ultrasound is increasingly being applied in practical medicine for both clinical diagnosis and therapeutic purposes.1 , 2 for diagnostic applications , a better resolution of the morphological features of organs is desirable . one of the most important factors in such diagnostic applications is the avoidance of biological damage.3 , 4 , 5 , 6 for therapeutic purposes , various applications have been developed including the healing of wounds in skin , muscle and other tissues , hemostasis , transdermal drug delivery , targeted drug delivery , in vivo oxygen delivery , and clot lysis.7 , 8 , 9 , 10 , 11 , 12 with regard to these applications , it is important to evaluate the effect of ultrasound sonication on the living body and cells.13 , 14 , 15 ultrasound has both thermal and nonthermal effects . ultrasound on a mhz scale is considered to have thermal and/or nonthermal effects , whereas ultrasound on the order of several tens of khz generates mostly nonthermal effects . although acoustic cavitation has both effects , it has been argued that the mechanical effect is dominant in the case of lowfrequency ultrasound . in addition , therapeutic ultrasound often uses pulse wave ( pw ) rather than continuous wave ( cw).12 in the present study we focused on the effect of the frequency of pulsing ultrasound on doublestrand breaks ( dsbs ) in genomic dna molecules . we used relatively lowfrequency , that is , several tens of khz , ultrasound , partly so that we can set the experimental conditions in a wellcontrolled manner to evaluate nonthermal effects . lowfrequency ultrasound has been applied to lithotripsy , phacoemulsification , ultrasoundassisted liposuction , tissue cutting and vessel sealing , and skin permeabilization.4 , 15 , 16 , 17 , 18 in these applications , the nonthermal effect , that is , cavitation effect , plays the major role . although several previous papers have discussed the cavitation effect on dna molecules ,   there have been few studies on the quantitative evaluation of damage to it is important to unveil the effects of ultrasound from the standpoints of both safety and basic science . dna damage is currently categorized into four types : base changes , crosslinking , and single and doublestrand breaks ( dsbs).25 among these , dsbs are considered to most strongly affect the function of genomic dna molecules.1 , 2 , 3 , 4 , 5 , 6 many studies have been performed to detect dsbs both in vivo and in vitro . the polymerase chain reaction can be used to detect dna damage through observation of the termination of amplification.7 , 8 immunological assays are also commonly used to detect oxidative dna damage through the use of an antibody or immunoglobulin.7 , 9 in situ hybridization provides information on specific changes in certain dna sequences.7 , 10 although several methodologies have been proposed to detect dsbs in dna molecules , including the comet assay and singlecell gel electrophoresis assay,7 , 8 , 12 , 26 it has been rather difficult to evaluate the number of dsbs per unit length of dna in a quantitative manner , especially for long , genomicsized dna molecules . recently , it has been demonstrated that the direct visualization of single giant dna molecules above the size of 100  kbp by the use of fluorescence microscopy can provide useful information on the structure and function of genomic dna molecules.26 , 27 , 28 , 29 , 30 it is becoming increasingly clear that giant dna molecules undergo large discrete changes in their higherorder structure accompanied by a change in density on the order of 1010 , whereas shorter oligomeric dna molecules do not exhibit this property.31 , 32 recently , we studied the effect of ultrasound irradiation in cw mode on dsbs in dna by singlemolecule observation , and evaluated cavitation power acoustically through the use of a hydrophone.28 we found that dsbs are generated above a threshold ultrasound power , corresponding to the critical power to generate cavitation . in the present study , we measured dsbs in genomesized dna through singlemolecule observation with highresolution fluorescence microscopy to clarify the effect of pulse irradiation in comparison to cw irradiation . figure  1 shows the results of the measurements of dsbs with different duty ratios for ultrasound sonication up to 60  s. as shown in the schematic in figure  1  a , we measured dsbs by changing the duty ratio of pw sonication : d=onon+off 
 , where on 
 is the sonication period and off 
 is the off period , that is , when sonication is not applied . a duty ratio of 1.0 corresponds to cw . the total ultrasound energy applied to the dna solution is linearly proportional to the duty ratio d. figure  1  b shows examples of fluorescence images of dna molecules stretched on a glass slide , indicating marked fragmentation for pulse sonication with a duty ratio of d=0.8 . figure  1  c shows the change in the average length of stretched dna molecules after ultrasound sonication , l 
 , depending on the duty ratio d ; there is a gradual decrease in l 
 with an increase in d. in this measurement , the average control length for more than 100 dna specimens under each experimental condition , l0 
 , was determined to be 29.5  m for samples without radiation ( d=0 ) . this is smaller than the natural contour length ( 57  m ) and can be attributed to the procedure used to extract and purify t4 gt7 dna molecules from the phage and to the process of sample preparation , which includes pipetting and mixing.29 by denoting the average number of breaks per average length before sonication as n 
 , we obtain n 
 = l0 
 /l 
 1 . to determine the frequency of dsbs per unit length n 
 , i.e. , per 10 kbp , we rescaled as n 
 = n 
 /l0 10 kbp , where l0 
 is in units of kbp.29 thus , figure  1  d shows the dependence of n 
 on the duty ratio d , where n 
 is almost linearly proportional to d , for d between 0 and 0.9 . interestingly , for d above 0.9 , there is a large deviation from a linear relationship , including at d=1.0 , that is , for cw sonication . although it may be worthwhile to clarify the degree of deviation from the linear relationship , under the experimental conditions in figure  1 , it is difficult for obtain the value of n 
 in a precise manner , since the experimental error for n 
 increases with greater fragmentation . under this situation , we performed additional experiments as described below . 
  a )  schematic representation of the periodic application , or pulsing , of ultrasound with different duty ratios , d. b )  fluorescence microscopy images of stretched dna molecules after exposure at various duty ratios ( see the procedure in figure  5 ) . l 
 , versus the duty ratio , d , under the same sonication period , ttotal=60s 
 . d )  number of dsbs versus duty ratio , d , under the same sonication period , ttotal=60s 
 . figure  2  a shows the experimental scheme that was designed to gain deeper insight into the effect of the duty ratio d , or pulse repetition period t 
 , on the degree of dsbs . in this scheme , the total input energy of ultrasound over 60  s is exactly the same for all of the experiments with different pulse repetition periods t 
 or different numbers of pulses n 
 p , where t=on+off 
 . 
  a )  schematic representation of the application of pulsed ultrasound with different pulse repetition periods , t 
 , under a constant ultrasound energy input . b )  average length of dna , l 
 , versus number of pulses , n 
 p , ( or pulse repetition period , t 
 ) under d=0.4 . c )  number of dsbs versus number of pulses , n 
 p , ( or pulse repetition period , t 
 ) under d=0.4 . figure  2  b shows the change in the average length l 
 with respect to the number of pulses n 
 p at an ultrasound pressure of 90  kpa and with a duty ratio of 0.4 , where the horizontal axis is on a logarithmic scale . in these experiments , the average length , l0 
 , was 22.9  m for about 100 dna molecules without sonication . figure  2  c indicates that , with a pulse repetition period t 
 above the order of second(s ) , there are fewer dsbs than with cw sonication . in contrast , the number of dsbs with t 
 below 1 second(s ) , becomes greater than that for cw , and tends to increase with a decrease in t 
 . figure  3 shows the results of a similar series of experiments as in figure  2 under the condition d=0.8 . the average length l 
 after sonication is somewhat smaller than that in figure  2  b. if we consider that the total input energy of ultrasound in figure  3 is twice that in figure  2 , it is natural to observe that dsbs are more frequent in figure  3 . interestingly , a closer inspection of figure  2 and figure  3 indicates a similar dependence of dsbs on the change in n 
 p ; i.e. , compared to dsbs under cw , dsbs tend to decrease with fewer pulses and tend to increase with a larger number of pulses , which reflect longer and shorter pulse repetition periods t 
 , respectively . a )  average length of dna , l 
 , versus number of pulses , n 
 p , ( or pulse repetition period , t 
 ) under d=0.8 . b )  number of dsbs versus number of pulses , n 
 p , ( or pulse repetition period , t 
 ) under d=0.8 . next , we consider the timedependent change in dsbs under ultrasound sonication . the experimental trend that a larger number of pulses causes greater damage to dna implies that the probability of dsbs per unit time tends to decrease gradually during the period of individual pulses thus , we assume that the probability of dsbs for a single pulse , x , is simply dependent on its duration or period , on 
 , as in [ eq . ( 1)]:(1)xon 
  where we regard 0<<1 , by considering the weaker effect on the probability of dsbs per unit time with a longer period for a pulse . the period is given as on = dttotalnp 
 , where d : duty ratio , ttotal 
 : total sonication period , and n 
 p : number of pulses . thus , the number of dsbs per unit length n 
 is given under the approximation that the dsbs caused by individual pulses are mutually independent [ eq .  ( 2)]:(2)nnpx = npdttotalnp 
  now , we may expect the following relationship between < n > and n 
 p.[eq . log relationship between the number of pulses , n 
 p , and the number of dsbs , < n>. from the linear portions of the lines for both d=0.4 ( the blue line ) and 0.8 ( the red line ) , we obtain =0.8 . ( 4)]:(4)log10n=0.2log10np+c 
  scaling relationship between the number of pulses , n 
 p , and the number of dsbs , < n > , shown as the log  log plot of the experimental data in figures  2 and 3 . ( 4 ) ] , whereas the curves are given by [ eq .  ( 6 ) ] . in other words , the difference in c is given as c 0.2 . from eq . thus , it has become clear that the parallel linear relationship depicted as blue and red solid lines in figure  4 can be well interpreted based on the theoretical expectation as in [ eq . the deviation of the plots for larger values of n 
 p with d=0.8 is attributable to the breakdown of the assumption that the timedependent change in the probability of dsbs is not influenced by prior pulses . in other words , when the resting time between neighboring pulses becomes on the order of 0.1  s , the aftereffect of the previous pulse becomes significant.33 from the experimental finding that the parameter  ( = 0.8 ) is smaller than unity , it becomes clear that the kinetics of dsbs exhibit a scaling behavior . this fact indicates the existence of a longer timetail compared to that under usual exponential decay . next , we can discuss the deviation from a linear relationship at small values of n 
 p , especially at n 
 p=1 . we can check the degree of deviation from a linear relationship by simply adding an additional term to [ eq . ( 6)]:(6)log10n=0.2log10np+c+0.3np. 
  this additional term results in the curved lines in figure  4 , suggesting that the fitting becomes rather good when we choose =2 . this parameter in the scaling equation implies rather rapid decay of the aftereffect of pulsed sonication . the detailed mechanism to account for why the probability of dsbs decays on a time scale of second(s ) during pulse sonication is not yet clear . however , the kinetic data together with their analysis reported here may contain important information on the timedependent change in the physicochemical effect of pulsed sonication , including the strength of the shockwave generated through cavitation . recently , we studied the effect of ascorbic acid against dsbs in dna and found that ascorbic acid has a marked protective effect against the damage induced by reactive oxygen species . in contract , ascorbic acid offers almost no protection against the damage caused by ultrasound.29 thus , dsbs caused by ultrasound are most likely caused by the shockwave under the generation of cavitation.28 the results reported here are expected to stimulate studies on the effects of periodic perturbations on the time evolution of nonlinear systems , including on many chemical and biochemical kinetics.34 it has been suggested that periodic perturbations significantly change the essential features of nonlinear dynamical systems , including the appearance of mode bifurcation , breakdown of additivity , etc.35 , 36 , 37 we studied dsbs in giant dna caused by ultrasound sonication by using singledna observation with fluorescence microscopy . the results showed that the probability of dsbs under pulse sonication is lower than that under cw when the repetition of pulses is above the order of second(s ) . in contrast , the probability of dsbs under pulse sonication is higher than that under cw when the pulse repetition is below the order of second(s ) . the discovery of this biphasic nature of the effect of ultrasound is expected to attract considerable interest from scientists in a wide range of disciplines , including not only the field of ultrasonics , but also biophysics , physical chemistry , and macromolecular science , to shed light on the biphasic effect of pulse sonication , we proposed a simple phenomenological model by considering a characteristic decay in the probability of causing dsbs during singlepulse sonication . the data analysis shows scaling behavior between the number of pulses and the number of dsbs , as in figure  4 . it may be interesting to clarify the actual physicochemical mechanism of the timedependent change in the probability of dsbs during pulse sonication in a future study . additionally , in the practical medical application of ultrasound , these results suggest that through the selection of a suitable pulsing time profile together with a consideration of the effect of ultrasound power28 , 29 , 38 , 39 it may be possible to minimize any harmful effects on the human body . similarly , we may be able to deduce the most suitable pulsing conditions for the treatment of malignant tumors . t4 gt7 dna ( 166 kbp , contour length 57  m ) and trishcl solution ( ph  7.5 ) were purchased from nippon gene ( toyama , japan ) . the fluorescent cyanine dye yoyo1 ( 1,1(4,4,7,7tetramethyl4,7diazaundecamethylene)bis4(3methyl2,3dihydro(benzo1,3oxazole)2methylidene)quinolinium tetraiodide ) was obtained from molecular probes , inc . the antioxidant 2me ( 2mercaptoethanol ) and poly(llysine ) were purchased from wako pure chemical industries ( osaka , japan ) and from sigma a pair of facing langevin transducers ( fbl28452hs ; fuji ceramics , fujinomiya , japan ) was attached to a cell so that they faced one another . the cell measured 808050  mm ( depth ) and was filled with distilled water . the experimental system was essentially the same as in a previous study.28 thus , we will only describe it briefly . a sinusoidal signal at a frequency of 30  khz was input to the transducers to form a standing acoustic wave . we measured the threedimensional distribution of the sound pressure amplitude and confirmed that , under the condition with the fixation of a test tube , the standing wave showed maximum amplitude in the center of the cell , as shown in ref .  . throughout the present study inside the cell , a polypropylene tube containing a dna sample was located at the central antinode . t4 gt7 dna ( final concentration : 0.1  m ) we examined the relationship between the current entering the transducers ( i 
 0p ) and the sound pressure from zero to the peak value ( p 
 0p ) . the sound pressure was measured using a calibrated hydrophone ( model 8103 ; brel & kjr , nrum , denmark ) with a frequency bandwidth ranging from 200  hz to 60  khz after the tube was removed from the cell . if we assume a linear relationship between the current and sound pressure , the pressure in the presence of the tube at the antinode was extrapolated from the i 
 0pp 
 0p curve . to visualize individual dna molecules by fluorescence microscopy , the fluorescent dye yoyo1 ( final concentration : 0.1  m ) and 2me ( 3.8  % ( v / v ) ) fluorescence images of dna molecules were captured by the use of an axiovert 135 tv microscope ( carl zeiss , oberkochen , germany ) equipped with an oilimmersed 100 objective lens , and recorded on a dvd through an ebccd camera ( hamamatsu photonics , japan ) . the recorded videos were analyzed by virtualdub , a free and opensource videocapture and videoprocessing utility for microsoft windows written by avery lee . the dna solution was subjected to ultrasound sonication for 60  s under different pulse conditions . after ultrasound exposure , for the measurement of dna length , dna molecules were fixed on a glass surface . glass slides were pretreated with poly(llysine ) ( concentration : 510  % ( v / v ) ) solution , and washed with distilled water . a droplet ( 5  l ) of a sample was adsorbed on a modified glass slide to obtain images of the elongated dna conformation . a droplet of the sample solution was situated on a glass slide and covered with a slip glass under weak shearing to observe elongated dna . the captured fluorescent images were analysed by imagej software ( national institutes of health , md , usa ) . the experimental error in the dna length is mainly due to the blurring effect associated with the fluorescence microscopic observation and is estimated to be on the order of 0.30.5  m . 
  experimental scheme to evaluate dsbs caused by exposure to ultrasound .