The hydrodynamic theory of tooth sensitivity, explained without jargon.
The hydrodynamic theory says a sensitive tooth hurts because fluid moves inside the microscopic channels that run through dentine, and the nerve endings at the inner end of those channels read that movement as pain. Nothing cold, sweet or sharp reaches the nerve itself: the trigger moves the fluid, and the fluid moves the nerve. That leaves a toothpaste exactly two places to work, the open mouth of the channel and the nerve at the far end, which is why S3 Sensitivity Science™ carries an active for each — 5% potassium nitrate for the nerve, 10% nano-hydroxyapatite and 5% biomimetic hydroxyapatite (both as solution) for the channel, with 1450 ppm fluoride kept in. The theory is sixty years old, it is still the working model, and the rest of this page is about what has been measured against it, what has not, and what the field has added since.
What was checked21 peer-reviewed studies, the Oral Health Foundation and the NHS
- Fluid moves; the trigger does not. Cold, sweetness, a toothbrush bristle and a blast of air all shift the fluid inside the tubule, and the nerve reads the shift.
- Flow through dentine has been measured in living human teeth, and no one has yet watched the fluid move inside a single tubule in a living tooth while the person reports the pain1.
- The current account adds a cell to the chain: fluid movement is thought to open ion channels on the odontoblasts that line the tubule, and those cells release ATP and glutamate onto the nerve2.
- Two randomised trials from one research group, one of them co-authored by a scientist employed by a toothpaste manufacturer, disagree about whether the amount of a tooth's dentine that is sealed tracks how much that tooth hurts34.
- The theory names two places to intervene and S3 puts an active at each: hydroxyapatite occludes, potassium nitrate desensitises, and neither does the other's job.
What does the hydrodynamic theory actually say?
A tooth is built in layers. Enamel, the hard shell on the outside, has no nerve supply and feels nothing at all. Underneath it lies dentine, and dentine is not solid: it is threaded with dentine tubules, microscopic tunnels running from its outer surface towards the pulp, the living core where the nerve and the blood supply sit. Every tubule is full of fluid. The Journal's explainer on what dentine tubules are has the anatomy in detail; this page is about what the fluid inside them is supposed to be doing.
The theory holds that pain begins when something at the open end of a tubule makes that fluid move. The nerve endings are not in the tubule with the fluid. They sit at the pulpal end, in and just inside the pulp, and they are stretched or squeezed when the column of fluid shifts past them. Hydro for the fluid, dynamic for the movement: the name is the entire idea.
It was set out in 1966 by Martin Brännström, a Swedish dental scientist who spent his career on the behaviour of dentine. One honest note about that founding citation, since this page is going to be strict about evidence elsewhere: the 1966 paper has no abstract deposited in PubMed and no open full text, so it is quoted here for the idea and its date and for nothing else.
Two things follow, and they are the reason any of this matters to somebody buying a toothpaste. First, the tubule has to be open at the outer end for the mechanism to work at all — under sound enamel or healthy gum, nothing moves and nothing hurts. Second, a stimulus never has to reach the nerve to be felt. Cold does not travel down the channel. It makes the fluid contract and pull outwards, and the nerve reads the pull.
Why does cold hurt most, if nothing cold reaches the nerve?
Because cold moves the fluid fastest, and speed rather than temperature is what the nerve appears to be reading. In a computer simulation of one tubule and the cell that lines it, built from measurements of eleven cats' teeth — an animal geometry, and a calculation rather than an observation — a cold stimulus drove the fluid outwards at around 410 micrometres a second while a hot one pushed it inwards at around 205, and the stress from cold built about 2.9 times faster than the stress from heat5. That is still the clearest published picture of what the theory claims is happening from moment to moment.
There is a second asymmetry, and this one was measured in people. In sixteen premolars in thirteen volunteers, pressure was applied in vivo to exposed dentine in small steps while each person marked the pain on a scale; the threshold came at a flow rate of 3.29 nanolitres per second per square millimetre when the fluid was drawn outwards and 5.75 when it was pushed inwards6. Less outward movement is needed to hurt than inward movement, which is what you would expect if cold, which pulls fluid out, is the trigger people notice first. The catch, and the authors state it plainly, is that the volunteers marked their scores in the chair while the flow rates came from those same teeth in the laboratory a few hours after extraction.
What cold does inside one tubule, second by second, has a page of its own; this page stops at the principle.
What the theory predicts, and what has been measured
A theory earns its keep by making predictions somebody can go and check. The hydrodynamic theory makes at least six. The column that matters most below is not the verdict but the one before it: where. It says, at a glance, how much of this has ever been tested in a living person.
| What the theory predicts | What would confirm it | What has been measured | Where | Verdict | Source |
|---|---|---|---|---|---|
| Fluid moves in the tubule when a stimulus is applied | Fluid seen moving inside a tubule as the stimulus lands | A steady outward flow of 0.36 microlitres per minute per square centimetre through dentine in vital premolars; flow through dentine measured in real time at subnanolitre scale under 32 cm H₂O of simulated pulpal pressure; velocities computed for hot and cold in a fluid–structure model | Living human teeth, bulk flow across dentine only; bovine dentine; computer model | Supported; never watched inside one tubule in a living tooth | Ciucchi 1995; Kim 2026; Gholampour 2018 |
| The nerve fires in response to the movement, not to the stimulus | Pain thresholds in people tracking the rate of flow | Pain thresholds in sixteen premolars in thirteen people came at flow rates of 3.29 and 5.75 nanolitres per second per square millimetre, outward and inward | Human, but the pain in the mouth and the flow after extraction | Partly supported | Charoenlarp 2007 |
| Sealing the tubule reduces the movement | Permeability falling when a sealing agent is applied | Desensitising toothpastes cut flow through bovine dentine by 44% to 70%, water alone by about 30%; in one comparison the rinse with the best surface coverage was not the one that reduced flow most | Bovine dentine; extracted human dentine | Supported in the laboratory | Kim 2026; Hill 2015 |
| Reducing the movement reduces the pain | Occlusion measured in the mouth predicting pain scores | Two four-week randomised trials from one research group, of nineteen and twenty adults: one found no significant correlation between occlusion and pain, the other found a significant one; in-office hydroxyapatite obliterated tubules under the microscope and its clinical advantage was gone by eight weeks | Human mouths | Contested | Seong 2018a; Seong 2018b; Shetty 2010 |
| Cold produces the largest movement, so cold should respond best to sealing | Pooled trials showing the biggest effect on cold | A meta-analysis of six four-week randomised trials put nano-hydroxyapatite ahead of its comparators on evaporative and tactile stimuli and no better than them on cold (SMD −0.17, p = 0.61) | Human mouths, pooled | Not supported | de Melo Alencar 2019 |
| Calming the nerve works without sealing anything | Relief from an agent that occludes nothing | All sixteen double-blind randomised trials of potassium toothpastes in one review reported significant reductions, while the proposed mechanism has never been confirmed in intact human teeth; 5% potassium nitrate relieved without occluding under the microscope in one trial, and occluded in another laboratory study | Human mouths; extracted teeth | Supported clinically, mechanism unconfirmed | Orchardson 2000; Salian 2010; James 2017 |
Two of those rows need saying in words, because a table is easy to skim past. The other three get a section of their own further down.
The first row is the one most pages get wrong in both directions. Fluid movement across dentine has been measured in vivo, in living human teeth: in premolars waiting to be taken out for orthodontic reasons, a cavity was cut, sealed with a small chamber and connected to a hydraulic circuit, and every cavity showed a steady outward flow of 0.36 microlitres per minute per square centimetre, with the pressure needed to stop it averaging 14.1 cm H₂O across five teeth1. So the fluid is real, it moves, and at rest it moves outwards. What nobody has done is watch it move inside a single tubule in a living tooth at the moment the person feels the pain. The nearest thing is a laboratory rig: bovine dentine under 32 cm H₂O of simulated pulpal pressure, monitored for a thousand seconds at subnanolitre scale, which showed four desensitising toothpastes cutting fluid flow by between 44% and 70%7.
That same rig makes the third row honest in a way the marketing version never is. In the same in vitro run, distilled water sitting on the dentine cut measured flow by about 30% on its own and the flow rose again when the water was wiped off; one of the four pastes did not beat water by a significant margin; and the three that did differed in composition without differing much from each other, which led the authors to suggest that how a paste flows and clings may matter as much as which active it carries7. Occlusion measured on a bench is a real measurement of a real thing. It is also not one measurement but several, and they do not always agree: in an in vitro comparison of desensitising rinses, the rinse that covered the dentine surface best under the electron microscope was not the one that reduced fluid flow most8.
What has changed since 1966?
The short answer: the field kept the fluid and added a cell.
Brännström's account has a fluid, a nerve ending, and a mechanical event between them. The account now taught adds the odontoblast — the cell that laid down the dentine in the first place, and whose long thin process reaches up into the tubule — as a participant in its own right, not a bystander. In the version set out in a 2026 review of thermal tooth pain, a stimulus generates fluid movement and mechanical stress; that stress opens ion channels on the odontoblast; the odontoblast releases ATP, glutamate and other signalling molecules; and those bind receptors on the pulpal nerve fibre, which fires2. The review calls this coupling of fluid, cell and nerve the most widely accepted explanation of thermal sensitivity today.
A 2025 review in the Journal of Dentistry says the same thing from the other direction, and it carries some weight: David Pashley, whose laboratory produced much of the dentine-permeability work the fluid story rests on, is among its authors. It states that the prevailing account now integrates the hydrodynamic and odontoblast-transducer theories, with rapid fluid movement inside the tubule opening ion channels on odontoblasts and on trigeminal nerve cells9. That review also adds a practical note most consumer pages leave out: because those channels do many other jobs around the body, aiming a drug at them is difficult, so occluding the tubule and desensitising the dentine remain the safest and most effective strategies available9. A separate narrative review of dental pain lists five candidate mechanisms in all, of which Brännström's is one, and concludes that they are not mutually exclusive and that several probably contribute at once10.
Why this matters to someone reading the back of a box: it turns two apparently rival product strategies into two points on one chain. Seal the tubule and less fluid moves for the same trigger. Calm the nerve and the same movement produces a weaker signal. Neither claim contradicts the other, and neither is a different theory of what sensitivity is.
What does the theory still not explain?
Enough that "explained without jargon" would be a cheat if this section were missing.
Cold. The theory makes cold the strongest stimulus, so cold ought to be the stimulus that responds best to sealing. Pooled across six four-week randomised trials, nano-hydroxyapatite treatments came out ahead of their comparators on evaporative and tactile stimuli and no better than them on cold (SMD −0.17, p = 0.61)11. Cold is the trigger most people actually complain about, and it is the one the pooled evidence for the sealing approach does not cover.
Whether sealing predicts relief. Here the field contradicts itself, and the contradiction sits inside the work of a single group in Bristol. In a four-week randomised trial of nineteen adults, occlusion scored from silicone replicas of the tooth surface did not correlate significantly with pain scores, though the correlations ran in the expected direction, and the authors warned that impression material may itself have entered tubules and produced false readings; one co-author of that trial is employed by a toothpaste manufacturer, and the disclosure belongs beside the result3. In a second four-week randomised trial of twenty adults, from the same unit and by the same method, occlusion scores did correlate significantly with pain scores4. Two small trials, one technique, opposite headline answers. Anyone who tells you that sealing more tubules reliably means less pain is ahead of the evidence. The most striking single result is older: professionally applied hydroxyapatite obliterated the tubules under the electron microscope in a randomised trial of 45 patients and beat water and no treatment from one day to four weeks, and by eight weeks the treated and untreated teeth no longer differed12.
How potassium works. A review of twenty-seven clinical trials found that all sixteen double-blind randomised trials of potassium toothpastes reported significant reductions in sensitivity, and stated in the same paper that the proposed mechanism — potassium ions diffusing up the tubule to quieten the nerve — has never been confirmed in intact human teeth13. Whether potassium nitrate also blocks tubules is unresolved rather than settled. In a four-week double-blind randomised trial of thirty adults with a companion microscope test, 5% potassium nitrate relieved sensitivity without occluding a single tubule14. In an in vitro study of ninety dentine samples, a potassium nitrate toothpaste applied twice daily did produce occlusion at three, seven and fourteen days15. Both are on the record and neither cancels the other; what a nerve-only toothpaste leaves undone takes the question on from there.
The placebo response, about which the theory says nothing at all. In a six-week double-blind randomised trial of 120 adults, potassium nitrate, strontium acetate and an ordinary fluoride paste all reduced sensitivity, with no significant difference between the three, and the fluoride-only arm improved significantly on cold air16. In a split-mouth randomised study of twenty-two adults, a dressing placed over a sensitive tooth cut the reported pain by 95% to a thermal stimulus against no dressing at all, from a single application, which the authors read as evidence that the sense of being treated shifts the perception itself17. A 2019 network meta-analysis of thirty randomised trials measured a placebo effect directly, and in that network neither potassium toothpaste nor fluoride toothpaste separated significantly from placebo18. None of that is predicted by anything in the hydrodynamic account, and all of it turns up in trials of products built on it.
Whether fluid movement is the only route. In a laboratory study on extracted bovine incisors fitted with strain gauges, a five-second thermal stimulus on the enamel produced measurable deformation at the inner surface of the dentine before any temperature change reached the junction between enamel and dentine; the authors propose that this mechanical flexing of the tooth may trigger the nerve directly, or may itself be what drives the fluid19. It is animal work on a bench, and it is titled as a question rather than an answer, which is about the right weight to give it.
Where does S3 sit in the hydrodynamic theory?
At both ends of the chain, by design. The theory says a sensitive tooth has two things wrong at once — tubules open at the surface and a nerve that fires too readily — and most sensitivity toothpastes are built to address one of them. Hydroxyapatite occludes and potassium desensitises, and neither does the other's job.
Where each S3 active is meant to act follows the theory's own geography: potassium calms the nerve, nano-hydroxyapatite works inside the tubule, and biomimetic hydroxyapatite works on the surface, each doing a job the others cannot. The two hydroxyapatites are different sizes for that reason — the nano form is under 100 nm, rod-shaped and crystalline, sized for the channel; the biomimetic form is around two microns and less crystalline, sized for the surface. The fluoride is sodium monofluorophosphate rather than a more reactive salt, chosen because it does not react with the calcium in hydroxyapatite inside the tube. S3 is water-based, which is what lets it carry potassium nitrate alongside hydroxyapatite. Anhydrous formulas built around bioactive glass cannot.
One number on the pack needs reading carefully, and S3 publishes both halves of it: 10% nano-hydroxyapatite and 5% biomimetic hydroxyapatite are inclusion levels of the ingredient as supplied, and the active hydroxyapatite content is lower than those figures suggest.
| Lever | What it changes in the theory | What pulls it on the UK shelf | What it cannot do |
|---|---|---|---|
| Seal the open end of the tubule | Less fluid moves for the same trigger | Hydroxyapatite in its nano and biomimetic forms, calcium sodium phosphosilicate, arginine, stannous fluoride | Nothing to how readily the nerve fires |
| Calm the nerve at the far end | The same fluid movement, a weaker response | Potassium nitrate, potassium citrate, potassium chloride | Closes no channel |
| Both at once | Less movement and a less reactive nerve | S3: 10% nano-hydroxyapatite and 5% biomimetic hydroxyapatite as supplied, 5% potassium nitrate, 1450 ppm fluoride | Nothing quickly; both levers need weeks of daily use |
Which lever a particular tube pulls is readable from its ingredient list, and the category review of UK sensitivity toothpastes by ingredient sets them out side by side. What the theory cannot do is settle which lever is better for a given mouth. Where the two approaches have been compared head to head, the occlusion-versus-desensitisation page has the summary; a 2026 network meta-analysis of ninety-three randomised trials in 9,548 participants put stannous fluoride and arginine forward as first-line self-care options, and noted that most of the trials in it were industry funded, from 96% of the stannous studies down to 33% of the nano-hydroxyapatite ones20. A UK guideline review for general practice puts it more bluntly still: there does not currently appear to be one ideal desensitising agent that can be recommended21.
The mechanism is not the outcome. A page that understands the hydrodynamic theory understands, above all, that a picture of a plugged tubule is a picture of a plugged tubule, and the ranked review of the microscope evidence is written on exactly that basis.
When the pain is not the tubules
The hydrodynamic account describes one kind of pain: a sharp twinge that arrives with the trigger and leaves when the trigger does. Pain with a different shape usually has a different cause. The NHS lists decay, an abscess, a cracked or damaged tooth, a loose or broken filling, an infection around a tooth coming through, gum disease and grinding among the causes of toothache, and says to see a dentist about toothache that lasts more than two days, that painkillers do not settle, or that comes with a high temperature, pain on biting, red gums or a bad taste22. The Oral Health Foundation, on a page supported by an educational grant from a toothbrush manufacturer, adds the thresholds specific to sensitivity: pain that is severe, sensitivity that has run for more than a few weeks, one tooth affected on its own, or pain that arrived suddenly23.
None of those is a toothpaste's job, and the two causes of sensitive teeth the Journal describes are both about exposed dentine, not about a tooth that is damaged underneath.
Frequently asked questions
Is the hydrodynamic theory proven?
It is the working model, which is not the same thing. The fluid is real, and its movement has been measured in vivo across dentine in living human teeth1. Pain thresholds measured in people, tooth by tooth in vivo, track the rate of that movement6. Sealing agents cut the same flow in laboratory measurements on bovine dentine7. What has not happened is anyone watching the fluid move inside a single tubule in a living tooth as the person reports the pain, and a review of dental pain mechanisms still lists five proposed accounts rather than one10.
Does cold actually reach the nerve?
No. The cold stays near the surface; it is the fluid that carries the event inwards, by contracting and pulling outwards fast enough for the nerve to register it. In an animal-derived fluid–structure simulation of one tubule, the modelled cold flow ran at about twice the speed of the modelled hot flow and built up nearly three times faster5, which is the usual explanation for why an iced drink is the trigger people notice first.
Does S3 seal dentine tubules?
In two parts, honestly. Hydroxyapatite as an ingredient class has a large body of electron-microscope evidence behind it for occluding tubules, and S3's own formula has been tested at the University of Reading. But a laboratory picture of a blocked tubule is a picture, not a measurement of how much anyone's tooth hurt afterwards. The two four-week trials that have tried to link occlusion and pain inside real mouths disagree with each other, and one of them was co-authored by a scientist employed by a toothpaste manufacturer34. The ranked review of the microscope evidence goes ingredient by ingredient, with the same caveat attached.
If my tubules are sealed, why does my tooth still hurt?
Three possibilities, and the theory covers only the first two. Seals wear: in a randomised trial of 45 patients, professionally applied hydroxyapatite that had obliterated tubules under the microscope no longer differed from no treatment at eight weeks12. The nerve may be the part that is over-reactive, which occlusion does nothing about. Or the pain is not hydrodynamic at all, in which case its shape — lingering, throbbing, one tooth, worse at night — is the clue, and the NHS threshold of toothache lasting more than two days applies22.
Who was Brännström?
Martin Brännström was a Swedish dental scientist who set out the hydrodynamic explanation of dentine pain in 1966 and spent much of his working life on dentine. His original paper is a curiosity in one respect worth stating plainly: it carries no abstract in PubMed and no open full text, so nobody citing it online is citing anything they can quote from it. The theory as it is used today rests on the sixty years of work since, not on that paper.
Where S3 sits
The theory says a sensitive tooth has two things wrong at once, an open tubule and an over-ready nerve, and a toothpaste that pulls one lever has left the other alone. S3 was formulated to sit at both points on that chain: hydroxyapatite where the fluid moves, potassium nitrate where the signal is read. More than 20 practising UK dentists own a stake in S3, and nine founding dentists advise on the formulation.
S3 Sensitivity Science™ pairs potassium nitrate with two hydroxyapatites and adult-strength fluoride in one daily paste.
See the toothpasteOne tube, three actives: potassium nitrate for the nerve, nano-hydroxyapatite inside the tubule, biomimetic hydroxyapatite on the surface, with 1450 ppm fluoride kept in. Calm, strengthen, protect: the three actions sensitive teeth need, in one daily toothpaste. The formula is patent-pending S3 Repair Technology™, UK application GB2604755.5. Read more about S3.