Faraday tilting of water-immersed granular beds.

Under low-frequency vertical vibration, a system of fine grains within a fluid is observed to tilt or to form piles, an effect studied by Faraday for grains in air. Here, we investigate the physical mechanisms behind Faraday tilting in a bed of vertically vibrated bronze spheres fully immersed in water. Experimental observations of surface tilting and bulk convection are compared with the results of molecular dynamics simulations in which the water is treated as an incompressible fluid. Our simulations reproduce the main features observed experimentally. Most tilt construction is shown to be due to horizontal fluid flow within the bed, principally occurring when the gap between the bed and the supporting platform is close to a maximum. Tilt destruction occurs by granular surface flow and in the bulk of the bed at times during each vibratory cycle close to and just later than bed impact. Destruction becomes more important for higher values of frequency and vibration amplitude, leading to lower tilt angles, partial tilting, or the symmetric domed geometry of Muchowski flow.

Comparing the anti-tumor effect of several bioreductive drugs when used in combination with photodynamic therapy (PDT).

PURPOSE: To compare the effect on the RIF-1 murine sarcoma of nine bioreductive agents from five different classes when used in combination with either photodynamic therapy or clamping. METHODS AND MATERIALS: RIF-1 tumors implanted intradermally in C3H mice were treated with either 50J photodynamic therapy or with 120 min clamping in combination with either misonidazole, pimonidazole, metronidazole, nimorazole, RB6145, RSU1069, SR4233, mitomycin-C, or RB90740. The tumors were measured 3 times-per-week until reaching 4 x their initial treatment volume. RESULTS: RSU1069 produced the greatest anti-tumor activity in combination with both photodynamic therapy and clamping. RB6145 also substantially enhanced the effect of photodynamic therapy and clamping whereas misonidazole induced a smaller, but significant increase. Mitomycin-C had no effect under clamped conditions, but greatly increased the tumorcidal effect of photodynamic therapy. Mitomycin-C also induced an effect when given with light alone. None of the other agents showed any augmentation of the tumor cell killing induced by photodynamic therapy. CONCLUSION: Of the bioreductive agents studied RSU1069, RB6145 and mitomycin-C showed the greatest anti-tumor response in combination with photodynamic therapy.

Radiolytic and photochemical reduction of the hypoxic cytotoxin 1,2-dihydro-8-(4-methylpiperazinyl)-4-phenylimidazo [1,2-a] pyrido [3,2-e] pyrazine 5-oxide (RB90740) and a potential mechanism for hypoxia-selective toxicity.

PURPOSE: To study the reduction of RB90740 (1), a fused pyrazine mono-N-oxide that has an oxic:hypoxic cytotoxicity ratio of > 10 in a range of murine and human tumor cells in vitro. METHODS AND MATERIALS: Reduction of 1 has been initiated radiolytically and photochemically in aqueous solution and the products isolated and characterized by high performance liquid chromatography (HPLC). RESULTS: Radiolytic reduction of 1 leads to the formation of the 2-electron reduced product, 2. The stoichiometry of the reduction is pH dependent, increasing from 1 to 2 with increasing pH, but independent of the presence of formate or 2-methyl 2-propanol in the reduction mixture. A dimerization product, 3, is also found, which is produced in greater yields at lower pH (< 6). Photochemical reduction of 1 to 2 was also found to be facile. Photolysis of 1 also leads to a deoxyribonucleic acid cleavage reaction. CONCLUSION: Since 2 is not cytotoxic towards hypoxic cells at concentrations at which 1 is toxic, a probable candidate as the cytotoxic species under hypoxic conditions is the 1-electron reduced intermediate species.

Pharmacokinetics, metabolism and distribution of 1,2-dihydro-8-(4-methylpiperazinyl)-4-phenylimidazo [1,2-A] pyrido [3,2-E] pyrazine-5-oxide in C3H mice.

PURPOSE: 1,2-Dihydro-8-(4-methylpiperazinyl)-4-phenylimidazo [1,2-a] pyrido [3,2-e] pyrazine-5-oxide (RB90740) is a bioreductive drug with an oxic to hypoxic toxicity ratio of 16 in cultured V79 cells in vitro. The aim of this study was to examine the pharmacokinetics, metabolism and distribution of the drug in tumor bearing C3H mice. METHODS AND MATERIALS: A high pressure liquid chromatography assay for the quantitative determination of concentrations of the drug and its metabolites has been developed and used to examine their distribution in blood, RIF-1 and KHT tumors, brain, muscle, and liver tissue. Urine and feces collected for 24 h after drug administration have been examined for the drug and its metabolism products. RESULTS: Three metabolites, two of which have been identified, have been observed in mouse tissue. 1,2-Dihydro-8-(4-methylpiperazinyl)-4-phenylimidazo [1,2-a]pyrido[3,2-e]pyrazine (RB92815) is the two-electron reduced species, which is observed in liver, urine and occassionally in tumor samples. 1,2-dihydro-8-(4-piperazinyl)-4-phenylimidazo [1,2-a]pyrido[3,2-e]pyrazine-5-oxide (RB1739), the N-demethylated compound, is observed in urine and liver. Elimination of the drug after an intraperitoneal dose of 50 mg/kg is biphasic with t(1)2 alpha = 3 min and t(1)2 beta = 219 min. The area under the curve for blood concentration vs. time is 1.4 mg ml min-1. The drug is preferentially taken up into tumor tissue as is apparent from the area under the curve values for RIF-1 (28.3 mg ml min-1) and KHT (18.4 mg ml min-1) tumors. CONCLUSION: From these values of the area under the curve it is suggested that the drug is present in tumor tissue at concentrations sufficient to eliminate the hypoxic fraction provided reduction to a toxic species occurs. Bioreduction by the addition of two electrons to form RB92815 occurs in some tumors, but it is not known if this is due to an obligate two-electron detoxifying step or if reduction occurs by single electron additions via a toxic free radical species.

Assessment of a range of novel nitro-aromatic radiosensitizers and bioreductive drugs.

In a directed search for the best compounds for clinical evaluation, some 150 selected nitroaromatic compounds, representing 6 distinct types, namely, furans, thiophenes, imidazoles, pyrazoles, pyrroles, and triazoles, have been synthesized and tested as hypoxic cell radiosensitisers and bioreductive drugs. These compounds have a wide range of one-electron redox potentials, ranging from -700 mV for 3-nitropyrroles to -250 mV for 5-nitrofurans. Within each series, those agents bearing alkylating moieties on the side chain are generally the more effective radiosensitisers in vitro. Studies in vivo demonstrated that the bifunctional nitroimidazoles were superior to the other nitroarenes tested. In terms of bioreductive cell killing, the best differential between oxic and hypoxic cell toxicity was shown for the bifunctional 2-nitroimidazoles, which had values greater than 20. In contrast, the other classes of nitroarines generally showed differential toxicities of less than 10.

Fused pyrazine mono-n-oxides as bioreductive drugs. II Cytotoxicity in human cells and oncogenicity in a rodent transformation assay.

PURPOSE: To determine what structural moieties of the fused pyrazine mono-N-oxides are determining factors in their in vitro cytotoxicity and oncogenicity. METHODS AND MATERIALS: A new series of experimental bioreductive drugs, fused pyrazine mono-N-oxides, was evaluated in vitro for aerobic and hypoxic cytotoxicity in the HT29 human colon adenocarcinoma cell line by using clonogenic assays. The relative oncogenicities of these compounds were also determined in aerobic cultures of C3H 10T1/2 mouse embryo fibroblasts by using a standard transformation assay. RESULTS: Removal of the 4-methyl piperazine side chain from the parent compound, RB 90740, reduced the potency of the hypoxic cytotoxin. Reduction of the N-oxide function increased the aerobic cytotoxicity and eliminated most of the hypoxic/aerobic cytotoxic differential. The reduced N-oxide also had significant oncogenicity, consistent with a mechanism of genotoxicity following bioreduction of RB 90740. CONCLUSION: This new series of bioreductive compounds may be effective in cancer therapy, particularly the lead compound RB 90740. The oncogenic potential of these compounds is similar to that for other cancer therapies. Further studies should include evaluation of these compounds in vivo and the development of analogs with reduced oncogenic potential and retention of the hypoxic/aerobic cytotoxicity differential.

Synthesis of a series of nitrothiophenes with basic or electrophilic substituents and evaluation as radiosensitizers and as bioreductively activated cytotoxins.

A series of 2- and 3-nitrothiophene-5-carboxamides bearing N-(omega-aminoalkyl) side chains has been prepared by treatment of the thiophenecarbonyl chloride with the appropriate (protected) omega-aminoalkylamine. Analogous N-(oxiranylmethyl)nitrothiophene-5-carboxamides have been synthesized by epoxidation of the corresponding N-allylamide. Compounds in both classes were evaluated in vitro both as radiosensitizers of hypoxic mammalian cells and as selective bioreductively activated cytotoxins. The most potent radiosensitizers were those agents with strong tertiary amine bases or oxiranes in the side chain. Studies in vivo showed that 2-methyl-N-[2-(dimethyl-amino)ethyl]-3-nitrothiophene-5- carboxamide caused slight radiosensitization of the KHT sarcoma in mice given 0.34 mmol kg-1. However, administration of this and related tertiary amines at higher doses was precluded by systemic toxicity.

Synthesis and evaluation of novel electrophilic nitrofuran carboxamides and carboxylates as radiosensitizers and bioreductively activated cytotoxins.

A series of 5-nitrofuran-2- and 3-carboxamides bearing alkylating side-chains has been synthesized and tested for their ability to radiosensitize selectively hypoxic Chinese hamster cells (V79) to the lethal effects of ionizing radiation and also for their ability to act directly and selectively as cytotoxic drugs on hypoxic V79 cells. The compounds were extremely efficient radiosensitizers of such cells in vitro and were more efficient than known nitroimidazoles of similar type. Their efficiencies as radiosensitizers correlated with their high electron affinity (E7(1] as measured by pulse-radiolysis. However the compounds showed little radiosensitizing activity towards KHT sarcomas in C3H mice. The compounds in this series of nitrofurans were generally more toxic towards hypoxic cells than towards oxic cells in vitro but were less effective upon the basis of a differential effect than were similar nitroimidazoles reported previously.

2-Nitroimidazole dual-function bioreductive drugs: studies on the effects of regioisomerism and side-chain structural modifications on differential cytotoxicity and radiosensitization by aziridinyl and oxiranyl derivatives.

A series of 2-nitroimidazoles bearing side chains terminating in or containing aziridinyl and oxiranyl groups has been prepared, and the compounds were evaluated in vitro as hypoxia-selective bioreductively-activated cytotoxins and selected compounds tested for their radiosensitizing properties toward hypoxic mammalian cells. Compounds were either the regioisomers of analogues of the potent dual-functional 2-nitroimidiazole alpha-[(1-aziridinyl)-methyl]-2-nitro-1H-imidazole-1- ethanol (RSU-1069, 1) with additional methyl groups or related oxiranes of varying side-chain length and type. Oxiranyl derivatives showed little differential toxicity, and those tested were less effective as radiosensitizers, and although these properties were influenced by side-chain length, differences were not great. Aziridinyl compounds related to 1 but with increased side-chain lengths were unstable. Methylation of 1 in various regions had little effect on radiosensitization and no clear advantages over 1 as differential cytotoxic drugs. Progressive methylation at C-3 was found to increase toxicity but decrease hypoxia selectivity. Incorporation of a cyclohexane side chain in 1,2-cis-2,3-trans-3-aziridin-1-yl-2-hydroxy-1-(2-nitroimidazol+ ++-1- yl)cyclohexane (26) abolished hypoxia-selective toxicity and unexpectedly reduced radiosensitizing efficiency. Of the aziridines, 1-(2-nitro-1-imidazolyl)-2-methyl-3-(1-aziridinyl)-2-propanol (20) was comparable in efficacy to 1 as a bioreductively-activated cytotoxin with slightly lower aerobic toxicity; however, the prodrugs of 1 remain as preferred candidates for clinical evaluation.

Bioreductive activation of a series of indolequinones by human DT-diaphorase: structure-activity relationships.

A series of indolequinones including derivatives of EO9 bearing various functional groups and related indole-2-carboxamides have been studied with a view to identifying molecular features which confer substrate specificity for purified human NAD(P)H:quinone oxidoreductase (DT-diaphorase), bioreductive activation to DNA-damaging species, and selectivity for DT-diaphorase-rich cells in vitro. A broad spectrum of substrate specificity exists, but minor changes to the indolequinone nucleus have a significant effect upon substrate specificity. Modifications at the 2-position are favorable in terms of substrate specificity as these positions are located at the binding site entrance as determined by molecular modeling studies. In contrast, substitutions at the (indol-3-yl)methyl position with bulky leaving groups or a group containing a chlorine atom result in compounds which are poor substrates, some of which inactivate DT-diaphorase. Modeling studies demonstrate that these groups sit close to the mechanistically important amino acids Tyr 156 and His 162 possibly resulting in either alkylation within the active site or disruption of charge-relay mechanisms. An aziridinyl group at the 5-position is essential for potency and selectivity to DT-diaphorase-rich cells under aerobic conditions. The most efficient substrates induced qualitatively greater single-strand DNA breaks in cell-free assays via a redox mechanism involving the production of hydrogen peroxide (catalase inhibitable). This damage is unlikely to form a major part of their mechanism of action in cells since potency does not correlate with extent of DNA damage. In terms of hypoxia selectivity, modifications at the 3-position generate compounds which are poor substrates for DT-diaphorase but have high hypoxic cytotoxicity ratios.

2-Cyclopropylindoloquinones and their analogues as bioreductively activated antitumor agents: structure-activity in vitro and efficacy in vivo.

A series of 2-cycloalkyl- and 2-alkyl-3-(hydroxymethyl)-1-methylindoloquinones and corresponding carbamates have been synthesized and substituted in the 5-position with a variety of substituted and unsubstituted aziridines. Cytotoxicity against hypoxic cells in vitro was dependent upon the presence of a 5-aziridinyl or a substituted aziridinyl substituent for 3-hydroxymethyl analogues. The activity of 5-methoxy derivatives was dependent upon the presence of a 3-(carbamoyloxy)methyl substituent. Increasing the steric bulk at the 2-position reduced the compounds' effectiveness against hypoxic cells. A 2-cyclopropyl substituent was up to 2 orders of magnitude more effective than a 2-isopropyl substituent, suggesting possible radical ring-opening reactions contributing to toxicity. Nonfused 2-cyclopropylmitosenes were more effective than related fused cyclopropamitosenes reported previously. The reduction potentials of the quinone/semiquinone one-electron couples were in the range -286 to -380 mV. The semiquinone radicals reacted with oxygen with rate constants 2-8 x 10(8) dm3 mol-1 s-1. The involvement of the two-electron reduced hydroquinone in the mediation of cytotoxicity is implicated. The most effective compounds in vitro were the 2-cyclopropyl and 5-(2-methylaziridinyl) derivatives, and of these, 5-(aziridin-1-yl)-2-cyclopropyl-3-(hydroxymethyl)-1-methylindole-4 ,7-dione (21) and 3-(hydroxymethyl)-5-(2-methylaziridin-1-yl)-1,2-dimethylindole+ ++-4,7-dione (54) were evaluated in vivo. Both compounds showed antitumor activity both as single agents and in combination with radiation, with some substantial improvements over EO9 (3) at maximum tolerated doses and as single agents against the RIF-1 tumor model and comparable efficacy in the KHT tumor model.

Synthesis and evaluation of alpha-[[(2-haloethyl)amino]methyl]-2- nitro-1H-imidazole-1-ethanols as prodrugs of alpha-[(1-aziridinyl)methyl]-2- nitro-1H-imidazole-1-ethanol (RSU-1069) and its analogues which are radiosensitizers and bioreductively activated cytotoxins.

alpha-[(1-Aziridinyl)methyl]-2-nitro-1H-imidazole-1-ethanols, of general formula ImCH2CH(OH)CH2NCR1R2CR3R4, where Im = 2-nitroimidazole and R1, R2, R3, R4 = H, Me, are radiosensitizers and selective bioreductively activated cytotoxins toward hypoxic tumor cells in vitro and in vivo. Treatment of the aziridines with hydrogen halide in acetone or aqueous acetone gave the corresponding 2-haloethylamines of general formula ImCH2CH(OH)CH2(+)-NH2CR1R2CR3R4X X-, where R1, R2, R3, R4 = H, Me, and X = F, Cl, Br, I. These 2-haloethylamines were evaluated as prodrugs of the parent aziridines. The rates of ring closure in aqueous solution at pH approximately 6 were found to increase with increasing methyl substitution and to depend on the nature of the leaving group (I approximately Br greater than Cl much greater than F). A competing reaction of ImCH2CH(OH)CH2+NH2CH2CH2X X- (X = Cl, Br) with aqueous HCO3- ions gives 3-[2-hyroxy-3-(2-nitro-1H-imidazol-1-yl)propyl]-2-oxazolidinone. The activities of these prodrugs as radiosensitizers or as bioreductively activated cytotoxins were consistent with the proportion converted to the parent aziridine during the course of the experiment. alpha-[[(2-Bromoethyl)amino]methyl]-2-nitro-1H-imidazole-1- ethanol (RB 6145, 10), the prodrug of alpha-[(1-aziridinyl)methyl]-2-nitro-1H-imidazole-1-ethanol (RSU-1069, 3), is identified as the most useful compound in terms of biological activity and rate of ring closure under physiological conditions.

Indolequinone antitumor agents: reductive activation and elimination from (5-methoxy-1-methyl-4,7-dioxoindol-3-yl)methyl derivatives and hypoxia-selective cytotoxicity in vitro.

A series of indolequinones bearing a variety of leaving groups at the (indol-3-yl)methyl position was synthesized by functionalization of the corresponding 3-(hydroxymethyl)indolequinone, and the resulting compounds were evaluated in vitro as bioreductively activated cytotoxins. The elimination of a range of functional groups-carboxylate, phenol, and thiol-was demonstrated upon reductive activation under both chemical and quantitative radiolytic conditions. Only those compounds which eliminated such groups under both sets of conditions exhibited significant hypoxia selectivity, with anoxic:oxic toxicity ratios in the range 10-200. With the exception of the 3-hydroxymethyl derivative, radiolytic generation of semiquinone radicals and HPLC analysis indicated that efficient elimination of the leaving group occurred following one-electron reduction of the parent compound. The active species in leaving group elimination was predominantly the hydroquinone rather than the semiquinone radical. The resulting iminium derivative acted as an alkylating agent and was efficiently trapped by added thiol following chemical reduction and by either water or 2-propanol following radiolytic reduction. A chain reaction in the radical-initiated reduction of these indolequinones (not seen in a simpler benzoquinone) in the presence of a hydrogen donor (2-propanol) was observed. Compounds that were unsubstituted at C-2 were found to be up to 300 times more potent as cytotoxins than their 2-alkyl-substituted analogues in V79-379A cells, but with lower hypoxic cytotoxicity ratios.

The relative importance of NADPH: cytochrome c (P450) reductase for determining the sensitivity of human tumour cells to the indolequinone EO9 and related analogues lacking functionality at the C-2 and C-3 positions.

Analogues of EO9 (3-hydroxymethyl-5-aziridinyl-1-methyl-2[1H-indole-4-7-dione]prop-2-e n-1-ol) which lack functionality at either the C-2 or C-3 position were synthesised. The aim was to establish the importance of each group towards toxicity and to give an indication as to whether substitution at either position altered activation and toxicity after metabolism by cellular NADPH: cytochrome c (P450) reductase (P450R). MDA231 breast cancer cells were transfected with the cDNA for human P450R and stable clones were isolated. These high P450R-expressing clones were used to determine the aerobic and hypoxic toxicity of EO9 and the two analogues that lacked functionality at either C-2 or C-3. The results showed that P450R was strongly implicated in the bioactivation of EO9 and its analogues under both of these conditions. This data also showed that the C-3 functionality was primarily implicated in hypoxic toxicity.

Radiation-induced luminescence in DNA: evidence for long-range electron migration.

The radiation-induced "in-pulse" luminescence emission from solid DNA containing either metronidazole or a highly electron-affinic 5-nitrofuran in the range 3-2000 (w:w) base pairs per additive molecule has been investigated in vacuo at 293 K using electron pulses of energy below 260 keV. The luminescence intensity at 450 nm from DNA decreases with increasing content of the additive in the sample and approaches a limiting level at high concentrations of the additives. At these higher concentrations the limiting value represents about 50% of that observed from DNA alone. It is shown that the efficiency of the additives in reducing the luminescence intensity is dependent upon their redox potential E1(7); this dependence is consistent with these additives acting as electron acceptors. It is concluded that the ability of the electron acceptors to reduce the luminescence is related to the electron affinity of E1(7) of the acceptors and electron migration distances of at least 300 base pairs are proposed.

Recent advances in bioreductive drug targeting.

Advances in the chemistry of bioreductive drug activation have led to the design of hypoxia-selective drug delivery systems. These prodrugs, comprising a bioreductive "trigger", "linker" and "effector" were first explored with nitrobenzyl quaternary ammonium mustards. Alternative nitroheterocycles were subsequently developed, together with new avenues of prodrug activation in ADEPT and GDEPT. Major advances have also been made in utilising indolequinone reductive chemistry based upon an appreciation of the kinetics of oxygen-sensitive reductive elimination.

Electron transfer reactions in RB90745, a bioreductive drug having both aromatic N-oxide and nitroarene moieties.

The bifunctional hypoxia-specific cytotoxin RB90745, has a nitroimidazole moiety attached to an imidazol[1,2-a]quinoxaline mono-N-oxide with a spacer/linking group. The reduction chemistry of the drug was studied by pulse radiolysis using the one electron reductant CO2.-. As N-oxides and nitro compounds react with CO2.- at diffusion controlled rates, initial reaction produced a mixture of the nitro radical (lambda max 410 nm) and the N-oxide radical (lambda max 550 nm) in a few microseconds. Subsequently an intramolecular electron transfer (IET) was observed (k = 1.0 +/- 0.25 x 10(3) s-1 at pH 5-9), from the N-oxide to the more electron-affinic nitro group. This was confirmed by the first order decay rate of the radical at 550 nm and formation at 410 nm, which was independent of both the concentration of the parent compound and the radicals. The rates of electron transfer and the decay kinetics of the nitro anion radicals were pH dependent and three different pKas could be estimated for the one electron reduced species: 5.6 (nitroimidazole group) and 4.3, and 7.6 (N-oxide function). The radicals react with oxygen with rate constants of 3.1 x 10(7) and 2.8 x 10(6) dm3 mol-1 s-1 observed at 575 nm and 410 nm respectively. Steady state radiolysis studies indicated four electron stoichiometry for the reduction of the compound.

Novel N-oxides as bioreductive drugs.

A series of imidazo [1,2-a] quinoxaline mono-N-oxides and their aza- analogues have been synthesized together with analogues substituted in the 8-position. These compounds have been evaluated as bioreductively activated cytotoxins in vitro and in vivo. These compounds had differential cytotoxicities in vitro of up to 20 for 8-amino derivatives such as RB90740 and 65 for 8-aminoalkoxy derivatives such as 1,2-dihydro-8-(1-(demethylamino)ethoxy)-4-phenylimidazo [1,2-a] pyrido [3,2-e] pyrazine 5-oxide, but were disappointing in vivo with a maximum growth delay of 10 days compared with 30 days for SR4233 in the RIF-1 tumor model. RB90740 is only effective at killing V79 cells at extremely low levels of oxygen, in contrast to SR4233, and this oxygen dependence can explain the poor and often variable activity of the compound in vivo. 1,2-dihydro-8-(1-(demethylamino)ethoxy)-4-phenylmidazo [1,2-a] pyrido [3,2-e] pyrazine 5-oxide, as the most effective drug in vitro, remains the lead structure for any further drug development.

Chaotic dynamics of an air-damped bouncing ball.

A ball bouncing elastically upon a vertically vibrated platform is one of the simplest examples of a chaotic system. If dissipation is introduced at each bounce through a coefficient of restitution, the motion is no longer chaotic; the trajectories exhibit locking solutions that result in periodic behavior. Here we investigate the dynamics of a bouncing ball influenced by air damping. We consider the effects of both static air and air moving with the platform, and show that there is an exact mapping between them. In either case, the system has a rather complex dynamical behavior including truly chaotic trajectories. Our results highlight the importance of air effects for fine particulate systems.

Air-driven Brazil nut effect.

A large heavy object may rise to the top of a bed of smaller particles under the influence of vertical vibration, the "Brazil nut effect." Recently it has been noted that interstitial air can influence the Brazil nut rise time. Here we report that the air movement induced by vertical vibration produces a very strong Brazil nut effect for fine granular beds. We use a porous-bottomed box to investigate the mechanism responsible for this effect and to demonstrate that it is related to the piling of fine beds, first reported by Chladni and studied by Faraday. Both effects are due to the strong interaction of the fine particles with the air, as it is forced through the bed by the vibration.