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Computer Scientists Achieve ‘Crown Jewel’ of Cryptography




In 2018, Aayush Jain, a graduate student at the University of California, Los Angeles, traveled to Japan to give a talk about a powerful cryptographic tool he and his colleagues were developing. As he detailed the team’s approach to indistinguishability obfuscation (iO for short), one audience member raised his hand in bewilderment.

“But I thought iO doesn’t exist?” he said.

At the time, such skepticism was widespread. Indistinguishability obfuscation, if it could be built, would be able to hide not just collections of data but the inner workings of a computer program itself, creating a sort of cryptographic master tool from which nearly every other cryptographic protocol could be built. It is “one cryptographic primitive to rule them all,” said Boaz Barak of Harvard University. But to many computer scientists, this very power made iO seem too good to be true.

Computer scientists set forth candidate versions of iO starting in 2013. But the intense excitement these constructions generated gradually fizzled out, as other researchers figured out how to break their security. As the attacks piled up, “you could see a lot of negative vibes,” said Yuval Ishai of the Technion in Haifa, Israel. Researchers wondered, he said, “Who will win: the makers or the breakers?”

“There were the people who were the zealots, and they believed in [iO] and kept working on it,” said Shafi Goldwasser, director of the Simons Institute for the Theory of Computing at the University of California, Berkeley. But as the years went by, she said, “there was less and less of those people.”

Now, Jain — together with Huijia Lin of the University of Washington and Amit Sahai, Jain’s adviser at UCLA — has planted a flag for the makers. In a paper posted online on August 18, the three researchers show for the first time how to build indistinguishability obfuscation using only “standard” security assumptions.

All cryptographic protocols rest on assumptions — some, such as the famous RSA algorithm, depend on the widely held belief that standard computers will never be able to quickly factor the product of two large prime numbers. A cryptographic protocol is only as secure as its assumptions, and previous attempts at iO were built on untested and ultimately shaky foundations. The new protocol, by contrast, depends on security assumptions that have been widely used and studied in the past.

“Barring a really surprising development, these assumptions will stand,” Ishai said.

While the protocol is far from ready to be deployed in real-world applications, from a theoretical standpoint it provides an instant way to build an array of cryptographic tools that were previously out of reach. For instance, it enables the creation of “deniable” encryption, in which you can plausibly convince an attacker that you sent an entirely different message from the one you really sent, and “functional” encryption, in which you can give chosen users different levels of access to perform computations using your data.

The new result should definitively silence the iO skeptics, Ishai said. “Now there will no longer be any doubts about the existence of indistinguishability obfuscation,” he said. “It seems like a happy end.”

The Crown Jewel

For decades, computer scientists wondered if there is any secure, all-encompassing way to obfuscate computer programs, allowing people to use them without figuring out their internal secrets. Program obfuscation would enable a host of useful applications: For instance, you could use an obfuscated program to delegate particular tasks within your bank or email accounts to other individuals, without worrying that someone could use the program in a way it wasn’t intended for or read off your account passwords (unless the program was designed to output them).

But so far, all attempts to build practical obfuscators have failed. “The ones that have come out in real life are ludicrously broken, … typically within hours of release into the wild,” Sahai said. At best, they offer attackers a speed bump, he said.

In 2001, bad news came on the theoretical front too: The strongest form of obfuscation is impossible. Called black box obfuscation, it demands that attackers should be able to learn absolutely nothing about the program except what they can observe by using the program and seeing what it outputs. Some programs, Barak, Sahai and five other researchers showed, reveal their secrets so determinedly that they are impossible to obfuscate fully.

These programs, however, were specially concocted to defy obfuscation and bear little resemblance to real-world programs. So computer scientists hoped there might be some other kind of obfuscation that was weak enough to be feasible but strong enough to hide the kinds of secrets people actually care about. The same researchers who showed that black box obfuscation is impossible proposed one possible alternative in their paper: indistinguishability obfuscation.

On the face of it, iO doesn’t seem like an especially useful concept. Instead of requiring that a program’s secrets be hidden, it simply requires that the program be obfuscated enough that if you have two different programs that perform the same task, you can’t distinguish which obfuscated version came from which original version.

But iO is stronger than it sounds. For example, suppose you have a program that carries out some task related to your bank account, but the program contains your unencrypted password, making you vulnerable to anyone who gets hold of the program. Then — as long as there is some program out there that could perform the same task while keeping your password hidden — an indistinguishability obfuscator will be strong enough to successfully mask the password. After all, if it didn’t, then if you put both programs through the obfuscator, you’d be able to tell which obfuscated version came from your original program.

Over the years, computer scientists have shown that you can use iO as the basis for almost every cryptographic protocol you could imagine (except for black box obfuscation). That includes both classic cryptographic tasks like public key encryption (which is used in online transactions) and dazzling newcomers like fully homomorphic encryption, in which a cloud computer can compute on encrypted data without learning anything about it. And it includes cryptographic protocols no one knew how to build, like deniable or functional encryption.

“It really is kind of the crown jewel” of cryptographic protocols, said Rafael Pass of Cornell University. “Once you achieve this, we can get essentially everything.”

In 2013, Sahai and five co-authors proposed an iO protocol that splits up a program into something like jigsaw puzzle pieces, then uses cryptographic objects called multilinear maps to garble the individual pieces. If the pieces are put together correctly, the garbling cancels out and the program functions as intended, but each individual piece looks meaningless. The result was hailed as a breakthrough and prompted dozens of follow-up papers. But within a few years, other researchers showed that the multilinear maps used in the garbling process were not secure. Other iO candidates came along and were broken in their turn.

“There was some worry that maybe this is just a mirage, maybe iO is simply impossible to get,” Barak said. People started to feel, he said, that “maybe this whole enterprise is doomed.”

Hiding Less to Hide More

In 2016, Lin started exploring whether it might be possible to get around the weaknesses of multilinear maps by simply demanding less of them. Multilinear maps are essentially just secretive ways of computing with polynomials — mathematical expressions made up of sums and products of numbers and variables, like 3xy + 2yz2. These maps, Jain said, entail something akin to a polynomial calculating machine connected to a system of secret lockers containing the values of the variables. A user who drops in a polynomial that the machine accepts gets to look inside one final locker to find out whether the hidden values make the polynomial evaluate to 0.

For the scheme to be secure, the user shouldn’t be able to figure out anything about the contents of the other lockers or the numbers that were generated along the way. “We would like that to be true,” Sahai said. But in all the candidate multilinear maps people could come up with, the process of opening the final locker revealed information about the calculation that was supposed to stay hidden.

Since the proposed multilinear map machines all had security weaknesses, Lin wondered if there was a way to build iO using machines that don’t have to compute as many different kinds of polynomials (and therefore might be easier to build securely). Four years ago, she figured out how to build iO using only multilinear maps that compute polynomials whose “degree” is 30 or less (meaning that every term is a product of at most 30 variables, counting repeats). Over the next couple of years, she, Sahai and other researchers gradually figured out how to bring the degree down even lower, until they were able to show how to build iO using just degree-3 multilinear maps.

On paper, it looked like a vast improvement. There was just one problem: From a security standpoint, “degree 3 was actually as broken” as the machines that can handle polynomials of every degree, Jain said.

The only multilinear maps researchers knew how to build securely were those that computed polynomials of degree 2 or less. Lin joined forces with Jain and Sahai to try to figure out how to construct iO from degree-2 multilinear maps. But “we were stuck for a very, very long time,” Lin said.

“It was kind of a gloomy time,” Sahai recalled. “There’s a graveyard filled with all the ideas that didn’t work.”

Eventually, though — together with Prabhanjan Ananth of the University of California, Santa Barbara and Christian Matt of the blockchain project Concordium — they came up with an idea for a sort of compromise: Since iO seemed to need degree-3 maps, but computer scientists only had secure constructions for degree-2 maps, what if there was something in between — a sort of degree-2.5 map?

The researchers envisioned a system in which some of the lockers have clear windows, so the user can see the values contained within. This frees the machine from having to protect too much hidden information. To strike a balance between the power of higher-degree multilinear maps and the security of degree-2 maps, the machine is allowed to compute with polynomials of degree higher than 2, but there’s a restriction: The polynomial must be degree 2 on the hidden variables. “We’re trying to not hide as much” as in general multilinear maps, Lin said. The researchers were able to show that these hybrid locker systems can be constructed securely.

But to get from these less powerful multilinear maps to iO, the team needed one last ingredient: a new kind of pseudo-randomness generator, something that expands a string of random bits into a longer string that still looks random enough to fool computers. That’s what Jain, Lin and Sahai have figured out how to do in their new paper. “There was a wonderful last month or so where everything came together in a flurry of phone calls,” Sahai said.

The result is an iO protocol that finally avoids the security weaknesses of multilinear maps. “Their work looks absolutely beautiful,” Pass said.

The scheme’s security rests on four mathematical assumptions that have been widely used in other cryptographic contexts. And even the assumption that has been studied the least, called the “learning parity with noise” assumption, is related to a problem that has been studied since the 1950s.

There is likely only one thing that could break the new scheme: a quantum computer, if a full-power one is ever built. One of the four assumptions is vulnerable to quantum attacks, but over the past few months a separate line of work has emerged in three separate papers by Pass and other researchers offering a different potential route to iO that might be secure even from quantum attacks. These versions of iO rest on less established security assumptions than the ones Jain, Lin and Sahai used, several researchers said. But it is possible, Barak said, that the two approaches could be combined in the coming years to create a version of iO that rests on standard security assumptions and also resists quantum attacks.

Jain, Lin and Sahai’s construction will likely entice new researchers into the field to work on making the scheme more practical and to develop new approaches, Ishai predicted. “Once you know that something is possible in principle, it makes it psychologically much easier to work in the area,” he said.

Computer scientists still have much work to do before the protocol (or some variation on it) can be used in real-world applications. But that is par for the course, researchers said. “There’s a lot of notions in cryptography that, when they first came out, people were saying, ‘This is just pure theory, [it] has no relevance to practice,’” Pass said. “Then 10 or 20 years later, Google is implementing these things.”

The road from a theoretical breakthrough to a practical protocol can be a long one, Barak said. “But you could imagine,” he said, “that maybe 50 years from now the crypto textbooks will basically say, ‘OK, here is a very simple construction of iO, and from that we’ll now derive all of the rest of crypto.’”

Correction: November 10, 2020

A previous mobile version of the “Degrees of Obfuscation” graphic was incorrectly labeled. Degree-2.5 maps can be built securely and can be used to make iO, as correctly labeled on the desktop version.



Random walks




A college professor of mine proposed a restaurant venture to our class. He taught statistical mechanics, the physics of many-particle systems. Examples range from airplane fuel to ice cubes to primordial soup. Such systems contain 1024 particles each—so many particles that we couldn’t track them all if we tried. We can gather only a little information about the particles, so their actions look random.

So does a drunkard’s walk. Imagine a college student who (outside of the pandemic) has stayed out an hour too late and accepted one too many red plastic cups. He’s arrived halfway down a sidewalk, where he’s clutching a lamppost, en route home. Each step has a 50% chance of carrying him leftward and a 50% chance of carrying him rightward. This scenario repeats itself every Friday. On average, five minutes after arriving at the lamppost, he’s back at the lamppost. But, if we wait for a time T, we have a decent chance of finding him a distance sqrt{T} away. These characteristic typify a simple random walk.

Random walks crop up across statistical physics. For instance, consider a grain of pollen dropped onto a thin film of water. The water molecules buffet the grain, which random-walks across the film. Robert Brown observed this walk in 1827, so we call it Brownian motion. Or consider a magnet at room temperature. The magnet’s constituents don’t walk across the surface, but they orient themselves according random-walk mathematics. And, in quantum many-particle systems, information can spread via a random walk. 

So, my statistical-mechanics professor said, someone should open a restaurant near MIT. Serve lo mein and Peking duck, and call the restaurant the Random Wok.

This is the professor who, years later, confronted another alumna and me at a snack buffet.

“You know what this is?” he asked, waving a pastry in front of us. We stared for a moment, concluded that the obvious answer wouldn’t suffice, and shook our heads.

“A brownie in motion!”

Not only pollen grains undergo Brownian motion, and not only drunkards undergo random walks. Many people random-walk to their careers, trying out and discarding alternatives en route. We may think that we know our destination, but we collide with a water molecule and change course.

Such is the thrust of Random Walks, a podcast to which I contributed an interview last month. Abhigyan Ray, an undergraduate in Mumbai, created the podcast. Courses, he thought, acquaint us only with the successes in science. Stereotypes cast scientists as lone geniuses working in closed offices and silent labs. He resolved to spotlight the collaborations, the wrong turns, the lessons learned the hard way—the random walks—of science. Interviewees range from a Microsoft researcher to a Harvard computer scientist to a neurobiology professor to a genomicist.

You can find my episode on Instagram, Apple Podcasts, Google Podcasts, and Spotify. We discuss the bridging of disciplines; the usefulness of a liberal-arts education in physics; Quantum Frontiers; and the delights of poking fun at my PhD advisor, fellow blogger and Institute for Quantum Information and Matter director John Preskill


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How Dynamical Quantum Memories Forget




Lukasz Fidkowski1, Jeongwan Haah2, and Matthew B. Hastings3,2

1Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
2Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA
3Station Q, Microsoft Research, Santa Barbara, CA 93106-6105, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the “mixed” phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems $—$ i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears $—$ purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.

► BibTeX data

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[7] R. Fan, S. Vijay, A. Vishwanath, and Y.-Z. You, “Self-organized error correction in random unitary circuits with measurement,” (2020), arXiv:2002.12385.

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[10] J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth, “Quantum homeopathy works: Efficient unitary designs with a system-size independent number of non-clifford gates,” (2020), arXiv:2002.09524.

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[12] M. J. Gullans and D. A. Huse, “Scalable probes of measurement-induced criticality,” Phys. Rev. Lett. 125, 070606 (2020) 125, 070606 (2020b), arXiv:1910.00020.

[13] X. Cao, A. Tilloy, and A. D. Luca, “Entanglement in a fermion chain under continuous monitoring,” SciPost Phys. 7, 24 (2019), arXiv:1804.04638.

[14] X. Chen, Y. Li, M. P. A. Fisher, and A. Lucas, “Emergent conformal symmetry in nonunitary random dynamics of free fermions,” Phys. Rev. Research 2, 033017 (2020), arXiv:2004.09577.

[15] M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, “Entanglement phase transitions in measurement-only dynamics,” (2020), arXiv:2004.09560.

[16] A. Nahum and B. Skinner, “Entanglement and dynamics of diffusion-annihilation processes with majorana defects,” Phys. Rev. Research 2, 023288 (2020), arXiv:1911.11169.

[17] M. B. Hastings, “Random unitaries give quantum expanders,” Physical Review A 76, 032315 (2007), arXiv:0706.0556.

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Cited by

[1] Matteo Ippoliti, Michael J. Gullans, Sarang Gopalakrishnan, David A. Huse, and Vedika Khemani, “Entanglement phase transitions in measurement-only dynamics”, arXiv:2004.09560.

[2] Adam Nahum, Sthitadhi Roy, Brian Skinner, and Jonathan Ruhman, “Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory”, arXiv:2009.11311.

[3] Michael J. Gullans, Stefan Krastanov, David A. Huse, Liang Jiang, and Steven T. Flammia, “Quantum coding with low-depth random circuits”, arXiv:2010.09775.

[4] Jason Iaconis, Andrew Lucas, and Xiao Chen, “Measurement-induced phase transitions in quantum automaton circuits”, arXiv:2010.02196.

[5] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, “Topological order and criticality in (2+1)D monitored random quantum circuits”, arXiv:2011.06595.

[6] Sarang Gopalakrishnan and Michael J. Gullans, “Entanglement and purification transitions in non-Hermitian quantum mechanics”, arXiv:2012.01435.

[7] Matteo Ippoliti and Vedika Khemani, “Postselection-free entanglement dynamics via spacetime duality”, arXiv:2010.15840.

[8] Oliver Lunt, Marcin Szyniszewski, and Arijeet Pal, “Dimensional hybridity in measurement-induced criticality”, arXiv:2012.03857.

[9] Chao-Ming Jian, Bela Bauer, Anna Keselman, and Andreas W. W. Ludwig, “Criticality and entanglement in non-unitary quantum circuits and tensor networks of non-interacting fermions”, arXiv:2012.04666.

[10] Shengqi Sang, Yaodong Li, Tianci Zhou, Xiao Chen, Timothy H. Hsieh, and Matthew P. A. Fisher, “Entanglement Negativity at Measurement-Induced Criticality”, arXiv:2012.00031.

The above citations are from SAO/NASA ADS (last updated successfully 2021-01-18 07:19:20). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-01-18 07:19:18).


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Autonomous Ticking Clocks from Axiomatic Principles




Mischa P. Woods

Institute for Theoretical Physics, ETH Zurich, Switzerland

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There are many different types of time keeping devices. We use the phrase $textit{ticking clock}$ to describe those which – simply put – “tick” at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this paper is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The ticking clock model in [1] achieves high accuracy, yet lacks the autonomy of the less accurate model in [2]. Importantly, the model we introduce here achieves the best of both models: it retains the autonomy of [2] while allowing for the high accuracies of [1]. What is more, [2] is revealed to be a special case of the new ticking clock model.

► BibTeX data

► References

[1] M. P. Woods, R. Silva, G. Pütz, S. Stupar, and R. Renner, “Quantum clocks are more accurate than classical ones,” (2018a), arXiv:1806.00491v2 [quant-ph].

[2] P. Erker, M. T. Mitchison, R. Silva, M. P. Woods, N. Brunner, and M. Huber, Phys. Rev. X 7, 031022 (2017).

[3] H. Salecker and E. P. Wigner, Phys. Rev. 109, 571 (1958).

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[7] S. Ranković, Y.-C. Liang, and R. Renner, “Quantum clocks and their synchronisation | the Alternate Ticks Game,” (2015), arXiv:1506.01373v1 [quant-ph].

[8] M. P. Woods, R. Silva, and J. Oppenheim, Ann. Henri Poincaré (2018b), 10.1007/​s00023-018-0736-9.

[9] S. Khandelwal, M. P. Lock, and M. P. Woods, Quantum 4, 309 (2020).

[10] Y. Yang, L. Baumgärtner, R. Silva, and R. Renner, “Accuracy enhancing protocols for quantum clocks,” (2019), arXiv:1905.09707 [quant-ph].

[11] N. Yunger Halpern and D. T. Limmer, Phys. Rev. A 101, 042116 (2020).

[12] P. A. Hoehn, A. R. H. Smith, and M. P. E. Lock, “The Trinity of Relational Quantum Dynamics,” (2019), arXiv:1912.00033 [quant-ph].

[13] W. Pauli, in Handbuch der Physik, Vol. 24 (Springer, 1933) pp. 83–272.

[14] W. Pauli, Encyclopedia of Physics, Vol. 1 (Springer, Berlin, 1958) p. 60.

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[17] R. Gandy and C. Yates, Mathematical Logic, Vol. 4 (Elsevier, 2001) (see page 267).

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[19] B. Misra and E. C. G. Sudarshan, J. Math. Phys. 18, 756 (1977).

[20] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2007) . See section 3.3 Microscopic derivations. In particular, 3.3.1 Weak-coupling limit and 3.3.3 Singular-coupling limit.

[21] P. F. Palmer, J. Math. Phys. 18, 527 (1977).

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[23] S. Stupar, C. Klumpp, N. Gisin, and R. Renner, “Performance of Stochastic Clocks in the Alternate Ticks Game,” (2018), arXiv:1806.08812 [quant-ph].

[24] Y. Yang and R. Renner, “Ultimate limit on time signal generation,” (2020), arXiv:2004.07857 [quant-ph].

[25] I. Pikovski, M. Zych, F. Costa, and Č. Brukner, Nat. Phys. 11, 668 (2015).

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[28] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th ed. (Cambridge University Press, USA, 2011).

[29] K. Kraus, A. Böhm, J. D. Dollard, and W. H. Wootters, eds., States, Effects, and Operations Fundamental Notions of Quantum Theory, Lecture Notes in Physics, Vol. 190 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1983).

[30] M.-D. Choi, Linear Algebra and its Applications 10, 285 (1975).

Cited by

[1] Antoine Rignon-Bret, Giacomo Guarnieri, John Goold, and Mark T. Mitchison, “Thermodynamics of precision in quantum nano-machines”, arXiv:2009.11303.

[2] G. J. Milburn, “The thermodynamics of clocks”, Contemporary Physics 61 2, 69 (2020).

[3] Emanuel Schwarzhans, Maximilian P. E. Lock, Paul Erker, Nicolai Friis, and Marcus Huber, “Autonomous Temporal Probability Concentration: Clockworks and the Second Law of Thermodynamics”, arXiv:2007.01307.

The above citations are from SAO/NASA ADS (last updated successfully 2021-01-18 06:59:53). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-01-18 06:59:51).


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‘Ultrasound drill’ and nanodroplets break apart blood clots




Ultrasound drill
On target: artist’s impression of how an ultrasound drill and injection tube for nanodroplets could be used to break up blood clots in the body. (Courtesy: North Carolina State University)

A precision “ultrasound drill” combined with specially engineered nanodroplets could soon be used inside the body to break up stubborn, impenetrable blood clots – according to Leela Goel, Xiaoning Jiang  and colleagues at North Carolina State University. The team has done in vitro experiments demonstrating the technique, which if approved for clinical trials, could lead to promising new treatments for dangerous forms of thrombosis.

If blood clots do not break down quickly enough, they can retract over periods of several days, forming dense, non-porous clumps of cells. Each year, up to 600,000 people in the US alone can be affected by these clots – known as deep vein thromboses. In the past, their treatment has largely involved drugs that activate certain enzymes in the blood to break down the structures of the clots. However, the high drug doses and long treatment times required in this approach can cause significant damage in surrounding tissues.

More recently, a technique called sonothrombolysis has emerged. This uses ultrasound waves to cause microbubbles surrounding a clot to oscillate – enhancing both mechanical erosion and drug diffusion in the clot. However, this technique relies on large external ultrasound transducers, and cannot be used to treat veins that are obscured by ultrasound-blocking organs like the lungs or ribs.

Low boiling point

In their study, the North Carolina State team delivered nanodroplets to a clot created in an experimental apparatus. Because of their small size, the nandroplets easily penetrate retracted clots. Alongside the tube that delivers the nanodroplets is a catheter-based ultrasound “drill”, which produces precisely-aimed acoustic waves via a tiny, forward-viewing transducer.

The nanodroplets are specially engineered to have a low boiling point. The small amount of energy delivered by the drill is enough to vaporize the nanodroplets forming gas-filled microbubbles that rapidly expand and contract. These oscillations break down the clot through the process of cavitation – the creation of microscale streams and jets that weaken the clot’s mechanical structure. At the same time, the vibrations open up holes in the clot that enable enzyme-enhancing drugs to penetrate more easily. This enhances breakdown even further, while avoiding the need for high drug doses and long treatment times.

Over 30 min timescales, they found that clot masses could be reduced by around 40% – much more than the 17% for treatments that combine ultrasound, microbubbles, and enzyme-activating drugs. Although the team’s approach is still a long way from entering clinical practice, their results suggest that a breakthrough in the treatment of deep vein thromboses could be just over the horizon.

The technique is described in Microsystems & Nanoengineering.


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