ 3R 0 δ 2 k j + k 3 V 2/3 H √ L k 3 2 |k ⊥j | u n (r h )e -G W /2 , ( 29
)
where δ 2 k j + k 3 is a two dimensional Dirac-delta, and e is the elementary charge. Thus we obtain

g 0 (k ⊥j ) = 64π 3 e 2 √ 3R 0 δ 2 k j + k 3 V 2/3 H √ L k 3 2 |k ⊥j | u n (r h ). ( 30
)
Consequently in the state after fusion k 3 = -k j .

The Our aim is to estimate the threshold current of the electrolysis, that is the pumping mechanism of BIF, therefore instead of a rigorous quantum optical laser calculation [START_REF] Nussenzveig | Introduction to Quantum Optics[END_REF] we do it in the simplest manner. Therefore we investigate the gain that determines the threshold number density n a,th of the number density n a of the states |a l by the threshold condition of the gain [START_REF] Milonni | Lasers[END_REF].

3 Threshold condition of electron assisted that fulfills the condition of population inversion.

In our case the steady state gain [START_REF] Milonni | Lasers[END_REF]

G = σ ab n a -α loss , ( 32
)
where σ ab is the cross section of the induced transition a → b, n a is the steady state number density of systems in state |a and α loss is the loss parameter. The threshold value G th of the gain, at which the BIF process begins, is determined by the

G th = -ln r c /L (33)
condition [START_REF] Milonni | Lasers[END_REF], where r c is the reflection coefficient of the for the threshold number density n a,th of the number density n a .

For the energy loss per length ε = 12 eV/ Å was obtained for He + ions of energy 25 keV channeling in Au foil [29]. In the experiment both planar and directional channeling were present. We estimate α loss taking

α loss = ε ∆E E kin,
→ [H/(2π)] 2 d 2 k ,e (37)
substitutions are applied, where H × H is the area of the resonator plates of linear dimension H. The cross section σ ab is determined from W ab as usual, i.e. σ ab = W ab /F He ,

where The number N a of the systems in the upper state is

F He = v ⊥ / H 2 L
N a = N e,i N d,las (N d,las -1) /2 N e,i N 2 d,las /2, ( 38
)
where N d,las is the number of quasi-free deuterons, that can take place in the BIF process, and N e,i is the number of initial electrons in the sample, that may be taken

N d,th = K V 1/3 s ξu n (r h )e -G W /2 √ δ ( 39
)
for the threshold deuteron number of BIF in the sample, where K = 7.6 × 10 14 cm -3/2 and V s is the volume of the sample. N d,th can be connected with the threshold electric current density j th of the electrolysis as j th = eN d,th /(F τ rec ), where τ rec is the time of recombination of a quasi-free deuteron into a bound state, F is the surface of the Pd cathode and e is the elementary charge. As a typical value we take V 1/3 s F -1 = 0.15 cm -1 that corresponds to a Pd rod of length 5 cm and of diameter 0.3 cm [17]. j th = 0.35 A/cm 2 value [17], [4] with τ rec = 7.0 × 10 -3 s. It is reasonable to suppose that above u = 1, which is the concentration of filled octahedral interstitial sites, τ rec increases significantly, as approaching u = 1 the empty interstitial lattice sites decrease and so a quasi-free deuteron needs more time in order to be able to find a vacant site.

Thus j th A/cm 2 = 0.165×u -1 n (r h )e G W /2 cm 1/2 /τ rec [s].
Therefore it is expected that the observed threshold current density can be reached at much lower value of u.

Discussion

The fit of the results of numerical calculations of the threshold current density with the observations indicates a good coincidence. This is the main goal of this work since it indicates that mechanisms of BIF type may have realistic ground.

In order to have an outlook for the efficiency of BIF we enumerate from the family of the possible BIF reactions two that may also be responsible for 4 He and/or heat production. One such reaction is the deuteron assisted BIF In [9] it was obtained that the Gamow factor of the p + d → 3 He process increases most rapidly and therefore the deuteron assisted BIF may be partly responsible for heat production. Furthermore, if the double BIF with outgoing deuteron works than its quantized deuteron mode, as a cross effect, may couple to and induce reaction (41).

The fast electrons having 23.77 MeV energy, that are expected in (3), were not found in observations. One of the possible explanation is the degenerate parametric amplifier mechanism [START_REF] Walls | Quantum Optics[END_REF] that may couple the quantized per- In order to determine the relationship between their rates, their threshold currents and their cross effects a detailed and systematic analysis of all the possible and competing BIF processes is necessary. The coupling of the different BIF processes may lead to strong nonlinearities and phenomena similar to the processes that appear in nonlinear and quantum optics because of the coupling of two or more laser modes (see e.g. [START_REF] Meystre | Elements of Quantum Optics[END_REF]). Considering that the reaction, which will be actually started corresponds to the process of lowest threshold current, it is most impor-

Summary

In order to demonstrate the idea of BIF the analogy between an electron assisted BIF reaction, that may take place in deuterized metal environment during electrolysis,

  traction between the quasi-free particles (the depth of the potential can reach hundreds of eV) they can not form strongly bound pairs. Their binding energy E rel in their relative motion must fulfill the |E rel | ω O (u) condition, where ω O (u) is the energy of the optical phonon (e.g. ω O (u = 1) = 31 meV [9], [10]). Namely, if |E B | → ω O (u) then the attraction disappears as can be seen from (2). Consequently the potential well formed by the sum of the attractive potential and the repulsive Coulomb potential (see e.g. Fig.1 curve (b) in [9]) may cause some kind of weak pairing but not a strong binding. So one can say that the main consequence of the attraction due to phonon coupling is the sometimes drastic reduction of the width of the potential hill which they have to tunnel and the huge increase of the Gamow-factor. The proposed mechanism is fairly general and the calculations may be repeated for deuterized Ti, Ni crystals too and therefore it is reasonable to think that it can explain the possibility of low energy fusion reactions in general.

2

  Electron assisted boson ( 4 He) induced fusion (BIF) reaction in crystal lattices Bosons ( 4 He) are created in the vicinity of, or inside a crystal that, because of the Bragg law, may work like a resonator. The energy eigenstates of the boson in the res-

  where d j is the distance of the resonator planes. We assume an open resonator with length L = d j . The area of the resonator plates of linear dimension H is H × H. The resonators select Ψ 2 (r), because the sine-like coupling has nodal points on the crystal planes thus absorption and outscattering are less in-

  energy relations are as follows. The nuclear reaction energy Q = 2m d0 c 2 -m He0 c 2 = 23.846 MeV, and it is shared between the 4 He and the electron as 75.7 keV and 23.77 MeV, respectively, in a normal single reaction.(E kin,1 and E kin,2 are much less than Q.) E B is the energy of a bound deuteron state at the octahedral sites in the Pd lattice of face-centered cubic (fcc) structure. The barrier height E barr between the minima is 0.23 eV[START_REF] Ichimaru | [END_REF].Thus E B = -E barr + 3 ω d /2 relative to the top of the barrier, where ω d = 48 meV[11] producing the energy of a ground state of an oscillator 3 ω d /2 = 72 meV[START_REF] Wicke | Hydrogen in Palladium and Palladium Alloys[END_REF].The number density of deuterons in this state is n d . The bound deuterons are responsible for the optical phonon branch, they cause the attractive optical phonon exchange induced potential. Its depth U 0 (0) as a function of E kin has a sharp minimum at E kin = ω O (u)[9],[10], which is the energy of the optical phonon (e.g.ω O (u = 1) = 31 meV), E kin = E kin,1 = E kin,2 is the energy of the quasifree particles measured from the top of the barrier. The minimum in U 0 (0) at E kin = ω O (u) causes a peak in the Gamow-factor exp (-G W ) [see Eq.(18)] the width of which determines the energy width ∆E of the "lasing" of the ensemble of two-level systems. The numerical calculation for ∆E results a few meV around u = 1.

( 4

 4 He) BIF First the conditions of BIF (the conditions of "lasing") must be investigated. The life times of states |a and |b are τ a and τ b , respectively. τ a is mainly determined by the characteristic time τ ph 100 fs [26] of phonon electron interaction since the characteristic time τ ab of the spontaneous transition |a → |b is so large that τ ab τ a,ph ∼ τ ph for every u. Therefore one can take τ a = τ ph resulting dE a = 2π /τ a = 1.05 meV. τ b is the characteristic time of energy loss of the outgoing electron determined by the ∆E = dE dx loss,e v e τ b (31) condition, where v e is the velocity and (dE/dx) loss,e is the energy loss per length of the electron with v e c, the velocity of light. For the energy E e of the outgoing electron E e Q. (dE/dx) loss,e is mainly the result of bremsstrahlung [27], [28]. In the following ∆E = 1.0 meV is used. It is in accordance with the fact that the magnitude of the effective energy interval for the phonon exchange between the initial free deuterons is a few meV as it was obtained investigating the u dependence of the Gamow-factor. Carrying out the calculation for Pd of charge number Z = 46 and volume of unit cell v c = d 3 P d /4 with d P d = 3.89 × 10 -8 cm, that is the lattice parameter, we obtain τ b 4 × 10 -18 s. As a result, τ a /τ b 2.5 × 10 4

  planes. Standing waves correspond to r c = 0.5 and t c = 0.5 at each plane (t c is the transmission coefficient) and consequently if we take L = d r than neighboring resonators work like one resonator with r c = 1, therefore G th = 0 is the condition of threshold of BIF process, that gives n a,th σ ab = α loss (34)

is the corresponding 4

 4 He flux represented by the motion of one particle of velocity v ⊥ in the ⊥ direction.

  into account in the initial state. N d,las is approximately determined as N d,las = N d ξ, where N d is the steady state number of quasi-free deuterons in the sample, and the notation ξ = ∆E f d (E kin ) dE kin is introduced, where f d (E kin ) denotes the energy distribution function of quasifree deuterons. Using Bose-Einstein distribution of a free deuteron gas we obtain ξ(u = 1) = 0.0078 at room temperature (k B T = 25 meV). Thus the threshold number N a,th of N a is N a,th = N e,i N 2 d,th ξ 2 δ/2, where N d,th is the threshold steady state number of quasi-free deuterons in the sample, and δ = δΩ/ (4π) is a solid angle correction factor, which takes into account the requirement that the wave vectors of the initial deuterons must be approximately parallel [10], where δΩ is the allowed solid angle deviation. We have used δ = 2.5 × 10 -3 . Thus n a,th = n e,i N 2 d,th ξ 2 δ/2, where n e,i = 10/v c is the number density of the initial ten 4d electrons of Pd. Substituting everything into Eq.(34) one obtains

τ 2 ]Fig. 1 .

 21 Fig. 1. The u dependence of the threshold deuteron number N d,th of the sample and of u n (r h )e -G W /2 [cm -1/2 ] (see the text) of BIF. u = n d /n ion is the deuteron over metal ion number density.

d

  bound + d f ree + d f ree → 4 He + d (40) in which a localized (bound) deuteron sitting initially in an interstitial lattice site assists the BIF process. This process has a further advantage as the outgoing deuteron is also a boson. So it may also interact with the crystal resonator and the part of the outgoing deuteron (also bosonic) motion orthogonal to the resonator planes may be also field quantized. In this process the induced emission both in the quantized 4 He and in the quantized deuteron modes may work and two coupled modes are built up in the resonator. (Process of that type may be called double BIF.) These processes may be treated in a more complicated two mode laser model different from the one discussed here for the sake of demonstration of the main thought of BIF. (In process (40) the 23.846 MeV reaction energy is shared between the 4 He and the deuteron in a ratio 1 : 2, the 4 He and the deuteron will have 7.949 MeV and 15.897 MeV energy initially after fusion, respectively.) From the point of view of total heat production the deuteron assisted p + d → 3 He reaction d bound + p f ree + d f ree → 3 He + d (41) must be also partly taken into account. In this process an initially bound deuteron assists the fusion reaction too but now BIF may work only in the outgoing deuteron mode.

  pendicular to resonator plates motion with the motion of charged particles paralell with resonator plates causing their deceleration. It is expected that the degenerate parametric amplifier mechanism is mainly responsible for loss in BIF processes in general and it can explain the essentially lower energies of the outgoing charged particles that are expected in (40) and (41) processes too. (This mechanism may be connected with the loss term Γ (E) introduced by [19] in their basic model showing promising results in the numerical evaluation.)

  tant to determine the relationship between the threshold currents. (The situation is similar to a laser-material, that is pumped uniformly and which has more than one lasing transition. The laser will work in the mode which has the smallest threshold number density of the corresponding upper state.)Nevertheless we can conclude from the surprisingly good qualitative agreement between the observed threshold current and the calculated one obtained in the demonstrative model discussed here that the importance of BIF reactions in explaining4 He and heat production in LENF processes can not be doubted. The family of BIF processes may explain some disturbing characteristics of LENF observations. First, one might expect that if low energy nuclear fusion reactions are observed, i.e. if the particles overcome Coulomb repulsion, than all the possible fusion reactions must be observed with a rate proportional to their individual cross sections. However,4 He production was not accompanied with the expected rate of other fusion products. But as a consequence of induced emission in the boson field the rate of any BIF process may come out of the rate of the normal nuclear fusion processes and may explain e.g. the lack of the expected rate of neutrons. Also, BIF may qualitatively explain the die away of the effect with increasing time of electrolysis as the large energy density dissipated by the emerging energetic fusion products may damage the crystal, create crystal defects, e.g. dislocations, the increasing density of which decreases the number of possible resonators leading to a halt in BIF. Furthermore, the mechanism heavily depends on u through the u dependence of the threshold current density that, however, may have other, unknown dependences, e.g. dependence on the density and type of lattice defects, dependence on the grain size etc. Therefore the detailed analysis of BIF and the loss mechanism proposed may help to give new guide-lines to plan more informative and reproducible experiments and possibly may help in the deeper and better understanding of LENF reactions.

  and the system of quantized photon field coupled with a two-level atom ensemble in a resonator was discussed. The possibility of population inversion was pointed out. Adapting the gain condition of quantum electronics and calculating the cross section of the boson induced process the u dependence of the threshold of the quasi-free deuteron number N d,th of the sample, that is necessary to the laser like BIF process, was determined. With the aid of the N d,th numbers the threshold of the electric current density of the electrolysis was estimated and compared with the experimentally observed value. On the basis of the obtained realistic values of N d,th and of the good agreement between the estimated and the experimentally observed threshold electric currents one can say that when fusion reactions happen in deuterized metal environment of crystalline structure during electrolysis, the effect of boson induced nuclear fusion processes may be responsible for the observed extra 4 He and heat production. A degenerate parametric amplifier loss mechanism is put forward in order to explain the lack of expected fast electrons and the difference between the expected and observed energies of the outgoing charged fusion products. Other possible BIF reactions and their cross mechanisms are also discussed.

4

  He in directions parallel with the resonator planes and of the scattered electron. E e,f and |e f are the energy and state of the electron in the final state, respectively. m He0 c 2 is the rest energy, |He is the sate and

	E kin,He, =	2 k 2 2m He0 j	(11)

is the kinetic energy of the motion parallel with resonator planes of 4 He. The states |b are degenerate states, as states |e f ⊗ |He of different directions may have the same energy. (This degeneracy has to be taken into account later, in the cross section calculation by summing up over all the possible final states.) One pair of states |a and |b corresponds to a two-level system.

  Eq.(35), therefore the smallest E kin,He,⊥ corresponding to n B = 1 with d j = d P d is used in the numerical calculation.

	The transition probability per unit time W ab of the
	process can be obtained from (29) with standard methods
	with the modification that for the sums over the possible
	final states in determining W ab the
	→ [H/(2π)] 2	d 2 k ,He	(36)
	k ,He
	and
	k ,e
			He,⊥ E kin,He,	.	(35)
			As the charge number of Au is larger than the charge
			number of Pd so the energy loss is overestimated in that
			manner. It is expected, that the possible lowest value of
			n B in the Bragg law is effective because in this case the rel-

ative (referred to the lattice plane distance) displacements of Pd atoms caused by thermal motion are less disturbing, furthermore the loss is the smallest as can be seen from

Péter Kálmán et al.: Boson induced nuclear fusion in crystalline solids


Rasmeet K Chadha¹

Ahalya Subramanian

The Effect of Visual Impairment on Quality of Life of Children aged 3-16 years

Background: It is well known that Visual impairment (VI) has a detrimental effect on Quality of Life (QoL) in adults. Little is known about the effects of VI in childhood.

Aims:

To evaluate the effects of VI on QoL of children.

To the authors' knowledge, this is the first study containing a comparison arm for children with VI.

Methods: QoL in children with VI (n =24, age 10.13 ± 2.89, 18 male, 6 female) was compared to an age matched comparison group (n =24, age 9.83 ± 2.81, 18 male, 6 female) using the Low Vision Quality of Life Questionnaire.

Factors (distance and near visual acuity and age) that could be used as predictors of QoL were assessed. These were measured with standard clinical tests.

Results:

Children with VI had significantly lower QoL scores than the comparison group (P < 0.001), resulting in a 35.6% reduction in total QoL score.

QoL scores in children with VI were correlated with distance and near visual acuity (P < 0.05). 38% of the variance could be predicted by these factors and age.

Conclusions: Consideration of the effects of this reduced QoL must be made. Further studies are needed to establish the benefit to QoL of different habilitation strategies.

INTRODUCTION

Visual impairment (VI) in childhood has life long implications for both the child and their family. Indeed it affects the child's development, education, and the care given by families and professionals. It also shapes the adult the child will become, affecting employment and social prospects. [START_REF] Rahi | Severe visual impairment and blindness in children in the UK[END_REF] Although less common than VI in adulthood [START_REF] Charles | Estimates of the number of older people with a visual impairment in the UK[END_REF] the number of 'blind years' experienced by these children in their lifetime is of particular significance. [START_REF] Gilbert | Childhood blindness in the context of VISION 2020the right to sight[END_REF] The enduring needs of these children, their parents and families should be considered from a lifelong perspective. [START_REF] Fielder | A Charter for Families of Young Children with Visual Impairments[END_REF] There are no consistent national estimates on the prevalence of childhood VI as the methods to record prevalence vary between surveys. [START_REF]RNIB Complexity of prevalence stats for children[END_REF] Certification in England, completed on a Certificate of Visual Impairment (CVI), is as Sight Impaired (Partially sighted) or Severely Sight Impaired, (Blind). Using the most recent registration data from 2006 there were approximately 3825 children (0-17years) registered severely sight impaired and 4800 children registered sight impaired [START_REF]The information centre for health and social care. People Registered as Blind and Partially Sighted (Triennial) 2006 England[END_REF] . The aetiology of childhood VI in the UK is changing, demonstrating a decrease in isolated VI and increase in VI with coexisting neurological disability. [START_REF] Flanagan | Visual Impairment in childhood: insights from a community based survey[END_REF] It is important to appreciate that the impact of childhood VI is different to VI in adulthood. It differs not only in terms of age of onset and cause of impairment but perhaps more importantly in terms of the lifetime of disability these children endure and the impact that their VI has on family, friends and relationships as they grow up. In addition childhood VI poses particular, and distinct, assessment and management challenges to professionals. [START_REF] Gilbert | Childhood blindness in the context of VISION 2020the right to sight[END_REF] Children with VI can not be considered to be scaled down adults and therefore, the outcomes of studies relating to Quality of Life (QoL) in adults with VI can not be extended to relate to childhood VI. Further more whilst adult standards exist for low vision services [START_REF]Low Vision Services Consensus Group Recommendations for future service delivery in the U K[END_REF][START_REF]Low Vision Working Group Recommended Standards for Low Vision Services[END_REF] it is impossible and inappropriate to benchmark paediatric services against these.

It has been estimated that 80% of education is provided through sight. [START_REF] Kelley | Vision Impairment in children and youth[END_REF] The majority of children with VI in the UK are educated in the mainstream setting alongside normally sighted peers [START_REF]RNIB Education provision for blind and partially sighted children and young people in England[END_REF] and are encouraged to be integral members of society. It is therefore important to look at their QoL relative to their sighted peers.

There are very few studies on QoL in children with VI. [START_REF] Pilling | Social and visual function in nystagmus[END_REF][START_REF] Chak | The quality of life of children with congenital cataract: findings of the British Congenital Cataract Study[END_REF][START_REF] Boulton | Health-related quality of life of children with vision impairment or blindness[END_REF] There have been some recent developments in the design of children's vision QoL questionnaires: the Children's Visual Function Questionnaire (CVFQ) [START_REF] Felius | Development of an instrument to assess vision-related quality of life in young children[END_REF], LV Prasad Functional Vision Questionnaire (LVP-FVQ) [START_REF] Gothwal | The development of the LV Prasad-Functional Vision Questionnaire: a measure of functional vision performance of visually impaired children[END_REF] and The Impact of Visual Impairment on Children (IVI_C) [START_REF] Cochrane | Defining the content for a new quality of life questionnaire for students with low vision (the Impact of Vision Impairment on Children: IVI_C)[END_REF] . The IVI_C was unpublished at the time of this study and to the author's knowledge is not available for general use. The LVP-FVQ and CVFQ were inappropriate for use in this study. The LVP-FVQ was designed in India as a screening tool for developing countries and so the specificity of the questions to the given cultural group made it difficult to use in the western population. The CVFQ was designed for use by proxys for children up to the age of 7 and has been shown to demonstrate meaningful differences in children with varying levels of VI. [START_REF] Birch | Validity and reliability of the Children's Visual Function Questionnaire[END_REF] The children in the current study were between the ages of 3-16.

AIMS

To our knowledge, this is the first study to contain a comparison arm for children with VI in the UK allowing us to relate the effects of their impairment to the society in which they live by asking 2 questions:

1. Is there a statistical difference in QoL in children with VI compared to an age matched comparison group? 2. Are there any demographic or clinical factors that can be used as correlates or predictors of QoL for children with VI?

MATERIALS AND METHODS

Participants

The children were divided into Age matched comparison group: Attended either the paediatric orthoptic (for investigation and management of a binocular vision anomaly e.g. unilateral amblyopia) or colour vision (for investigation of a suspected congenital colour vision defect) clinic at Oxford Eye Hospital. Thus they were matched for hospital attendance but had no known visual disability. They were asymptomatic and not undergoing any form of non optical treatment (e.g. patching or surgery) at the time of participation.

Eligibility criteria

Children with VI had visual acuity (VA) in their better eye of ≤ LogMAR 0.30.

Children in the age matched comparison group had VA in their better eye ≥ LogMAR 0.00.

In both groups, children with a significant non visual physical or learning difficulty were excluded.

Outcomes

The outcomes followed the tenets of the declaration of Helsinki and informed consent was obtained for all. NHS ethics approval was granted in December 2006.

The Low Vision Quality of Life Questionnaire (LVQOL) [START_REF] Wolffsohn | Design of the low vision quality-of-life questionnaire (LVQOL) and measuring the outcome of low-vision rehabilitation[END_REF] was chosen as the outcome measure for this study. The maximum score is 125 with a higher value reflecting a better QoL score. Of the available vision specific QoL questionnaires (excluding the paediatric versions for reasons described above) it was most suited to use with children (there are no questions that related solely to an adult population) and was quick to complete (improving response rates).

QoL scores of children in both groups were compared and correlates and predictors of QoL were investigated for children with VI. Parents were asked to complete the questionnaire but to involve their child to a level appropriate for the individual child. Hence the questionnaire was primarily completed by proxy. [START_REF] Wolffsohn | Design of the low vision quality-of-life questionnaire (LVQOL) and measuring the outcome of low-vision rehabilitation[END_REF] the minimum sample size in each group to give 90% power to detect a difference between the groups at a confidence level of P= 0.001 for an independent t test was 25 and using P = 0.05 with a power of 90% the sample size was 13. Using the values for means and standard deviations obtained in this study the sample size required to give a power of 90% at a confidence level of P = 0.001 is 12. Therefore, the sample size in the study (n = 24) allows for conclusions with a power of 90% and a confidence level of P = 0.001 to be made.

Statistical Analysis

Sample

Correlation and multiple linear regression were used to look at the relationship between QoL and factors of visual function in children with VI.

Data for children with VI was compared to children in the age matched comparison group using an independent samples t test. and the age matched comparison group (n = 18)) reported higher total QoL scores than male parents. This was statistically significant in the age matched comparison group (118.72 ± 9.09 vs. 107.83 ± 18.76 P < 0.001).

RESULTS

Patient demographics

Total QoL for children with VI was significantly correlated with distance LogMAR VA (Spearman's rho= -0.44) (P < 0.05) and near LogMAR VA (Spearman's rho=-0.52) (P < 0.01). Multiple regression of these factors against total QoL score revealed that 26.9% of the variability could be attributed to these variables. 38% of the variability in total QoL score could be attributed to distance LogMAR VA, near LogMAR VA and age. When assessed individually: distance LogMAR VA contributed 24.6% to the variance, near LogMAR VA 23.0% and age 0.27%. Age was included in the regression equation as there was an interesting trend relating to age and QoL (reported above). There were unfortunately insufficient numbers (due to unequal numbers in the groups) to look for correlations between stability of the eye condition, age at diagnosis and field loss with total QoL scores.

DISCUSSION

In this study there was no control for the proxy effect. This is an accepted limitation. It has been reported [START_REF] Russell | Assessment of health related quality of life in children with cancer: consistency and agreement between parent and child reports[END_REF][START_REF] Odom | Assessing Quality of Life in School-Aged Low Vision Patients: A Comparison of Child and Proxy Assessments[END_REF] that parents of children with serious disability usually report a poorer QoL for their child than the child would report themselves and vice versa for healthy children. It is plausible that this study has served to increase the differences in scores between the groups. Future studies will need to control for this proxy effect by ensuring that they obtain only the child's views or separate the views of all contributors, being clear whether the views are their own or proxy for the child. Moreover, since we found that female proxys tend to report higher QoL than their male counterparts consideration as to the sex of the proxy should be made.

Cochrane et al [START_REF] Cochrane | Defining the content for a new quality of life questionnaire for students with low vision (the Impact of Vision Impairment on Children: IVI_C)[END_REF] recently demonstrated that the concerns expressed by support providers are different to that expressed by the child. Ensuring that all views are considered is of paramount importance when dealing with childhood VI to ensure that a complete assessment of the child's QoL is made. [START_REF] White-Koning | Parent and professional reports of the quality of life of children with cerebral palsy and associated intellectual impairment[END_REF] Having a specifically designed, age appropriate questionnaire that the children can complete independently such as the recently developed Cardiff Visual Ability Questionnaire (CVAQC) [START_REF] Khadka | Development of the 25-item Cardiff Visual Ability Questionnaire for Children (CVAQC)[END_REF] or the IVI_C [START_REF] Cochrane | Defining the content for a new quality of life questionnaire for students with low vision (the Impact of Vision Impairment on Children: IVI_C)[END_REF] will help.

Limitations aside, our results highlight some important points for to be considered by all those supporting children with VI. Habilitation may be of great benefit to the child with VI but can not fully restore QoL. These children throughout their lifetimes will continue to need to make modifications to their environment to improve their functioning but these are unlikely to fully restore visual functioning and so will have reduced QoL compared to their sighted peers. Future studies that include a control group for the type of habilitation, will help us establish whether habilitation can be tailored to meet individual needs to improve individual QoL scores.

The effect of age on QoL in childhood VI is very important. In this study older children with VI had poorer total QoL scores than their younger counterparts and there was no significant difference in VA in either group. With increasing age, even when VA remains essentially unchanged, the demands made upon the visual system increase (e.g. the requirement to read smaller print, to drive etc). It could be postulated that an increasing inability to meet these demands would result in a poorer QoL. Future studies looking at QoL and childhood VI must take into consideration the effect of age on QoL.

It would be helpful, in a clinical setting, to be able to identify the test results that most accurately represent QoL so as to alert the clinician to patients with significantly reduced QoL.

In the present study distance LogMAR and near LogMAR VA were significantly correlated with total QoL (P < 0.05 and P<0.01 respectively).

However, only 26.9% of the variability could be attributed to these variables. 38% of the variability could be attributed by a combination of distance VA, near VA and age. This finding of a significant correlation but high unaccounted variance is in keeping with other studies. [START_REF] Wolffsohn | Design of the low vision quality-of-life questionnaire (LVQOL) and measuring the outcome of low-vision rehabilitation[END_REF][START_REF] Mcclure | Macular degeneration: do conventional measurements of impaired visual function equate with visual disability?[END_REF] Vision is a highly complex function and so many clinical measures and non clinical factors of visual function are likely to work together to influence the manner in which the VI affects the individual. Contrast sensitivity, reading speed and visual fields would have been obvious additional clinical measures to consider but are not recorded for all children attending the paediatric low vision clinic. Therefore, in this study there were insufficient numbers to analyse this data. In childhood VI, it is important to consider the impact of wider non clinical factors such as family socio-economic status, appropriateness and access to support provided by the child's school and other providers, peer and family relationships. It is plausible that these factors also play a part in predicting QoL. Therefore, it is unsurprising that the current study finds, at best, 38% of the variance can be accounted for. Future studies will need to look at the additional clinical and non clinical factors that combine to predict QoL scores in children with VI.

By better understanding QoL in childhood VI, and the factors that can be modified to affect QoL, changes to habilitation services can be made to better support and personalise the care provided for these children and families.

Care providers can then work to eliminate the postcode lottery of paediatric low vision services in the UK and promote good quality, uniform, cost effective paediatric low vision services.

  Whilst providing valuable information in a field where very little is currently known, they have been limited by the lack of availability of child specific vision related QoL questionnaires at the time of their study. The studies to date have concentrated on comparing QoL in children with VI to children with other disease. They have not compared QoL of children with VI to normally sighted children without any disability.

  2 groups: Children with VI: Were regular attendees of the paediatric low vision clinic at Oxford Eye Hospital and had been given a diagnosis/working diagnosis of the aetiology of their VI. These children received comprehensive visual rehabilitation (now often referred to, and more correctly, as habilitation) and had access to ophthalmic and community support provided by a complement of multidisciplinary professionals working together, centered around the needs of the child and family. Services included investigative tests, formal diagnosis (where possible), emotional support, genetic counselling, low vision assessment, mobility training, support at home and in school.

  The finding that the total and subscale QoL scores in children withVI were significantly lower (P< 0.001) than in the age matched comparison group requires careful consideration. When compared to the maximum QoL score of 125, children with VI demonstrated a 35.6% reduction and the age matched comparison group a 7.2% reduction. Although the LVQOL was not designed specifically for the paediatric population, the significant difference between children with VI and the age matched comparison group serves to confirm the ability of the LVQOL to differentiate between these groups. Why do children with VI have lower QoL scores than children in the age matched comparison group despite having undergone comprehensive habilitation? At this stage we can only postulate on the reasons for this as there have been no other studies looking at QoL in children with VI compared to an age matched comparison group. However, Wolffsohn [19] also found that their adult patients, post rehabilitation, had lower QoL scores than those with normal vision.

Table 1

 1 outlines the demographics of the 2 groups whilst table 2 outlines the diagnosis of the children with VI. There was a 67% response rate for the children with VI (24/36).

	Group	Age (SD)	Sex	Distance VA	Near VA
				(LogMAR)	(LogMAR)
	Children with VI (n=	10.13 ± 2.89	18M	0.59 ± 0.28	0.80 ± 3.27
	24)		6F
	Age matched	9.83 ± 2.81	18M	At least 0.00	Not measured
	comparison group (n=		6 F
	24)

Table 1 : Demographics of participants Description of eye condition Number of children

 1

	Oculocutaneous albinism		4
	Dislocation of lens		1
	Retinal detachment with retinal	1
	break
	Hereditary retinal dystrophy	2
	Other retinal disorders in	1
	diseases classified elsewhere (
	in this case Battens Disease)
	Optic Atrophy			3
	Nystagmus			8
	Retinopathy of prematurity and	2
	Nystagmus
	Nystagmus and visual field	1
	defect	(in	this	case
	homonymous hemianopia)
	Congenital lens malformations	1

Table 2 : Ophthalmic diagnoses in children with VI Quality of life scores, demographic factors and factors of visual function as correlates or predictors of QoL Total

 2

	Subscale		QoL	score	QoL score age	Significance
			children with	matched
			VI		comparison
					group
	Distance	vision,	35.92 ± 12.93	54.98 ± 9.37	P < 0.001
	mobility and lighting
	(max 60)
	Adjustment (max 20) 14.98 ± 3.61	18.48 ± 2.40	P < 0.001
	Reading & fine work	15.19 ± 6.76	23.17 ± 3.14	P < 0.001
	(max 25)
	Activities of daily	14.32 ± 4.34	19.33 ± 1.69	P < 0.001
	living (max 20)
	Total LVQOL score	80.50 ± 25.21	116.00 ± 12.68	P < 0.001
	(max 125)

QoL scores and all sub scale scores in children with VI were statistically lower than in the age matched comparison group (Table

3

and figure

1

).

Table 3 : QoL scores for children with VI and age matched comparison group Figure 1: QoL Number of responses with a given QoL score:

 3

	16
	14
	12
	10
	8
	6
	4
	2
	0
	10-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100	100-110	110-120	121-130
	Whilst not statistically significant, older children with VI (n = 15 age 11-16),
	had poorer total QoL scores than their younger counterparts (n = 9 age 5-10)

(76.30 ± 27.28 vs. 87.50 ± 20.88). The reverse is true when looking at the age matched comparison group, where the older children (n = 10) had better total

Total QOL score Number of responses Children with VI Age matched comparison group

  QoL scores than their younger counterparts (n = 14) (118.05 ± 10.23 vs.114.54 ± 14.37).

	Female parents completing the questionnaires (in children with VI (n = 17)

ACKNOWLEDGEMENTS

The author's would like to thank the Optometry Department at Oxford Eye Hospital for their support and the two reviewers for their comments.

LICENCE FOR PUBLICATION

The corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non exclusive for government employees) on a worldwide basis to the BMJ publishing group to permit this article (if accepted) to be published in BJO and any other BJPGL products and sublicences such use and exploit all subsidiary rights, as set out in our licence (http://group.bmj.com/products/journals/instructions-forauthors/licence-forms).

COMPETING INTERESTS

Competing interest: None declared.