During the 84th session of the Global NMR Discussion Meetings held on April 30th, 2024 via Zoom, Prof. Giuseppe Pileio from the University of Southampton, UK gave a talk on the topic “Long-loved nuclear singlet spin order and its applications”. The recording serves as a tutorial.
Prof. Pileio’s research :
Abstract:
Nuclear singlet spin order is the population difference between the singlet and triplet states in a system of two coupled spin-1/2 nuclei. This form of order is long-lived, silent and accessible on demand. For almost two decades, my research activities were focused at exploiting these three main properties of nuclear spin order to develop new applications in NMR and MRI. In this talk, I will introduce the concept and the main features of singlet order as well as the tools developed for its manipulations. I will then show how we are using this form of order to enhance several NMR and MRI techniques for the long-term storage of hyperpolarisation, to obtain a new form of contrast in MRI, for the measurements of slow diffusion and flow, or for the determination of structural features of porous media such as tortuosity and structural anisotropy through singlet-assisted diffusion NMR.
Content of this video :
00:00 – 14:51 Introduction to long-lived spin order
14:52 – 21:00 Long-time storage of hyperpolarization
21:01 – 24:40 Ts contrast in MRI
24:41 – 27:47 Imaging macroscopic diffusion
27:48 – 31:16 Singlet-assisted q-space diffraction
31:17 – 39:03 Singlet-assisted diffusion tensor imaging
39:04 – 41:40 Singlet-assisted tortuosity measurements
41:41 – 50:42 Field-cycling singlet-assisted diffusion NMR
50:43 – 1:01:58 Q&A
Current organizers:
Adrian Draney (Creighton Uni., Chemistry)
Amrit Venkatesh (Florida State University, National High Magnetic Field Laboratory)
Asif Equbal (New York Uni., Abu Dhabi)
Blake Wilson (Robert Tycko Lab, NIH)
Michael Hope (Warwick Uni., Chemistry)
Mouzhe Xie (Maurer Lab, Uni. Chicago)
Nino Wili (Niels Chr Nielsen Lab, Aarhus Uni.)
Nesreen Elathram (Debelouchina Lab, UCSD)
Charlotte Bocquelet (HMRLab, CRMN Lyon)
yeah as the interaction said um it’s all today is all about long love nuclear spin States and applications uh I’ve been told this series here is uh part tutorial and part application so I’m going to uh split the talk in two parts so in the first part I will discuss a little bit about the states and then I would like to show um which kind of a were developed over the years and also uh how we are using this in now in my group to uh understand um well to basically find out information about molecule structure and things like that so we will see the details in a minute so um so well okay so I’ll start with this prologue about long lpin States and obviously there is a different ways to uh say this and I still find uh this way here probably the most instructive so let’s take like a spin pair like two spin a half which are coupled together and we all know there are like four energy levels and these four energy levels they are interconnected uh so you could realize transition between the move population around uh through connection given by the internal aonian terms in liquid state basically J coupling and chemical shift and also relaxation mechanisms connect the states so relaxation can scramble population around in the states and the relaxation is often see as the states are connected to the molecular environment so they exchange energy with all the rest of the molecule surrounding your spin system and this happened uh um due to a series of mechanisms which here I call I isolate one in particular the dipolar relaxation mechanism DD all the other they fall into the category other mechanism we will see those in details in a second and eventually all what this done it will discharge a non-equilibrium population you create among the four states with a Decay constant which we all know we all call T1 well then the reason the thing is this suppose we make some changes in either in the magnetic or electronic environment of this spin system we could move we could see the same Force spin State grouped in a different way we have a triple state so three states which are still interconnected by the internal lonian and the relaxation mechanisms so in some sense they relax to the molecular environment with the same Decay constants again T1 and then down here and then uh single state which we call singlet which is connected with the triple State through the difference in chemical shift between the two spins in the pair but if we manage to actually suppress this difference in chemical shift then we also have an isolated long spin State who is immune to the diol relaxation mechanism and is only connected to the lus through other mechanisms and there is an asterisk there because this other mechanis the connection to the other mechanism is different and often more convenient uh to us than uh the way the triplet are connected to the molecular environment so in other words this States decays uh with um so the population discharges into the triplet one much slowly much slowly than the T1 so in that sense we call them long Liv now um if we isolate the other mechanisms then there is a plora of those which have been known to the NMR Community for a long time this uh for into the name of chemical shift and isotropy spein rotation inter molecular dipolar cing out of pair dipolar coupling J of the second sorry scalar coupling of the second kind kind paramagnetic and so on now what was not new is obviously how this single state relaxes so how this mechanisms are written uh uh when we talked about the long Lin State rather than the conventional longitudinal or transverse magnetization right so my first task when I was a post dog with Malcolm it was to go one by one into this mechanism and trying to device uh a theory and uh eventually an analytical equation for for for this and here is just a summary of this equation found for the different mechanisms uh and at the top there you see basically the singlet actually here is not the lifetime but it’s actually the inverse so the rate of the singlet uh you know with regard the top one is with regard to the intra diol coupling is zero this means that they are immune and then there there is a series of equations here which basically show the behavior of this state with respect to all other mechanisms or at least the one that are in this table now what we learn from this well we learned that we could do a sort of intelligent design of the molecule and try to build in the knowled of these equations minimize all the terms all this other minor effects with the purpose to have longer and longer lifetimes of this States so here is an example still the one which detains the record in our uh institution here um which basically where we have the couple of spin 13 which may make uh the basis for the single States and then eventually we have like the environment of spin pair conversion conformationally inflexible this is to reduce like spin rotation Decay and then there are like small chemical shift difference between the member of the pair so we break the Symmetry by only uh very little So to avoid that mechanism and then if you go around you can read all the other uh um say criteria uh which were built in and a molecule should have to have longer and longer uh lifetimes and if you want a number for that then and how long is long then uh here is this molecule which has been measured in acetone and you can see from the number down here the T1 of this molecule is about a minute slightly more than a minute but the TS is longer than 70 minutes that happens in aceton deated so you can gain a factor of about 60 over the the T1 now this is you can see this is like a sort of artificial molecule we had to well we prepar it on purpose uh but there are lots of natural occurring molecules which have which satisfy partially this criteria so they have long lifetime in the sense they are longer than T1 but how long obviously depends on how well those criteria are satisfied another interesting example is the another well is the N2 uh in this case is M15 label where we have a lifetime of 3 seconds for the longitudinal magnetization to three minutes for the lunch du magnetization but we have about half an hour for the uh lifetime of the Long Live spin state right so uh well okay so I would like to show you some uh what we do with the states but before that obviously we need a sort of toolkit and the toolkit in NMR is essentially well could be obviously equipment and I’ll show you some uh equipment later on the talk but mainly it’s PSE sequences so the way we manipulate uh spin order essentially and uh I have to say over the years so now it’s it has been almost I think 20 years now since the Malcolm proposed this idea of long lpin States and there were a lot of uh group our groups Malcolm’s group obviously at the beginning and then my group and other groups developing P sequences to uh to play with these states and there are a pler out there so these are known as m2s Sleek adiabatic Sleek upso adapt uh generalized m2s symmet adaps m2s and so on among all this family of PSE sequences the one in the m2s family they are the most versatile at least to my judgment not only because they come from here but uh mainly because they could be adapted to uh experiments where uh you play this sequence along with p uh field gradients so they transport these ideas into the field of diffusion and MRI as I’m going to show you in extensively in the rest of the talk so here it’s one of this category the m2s sequences which basically takes some transfer magnetization at the beginning performs uh a pulse sequence a series of PS which is built upon like series of acos was a number of acos and Echo delay are carefully timed with the parameter of the spin systems and then gives out singlet order and then there is the the time reverse of that which is the s2m takes singlet order and converts back into transverse magnetization right now while you can uh do the first uh transition so from transverse Oro to singlet order uh in uh with with efficiency one so you can take all transfers sors into singlet order we have to be conscious that the inverse so going from singlet order to transfer magnetization can only be done with a maximum conversions efficiency of 2/3 so you trade away one3 of the signal but obviously you get something like 10 to 60 or more times longer lifetime so uh depends on what uh you want to do obviously with that now I mentioned why I like those sequence apart from the fact that were developed here is that they can easily be transformed into specially selective one so by playing you know by introducing shaped PS and the usual stuff so gradients or ref focusing gradients and so on you can now make the same transformation but only in selected location of space so the s2m at the top there basically takes transverse magnetization produce singlet order but only on a selected slice of the material and the bottom one again does the same transformation from singlet order to transvers but only on selected location of the sample and uh again is also very easy to modify those sequences and make them diffusion compatible so I’m sure people are aware about the way we measure diffusion there is more about that later in the talk but essentially you create some polar you can youate you you mark the spin position with some sort of gradient often a bipolar gradient and then you let spin the fuse and then eventually later you reconvert the magnetization into some observable while decoding the uh the the spin position with another pair of bipolar gradients and you can do the same within the m2s sequence so you can basically develop pulse gradients m2s and PSE gradients s to M and this is what we have done uh in in this in this uh part sequence here so well okay so in principle I’m ready to show you something uh but I would say so far I’ve just highlighted that the singlet order it’s long lived or long loved in that case but I maybe I would like to stress and everyone to be aware of the fact that there are two other important properties of singlet order one is that it is silent in the sense that it’s not a magnetic State it’s a in zero state so it doesn’t give an NMR signal on its own and also it is accessible on demand essentially we will have to transform some form of order into singlet order and VI Versa and we we can do that with very selective PSE sequences which do that either in some location of space but also in certain spin system because the sequen is adapted to the numbers right so the J coupling and the chemical shifts or whatever else is in the in the essence of the actual molecule we have in front of us now if you combine these three things together you could see that what you have in front of you it’s it’s what would be called a long LIF smart tag right so it’s a tag because you can follow it across you know long distance or long time uh and but it’s smart because you can actually access it only when you want so essentially my group now specialize in using this exploiting this smart TXS in magnetic resonance experiments of different kinds and here is a list of application which has been developed over the years by us and as well as other colleagues so for example we have been using those stes to store our polarization uh have a new form of contast in MRI track molecules over long time and L distances measure is low flow and all the way down the list and uh as you can see there are like uh uh pieces in Gray which is something I will not have time to talk today in the pieces in dark gray is something which I I will touch on in the rest in the rest of the talk so I hope uh this make a good um prologue to what is coming and I will stop here but I remind people that uh in 2020 I’ve edited a book which contains uh which discussed the theory behind that the Des sign of molecule or the P sequence developed up to that time and also the application of singlet order so I invite people who want to read more about that to look at this book and uh and and read more and and hopefully contribute to the field which is which I hope I will show at the end of the talk is an exciting one so moving on now I I’m going to selected a few of those application and I would like to show you how we deploy this knowledge and this P sequence and and and molecules which have been designed to support the states to perform this tasks and obviously Thee the first one which came to mind to us and I’m sure to everyone in the audience is well if you have something living long why don’t you store hyper polarized in order because we know hyper polarization is created by basically suddenly lost within a few T ons um so the idea of polarization at least in my mind could be tgh as in this way you have this B of thermal polarization that you have to build into the the system right and this is usually done by placing uh uh the spins into a magnetic field at some temperature and this is what um is called thermal magnetization right so longitudal mization if you want and then you can imagine the techniques developed over the year which we call H ation as a sort of pump which take from withdraw um signal more or less right from the thermal magnetization and deposited into a vessel and this vessel is uh as a top so we could uh withraw from this so we have like higher signal if we do experiment from this bot rather than from the thermal one but we don’t have to forget that there is a leak to this uh recipient and that leak is essentially the T1 right so is size by T1 So the faster the T1 the faster you lose the the fluid you have pumps through this top level well uh the singlet uh you can imagine the singlet act as a sort of tighter container of hyper polarization so you pump the H polarization in another container where you can you can take uh you know you can take uh some signal out of but they have a leak again to the termal BS but our leak is is much more small is smaller now the interesting things at that point when we realized that was can we make it even better than that can we actually include an idea of recycling in other words can we actually collect uh whatever it’s leaking and then put it back in the Hy hyperpolarized spin order recipient and the idea come actually as possible and we did this experiment in collaboration with a generic and K Lon in Copenhagen at that time and um I hope the idea will be explained in this uh pile sequence uh here so essentially you take a molecule which has uh a long LIF spin order so the number for this molecular down here the T1 is 45 seconds the TS is is about uh well it’s more than 10 15 minutes or so and uh and this is what I would call the container right so then you can take this container into the dissolution DMP machine of yic and create some hyper poiz spin order now that that spin order will be lost within a few t1s so literally a few minutes but what you do immediately it’s you can convert into into long lift spin order by running an m2s pulse sequence so out of the solution DMP machine you take the order into singlet order and now it can leave up to Alpha now or more and obviously so you have time to wait and do whatever you want to do with your sample and at some point you would like to detect and the detection obviously is the step which could in principle uh uh kill right the signal but if you want to recycle it you can make this you can convert it into magnetization okay in full or at least uh as much as you can within the limits of the two that I express before and any other sort of limitation coming from imperfection of PSE sequences and so on but once you are in the in the in the magnetization then you can actually observe it and I suggest during this observation you do a double Echo and collect four fids and then at the end of the fids which you by the way you can sum up and have also a factor of two in signal to noise and give you like the answer you want about this SP system then you could you end up having magnetization but this magnetization is still hyper polarized and it’s also still and you able still to Bing it back into the singlet container so that’s is what you do with an m2s and once it’s in the single container you can store it there for a longer time and eventually later come back to it read it again store it and come back and read it again and so on now it looks like uh an nice idea but is it true is it possible to do well we did the experiment in in lab in 2013 actually and here you see the decay of the longit well the Long Live spin order which is alive for you know even after half an hour if I remember correctly unfortunately I don’t have the number here the signal to noise is of the order a few thousands after five minutes and it’s still 60 after alpan hour now you clearly understand that the even the very first Spectrum here won’t be there if you use conventional method so if you storm the the hyper po magnetization as longitudinal order because the T1 was 44 seconds so after five minutes you nearly have nothing so here is a method to do to preserve this uh basically for for for as long as many minutes uh in fact hours uh with with those intell ently designed molecules well but then we also thought well if you have um a new a new Decay constant you probably have another mean to get contrast between different parts of an object different tissue perhaps of a body and indeed we try to do this experiment and it turns out that there there are molecules for which uh the um there is a huge contrast in TS whether the molecule is exposed to well while the solution is exposed to oxygen which is a paramagnetic substance or not you can think that could be also related to difference in PH or difference in whatever else condition surrounding the singlet molecule that you make comp par for that particular application in this particular application as a demonstration we took this molecule fumerate that we had around in the lab and we knew was was a nightmare to to to deal with because basically if you look at the number the T1 is 35 seconds if it’s the gas but only six seconds if it’s not the gas and the TS it’s five minutes if it’s the gas but only basically the same as T1 or 8 seconds just slightly more if it’s the gas if it’s not the gas sorry so it’s this it’s a molecule where oxygen probably can get very close to the to this pair and destroy the singlet order as well as the longitudinal order so well this is a perfect uh example for contrast right so what we did simply is we took a tube into another tube the inner tube contains a solution of this fumerate of this fumate diester which has been theas so we expect 35 seconds of T1 300 seconds on TS the outer one has not been deaged and the experiment here it’s very simple so you create some singlet order through the m2s block then you wait some time and then you have this t00 filter I’ll come to that in a moment and then eventually you convert back singlet into magnetization and then with a 90 you have again longitudinal order and this means that you can now start any Imaging sequence you want in this particular application we use equal planner Imaging to do like Fast MRI but in later you will see rare you can use any any other P sequence or you know Imaging P sequence you want or the best one for your sample in fact now the t00 filter you will see it from now on you will see it in every sequence that is basically a combination of of pulses and gradients which uh says uh which basically uh destroy everything else is not a single so this basically if the m2s creates byproducts these are destroyed before they actually compromise they all experiment and it’s always present from now on what you see in the images below is actually this experiment run a different time are different values of the tow time and you see the the signal so the image from the outer tube start disappearing to completely disappear after AIT 12 or 16 seconds while the other one can be seen the one from the inner tube can be seen even after 5 minutes so you created that form of contrast uh through uh going through the uh singlet order rather than um T2 or T1 contrast as usual in uh well known right in in MRI okay um well then the other thing we showed before I showed before was about combining these sequences with bipolar gradients and diffusion like techniques to uh to to measure the fusion but before I go into that I would say we have here a chance to actually observe molecule in the real space and image the fusion as it happened in in another in another way to track molecule and figure it out where they moved after a while right which is basically Imaging microscopic diffusion in real space now to do this experiment you have to use this specially selected m2s sequences so the way you do that you prepare some transverse order with an with a with with a selective pulse played along a gradient right and then you trans you transform that order into singlet only in that selected slice of the sun then again you wait some time if you want then you filter out everything which is not a singlet or or everything which is a singlet actually and then non selectively you convert all the singlet order into magnetization but wherever the moleular it is at that time right and now this gives you like again magnetization right with some sort of intensity everywhere the molecular has moved and you can picture that with an image again in this case an Epi will do so the experiment run as the follow as follow so here you have like a 10 mm tube this is this image here just for reference only Okay then if you do one of this experiment in which T is essentially zero then you can see these lies of I think 3 mm sagittal slice I selected in this experiment in the first part of the segment now obviously in that much SE that much micros seconds the molecule ever move move significantly so when you come and take take the image you just see the molecule in the original slides but if you now allow 1 minute 2 minutes 3 minutes or 5 minutes or whatever he time you have depending on the molecule you’re using then you can picture the molecule right in the new location as they have moved and the simulation below done within Mathematica uh by an algorithm you know programmed by myself then you can see that is exactly what you should see uh comp ible with the diffusion time of that particular molecule and and the time you have waited so here it’s a method to track molecule displacing right from the original position moving into a different one after uh basically a long distance or if you want after a long time um on this note um another interesting application came as a suggestion originally from William price in Australia and Sydney and then we team up with William and we did something together as well uh in terms of Q space defraction um so Q space defraction is a technique in which basically diffusion experiments are used to figure it out distance well geometrical information about po sizes or or or similar let’s say I think one of the most um notable experiment is you have two you have a cavity a rectangular cavity I would like to measure the distance between the two walls so you can do that with this experiment you see here which is a conventional stimulated Echo experiment right which is very conventional experiment for diffusion and if you if you basically plot the signal against what is called Q which is essentially a combination of the duration of the gradient the strength of the the gradient the gyromagnetic ratio uh you see uh Minima uh which in this part in this plot and this Minima occur at every Q which is actually the inverse of the distance between the the two um walls so essentially the molecule move uh eat the Wall comes back and in this motion they have a sort of defraction like pattern that defraction like pattern reflects right so repeats itself every every uh other inverse of the distance of the walls however if the cavity is too big in this in this simulation here the cavity was supposed to be 400 microns and you have even 10 seconds of diffusion time you barely see anything in the diffusion plot you need to have like 20 or even more seconds right to of diffusion time to highlight this a Me by measuring this deep you essentially measure the cavity size and obviously it is clear you can do these things with conventional diffusion but you can if you enance the diffusion time through singlet order right so the experiment is again is basically this time it’s the you use this P gradient uh m2s sequence to create uh singlet order but Mark the molecular position at sometime and then after a long diffusion time you decode the molecular position and you also convert the singlet back to detectable magnetization uh with the PG s2m and in the experiment here I’ve used two cavities these are like glass um rectangular capillaries where the inner cavity is either 8 or 2 mm so it’s really macroscopic and the the plots here the Dots here are actually the the results of the experiment and the line is the best fit is actually the fit it’s actually not the fit it’s actually the overlap with the theoretical equation you saw before and as you could see you can correctly measure these cavities even if they are too big for conventional defusion uh diffusion experiments and since we are talking about diffusion uh why not to use uh singlet to Hance also diffusion tensor Imaging experiment experiment by the way I forgot to say that the experiments you saw before and this one and the one coming next as well they all fall into what I called with the worst probably Acron acronym ever sad anmr which stands for singlet assisted diffusion NMR So within this uh name they fall you know there a number of experiments which fall including like uh measuring of flow and things like that anyway so let’s go into the fusion in tensor Imaging now I think so far i’ mentioned we we can measure diffusion coefficients but the fusion coefficients is not really the right word we all know the fusion is actually a tensor and it’s actually an it’s a rank two tensor so are like in principle nine independent diffusion constants but the tensor is symmetric so only six of them are uh important independent in fact um now to make to to retrieve the sh shape of the diffusion tensor right um one way is basically to force to constraint to restrict the molecule into some geometry of some shape the shape itself gives a shape to the tensor to the diffusion tensor because diffusion becomes different in different direction of space however there are some key concept here the molecu after they do this random motion they have essentially displaced they have moved right a given length and that length is proportional to the diffusion coefficient but also to the diffusion time so how long you let them diffuse for the geometry itself are some characteristic L this is an example of a cylinder for example the leg could be the radius of the cylinder but depends on the poe geometry obviously if it’s a sphere it’s the diameter again and things like that now if the diffusion the if if the diffusion length it’s smaller than the than the characteristic length of the structure so the molecule never touch any W right so they don’t exper and confinement so the tensor is uh uh is basically spherical so all the EG values are equal and you can talk about the diffusion coefficient which is essentially the 10 the uh one third of the trace of that right so the isotropic value of that tension however if you can restrict the motion or if the motion is restricted because the geometry is such for that or you can increase the diffusion length so that so the diffusion time so that the molecule start exploring the uh restrictions then the tensor acquires some degrees of linearity or n planarity okay now because Delta it’s limited by T1 in conventional NM NMR diffusion studies then the structural information may be misrepresented in structure where the the diffusion length is much smaller than the the diffusion structure so essentially you may think the molecule it’s in a in a spherical environment but it actually is not you just didn’t didn’t give enough time right to the molecule to explore the geometry of the structure right and now uh very shortly how we measure uh the diffusion tensor well you have six independent diffusion constant to measure so you do like six diffusion experiment along six independent Direction and then you fit that you get one of these curve every time you can fit them all together to get the six different uh diffusion coefficients which from which you use to build this uh tensor which is basically the diffusion in the laboratory frame then you can diagonalize it so you get now diffusivities along the principal Direction and The Ang Vector are actually the diffusion the the the direction where the diffusion are diffusivities right so the prefer direction of diffusion uh you can visualize that and people do that it’s nothing we invented obviously has been there for many many years uh through um an to what is called the diffusion ellipsoid so you basically build an ellipsoid whose direction of the axis follows the a values of the diffusion tensor and the radii are proportional to the diffusion or exactly equal to the diffusion coefficient in that direction ction if you want you can also convey this information in one single number that number is usually called um um fractional isotropy is very much used in MRI and that number goes from zero if that diffusion tensor is spherical to one if it’s highly anisotropic so the experiment we could do in this using singlets so how we announce the DTI experiment is again the same experiment we used before but now run along six different direction of space we collect this data and then we use standard techniques to process those data and retrieve the diffusion tensor diagonalize it and blah blah blah all all the things I show the sample here I’ve chosen to demonstrate that are well of course you have the sample which is the container the singlet container it’s the molecule down here in this corner right but then uh we would like to infer some information about the structure containing uh which you know containing this molecule and we fabricated some Phantom which are made by Plastics we drill some hole the holes are quite big it’s 1 mm so there you can’t do this experiment with conventional DTI and we also had another version of these hes which are tilted 30 Dees with respect the to the laboratory frame Zed uh axis which is the axis of the magnetic field so in doing that uh you could see so here is a series of experiment in which we basically vary the diffusion time right and we we measure the diffusion tensor and then we retrieve the fractional isotropy and also the angle between the Zed the principal Zed of diffusion and the axis of the mole and the sorry and the magnetic field axis okay uh which is also so essentially the alignment right of this uh which is the angle basically between the main axis of the holes here right and the magnetic field and as you can see if you don’t allow enough time you don’t get the correct fraction on isotropy but you also don’t get the correct angle only when you have like 30 seconds or a couple of minutes or 4 minutes you start to build up the right fraction on isotropy and figure it out the right Ang angle right of inclination o of this um contain of this um Chambers right with respect to magnetic field and the thing is even more evident where we know that the the channels are tilted by 30 degrees and you don’t get that angle until you get very long diffusion time as expected obviously from what I was saying before but here it’s like a way to Hance DTI and look at this structure this uh information right even if the container are microscopic there is another thing you could do uh and is actually quite important as we will see in a moment on on a number of practical porus media and this measuring tortuosity through single assisted diffusion NMR so T you can imagine this you have like a PO medium okay here it’s just a packed a sample of packed big right but it could be anything really and obviously there is if you take two points two cavities A and B the toos is how difficult to go from A to B since you can’t go in a straight line and the molecule have to go through you know whatever is the interconnection of uh uh the pores within that structure which is something natural now the uh it is known that you can retrieve this to toity value as by taking the diffusion um measuring the diffusion a long time and divide it by diffusion a a short time and this is uh called the ratio is basically tortuosity of that now um obviously to do that you need to have access to this restricted diffusion coefficient at infinitely long time okay or what the matter there is obviously having enough time for the molecule to go out from one port and TR you know and move toward through many ports right and explore the all geometry which obviously requires time and this time is granted Again by this experiment so the experiment is again the same as before but what you do here you take a series of diffusion measurement and as a function of the Delta so of the diffusion time you plot them down and what you see what you expect is that this points flatten up right to an astop and this astop is actually the tortuosity for a sample of P bits this tortuosity is actually known it could be calculated through algorithm and this is what is shown here by the dotted line so as you can see in any case so these are like three cases in which there are like different bit size so the pores and the system of pores is different every time time and when we do the experiment and we let the molecu fuse up to 4 minutes we reach in all cases we reach this astop which matches what is expected to be now moving on actually in fact moving on the same line right I’m going to talk about the very latest topic today which is field cying signal assist of the fusion NMR so one can think about well okay let’s put those things in practice okay where toity matters where toity matters for example in the field of batteries there is a lots of por stuff which they use in batteries to separate things right and and and and molecules have to move across those pores so it’s important to see how torous is that and there is also an even better and more interesting at least in in in my group uh field where this could be interesting it’s if you start cultivating cultivating cells in a 3D printed support the cell the cells infiltrate the scaffolds and they close up the pores so progressively you have an increasing tortuosity right can we track that this is a very strange heterogeneous uh sample which is basically heterogeneous in time because things grows with time and also in space because they also grow in different part in at different times right so very interesting sample to work with so now one can think okay you have the tools just apply it well actually what we didn’t really appreciate at the beginning was this we know to we know that the plastic there will bring some susceptibility hogenes this stability in obog genes will bring big gradients but then we say well very good singlet is insensitive to gradients so that would be even a plus with this application what we didn’t consider fully at the beginning was that obviously spins diffusing in this pores they have a sort of a fast T2 relaxation mechanism and now we have no time to play the Echoes so to play those false sequences to get into the singlet order in the first place so somehow the singlet is Long Live it’s insensitive to this gradients but you don’t have to the time to do uh uh to pre to prepare it so then we want to study this phenomenon and do something to to contact it so the way to study that is a bit long I’m going to cut it short because I’m conscious the time is running out but basically what we want to do is to take a real image to build some coding by the way some simulation coding that we succeeded in that which takes the actual structure of your polus medium through a micro CT uh image okay and then knowing what where the molecule can move we can build the magnetic field okay which is called the 3D magnetization of field so now the magnetic field Point by point in that structure let the molecule do a random walk and move across all the pores and and now we know the field experienced at each Instant by the molecule passing through that particular corner of the structure this is the fluctuating field here you see here when you learn when you learn actually relaxation in NMR you have been seen like the relaxation is caused by fluctuating field this is a way to track those flating field experienced by molecule in this case diffusing into a molecule which has sexability in homogene is in the magnetic field okay and now we use this a little bit of theory and so on and we could build um a numerical and in some cases also a welln solution an analytical solution to calculate how long the t2 of the spins is right uh um when they move in a field of in this case one Tesa Alpha Tesa or 0.1 Tesa and you obviously it’s very straightforward what you should expect the lower is the field the lower is this phenomenon because at the end of the day it’s all it’s all about this um the product between the magnetic field and the susceptibility mismatch the Delta guy okay so how do we actually perform experiments where the field is so low that this is then you don’t have this in homogenated problem but then you don’t lose right the signal and you don’t lose sensitivity and you don’t lose like resolution well the way we thought that could be done it’s in a field cycling cycling fashion so we went on building a shuttle and a two core magnet you see a schematics here there should be an animation down there where we basically have two probes we have the top probe tuned at 500 KZ plac at 46 mesla where the carbon resonate at 500 KZ and then we have all sorts of Hardware including some shiming where we B and and also three axis gradients in low field so we can basically now pulse uh radio frequency pulse and also 3 axis gradient in low field and we can polarize and also read the uh sample uh in the I field so retaining resolution and sensitivity um so here is some experiments and I’m going to stop literally in two slides so the experiment you could do with this kind of things so first of all uh the the the the dual core uh machine is actually General you can perform any sort of two field experiment okay so for example you can measure T1 in low field right so you just have to adapt your sequences to work in this two uh in in the two fields and in this particular case we have a molecule trapped into uh into a sample made by bits and we measure the T1 low field to be 20 seconds you also can adapt the m2s sequence to be to work in low well in this two field regime and we measure the lifetime of this molecule in the beats in low field which is about 5 minutes as you can see in this case uh the purpose of all obviously is now to get access to the diffusion all right in 3D so you need this 3D uh capabilities which is actually unique there are many shuttle in the world but this is the only shuttle which can do that so which retains R radio frequencies but also three axis grents in low field and here it’s just an example of how we measure the diffusion in different direction we reconstruct the uh ellipsoid for example of that molecule moving across the porce left through this simple sample of packed bits and again you can do the same you can measure toity and again we uh retrieve the value which is uh what is at the limit actually of what is said uh to be um calul calculable uh with theory in in in literature so I think that is probably all I wanted to say today so I hope I show you a lots of application where we basically coupled the uh concept of long list in state with the concept of pfield gradients and here it’s a long a long list of collaborators so uh I’ve show things made by the current group you see a picture of them around here some of them they actually left the group very recently past members Andrew uh and Franchesco Monique Terell and syvia they all somehow contributed to what you saw before other collaboration collaborators in chemistry and and and so on and so forth and I think I’ll leave you with that in fact I leave you with the next slid which reminds yourself that I’ve been active recently in publishing books so there is a book about uh spin dyamics on the left there but very recently just in February I also published a book about the quantum Quantum sorry the classical mechanics behind quantum mechanics so if anyone wants to read about that they are out there um from these um Publishers and I’ll stop here all right great gcp it was a really nice and very uh informative talk thank you so much uh so for the audiences if you have questions please PST them and in the qsa channel and we’ll uh select a few questions um to to to to discuss actually we have a lot of time to for discussion um let me actually make two quick announcement so in one week from now that’s May 7th we will have the next uh Global anmr lecture by Tamal wolf uh so it’s not in two weeks but in one week May the 7th and secondly uh I also want to remind everyone that we will have the um the online conference the global anmr online conference this summer um U please stay tuned for that um so I I will start with h a question um so in terms of the designing the molecules um are there certain let’s say directions or or some rationals of uh the Next Generation let’s say single been conserving molecules yeah yeah exactly yeah so essentially we we made a list of this criteria in fact they are in that book I I cited before uh so there is a whole chapter about that I would say it’s probably very quick to say that what what you try to achieve it’s the s so it’s obviously to have like this spin pair to isolate it from the closed space from other nuclei with spin often you have protons okay so you think okay an easy way is to replace the proton with uum but actually you have to be careful as well because uum can induce scolar coupling of the second order relaxation which could be also uh challenging so um and then you want to protect well you want to kind of have a sort of rigidity in the molecule so that basically the molecule doesn’t flip around this will generate some low uh torsion of low um how to say low frequency which also induce a a a spin rotation like mechanism okay we call it spin molecular measure rotation but you know never mind so there are mechanism of this kind and and then I think another important is trying to uh to protect it from the approach of other paramagnetic molecules you may have in solution one of one above all is oxygen uh but also you may have other contaminants right really that so um so it’s it’s all about about that let’s say so there are many molecule we had done I mean you know we have a full book of we have a good collaboration with chemist here it’s probably you know we have maybe 50 or so molecule uh of different uh you know basically we we we you know at each molecule we learn more about that mechanism and then we made the next one to be longer and long so what you see here is just the end more or less of that chain uh what would be interesting now is for people to pick up this and make it perhaps biologically active you know or or encapsulate some functionality you know sensitive to sensitivity to I don’t know pH or whatever makes it interesting for application right yes yes I agree I mean I I feel to some extent is kind of similar to designing a molecular Cubit you want a system that is sort of well isolated from environment uh and also preserving certain properties um so in your mind is this let’s say in the future the designing of the molecules would it be a more kind of a screening approach to just look through a vast library of molecules or more kind of build upon um the knowledge you learn little by little or kind of see different categories of molecules and then identify which best yeah so I would say I would say this I think from my experience is this uh if you work with protons so you have like a proton spin pair uh you are always so the protons usually very exposed in the molecule they have all sort of interaction with the solvent and everything so you never you won’t find like hours long lifetimes at least no no you know we haven’t found any like that I think there are good reason to justify that that kind of sentence um you would like to to work with core nuclei and possibly with low gamma the low gamma itself right protect you in the sense because every interaction is scaled by gamma right so you have suddenly you have like a factor to gain you know um so if you are concerned about J cing to a near spe spin right if your gum is low then the J cing is also lower so so essentially you may want to go uh that way but if you go that way then there are other concern obviously right uh to to keep in mind and um and I would say and then somehow you may want to kind of label those molecules so the process of intelligent design it’s important because can give you like shortcuts but there is still like a lot of synthetic chemistry involved techniques like hyperpolarization can amplify the signal of natural abundant spin Pairs and we have already suggested many times that that should be picked up and used to identify molecule with long lising State I think this is only very very I only see very few sample of that in the community unfortunately at the moment we we don’t run hyber polarization in in our Ian Southampton so we we can’t do it ourselves but but you know we have already put that in many congresses we have t to people and say you know if you could do this experiment I think there is something interesting then to learn great um so we have a question from floring uh hi Joseph B for the 3D demagnetization field simulations what is the relation between the strength of the fluctuating magnetic fields and the distance from the hores yeah right okay great yes great question hi floran by the way um no so essentially what we capture here so what I plot here it’s in fact the uh the fluctuating field Against Time right across the old trajectories the trajectory is actually 20 seconds so you see the molecule goes everywhere but actually what we really have we have a vector which which contains the position of the spin right at each time so we can actually we we basically we go and eat the walls and and reflect back as well right so we have all sort of sensitivity to the location so so the so the magnetization field is as precise as the structure because what we do we use like uh Fier convolution right so we we build one demagnetization field which is a diar fi in the middle and then we use the F transform the F convolution theorem to have in each point in which we have a point in the image and those points if I remember correctly for this approach were like three microns resolution so every three microns we have we have like a point in the in the microct right and every three microns we have we know the field the the field in that point uh three migrant it’s small compared to the size of the of the bits which are usually of the order of 200 microns up to 1 mm in fact in in our samples that that is is that answering the question for yeah okay thanks so are there any other questions so if you happen to be in the panelist and your audience uh if you have questions you can just uh unmute yourself and speak up uh we got another question from um Mohammad Sabah uh hi pep hi Joseph uh thanks for your wonderful talk I have a couple of questions one could you clarify what you meant by symmetry adapted S2s m2s and the second question is have you explored a compilation some of the wonderful experiments you showed on studies of diffusion using variance of cmet based sequences such as a PO pole yeah okay so hi Muhammad and so so mamad is probably just nearby here it’s obviously the ampt um well okay so symmetry adapted m2s I actually meant your sequences so the latest development uh uh of uh m2s so the word m2s here it’s more general for transformation between magnetization and singlet but what I really meant I I actually don’t know the way you prefer to call them but this where we use this symmetry right to develop sequences where you you can make the transformation between magnetization into singlet and vse so that’s what I meant so literally referring to your own paper and uh in indeed so the uh the second question was about using those sequences into that so obviously that was always a plan and I think I think I at some point I even interact with you right to and ask you about um those sequences but um but then taken by the development of the hardware so I presented very quickly but that double fi uh machine is you know it wasn’t simple to make obviously it involved actually Brooker as well to make Parts um and lots of issues in there So eventually we we haven’t done it yet so we haven’t used them but indeed I I see no problems in coupling those and we should do it really because your sequences perform better than than the the m2s you see on the slide now which is the original let’s say m2s