 What characterizes an organoid is that it performs certain functions specific to the organ concerned.  Organoids self-organize, spontaneously.  An organoid does not have the same properties and functions as the organ. It is therefore incorrect to refer to organoids as mini-organs.

Organoids Research: What Are the Ethical Issues?

In our Memo entitled "Research on Embryos and Embryonic Models for Scientific Use (EMSUs)", we examined the question of the moral and legal status of these new artifacts that, in many ways, resemble human embryos, created by researchers in order to better understand the development of the early embryo because they recapitulate certain aspects of it in terms of their organization and development. 1 These EMSUs, also referred to as "gastruloids", are part of what are now called "organoids". This Memo is devoted only to the ethical issues raised by research on entities created in the laboratory from post-natal cells; it will not revisit those raised by EMSUs as entities resembling human embryos.These organoids, developed from cell cultures, have become innovative tools for research in biology, as they enable a better understanding of the normal or pathological functioning of the organs they mimic. They are therefore a source of multiple therapeutic promises that need to be evaluated, not just medically, but also ethically. This is one of the reasons that led us to examine the ethical issues raised by research on organoids, issues which, as we shall see, are multiple.

What is an organoid?

First of all, it is necessary to clarify what is meant by "organoid". There are many definitions in the literature, two of which we found to be particularly relevant.

Here is the first: "The term organoid means 'resembling an organ'. Organoids are defined by three characteristics. The cells arrange themselves in vitro into three-dimensional organisation that is characteristic for the organ in vivo, the resulting structure consists of multiple cells found in that particular organ and the cells execute at least some of the functions that they normally carry out in that organ. [...] Gastruloids constitute a certain type of organoids that are cultured out of human pluripotent stem cells and that recapitulate early stages of embryonic development." 2 And the second: "Stem cell-derived or progenitor cell-derived 3D structures that, on much smaller scales, re-create important aspects of the 3D anatomy and multicellular repertoire of their physiological counterparts and that can recapitulate basic tissue-level functions." 3 The second definition clarifies the origin of organoids, which is either from stem cells or progenitor cells -to which primary cells must also be added. However, this remains somewhat restrictive because of the existence of certain structures comprised of adult differentiated stem cells that are also sometimes called "organoids". It is also important to emphasize that the use of stem cells (embryonic or increasingly often induced to pluripotency from adult somatic cells) makes it possible to obtain a quantity of human organ models that has been impossible to achieve so far.

Many types of organoids have been developed, particularly for the pancreas, kidney, liver, thyroid gland, retina, ovary, and brain. These 3D structures present some of the functions4 of the whole organ in vivo, structures that nevertheless only quite remotely reflect the organ that they mimic, in terms of its architecture, the cell diversity of the tissue reproduced, and its functions. Some authors use the term "mini-organs", which we shall see is misleading, although rhetorically striking.

Tumor organoids, called "tumoroids", have also been created in order to study certain types of cancer and to test novel therapeutic approaches -even though it is not cancer that has benefited the most from this approach so far. 5 In the literature, the term "organoid" is often used in a general and somewhat vague sense: for a decade it has been employed to designate an entire series of cell cultures that can sometimes be quite different. 6 We feel it is important to characterize more thoroughly their use and therefore introduce the following distinctions and clarifications: 7 Organoids are not simple 3D cell cultures, because in the latter the function of the organ is not present. What characterizes an organoid is that it performs certain functions specific to the organ concerned.

 Organoids self-organize, spontaneously, which is not the case of bioengineering products that use a biocompatible synthetic matrix (scaffold), which can be natural or artificial. However, the two approaches have been known to be used simultaneously. 8 Self-organization is often stimulated by forces setting the organoid in motion and by air-media interface or culture media conditions. 3D printing is a technological tool used to create biological models and nothing more. It can also be used to create organoids.  The part does not have the same properties and functions as the whole; thus an organoid does not have the same properties and functions as the organ as a whole, a cell does not have the same properties and functions as the tissue or the organ of which it is a part. It is therefore incorrect to refer to organoids as miniorgans. In particular, it is inappropriate to refer to organoids derived from brain cells as "mini-brains"; we will avoid this expression in favor of "cerebroids".

 Some authors consider that organoids fall within the scope of synthetic biology because they manifest spontaneous organization.I It does not seem judicious to us to consider them thus, synthetic biology being often associated with attempts to create artificial living organisms, like Craig Venter's Mycoplasma. 9 The project to develop human quasi-organs in vitro is nothing new. Since the beginning of the 20th century, researchers have sought to imitate organogenesis in culture 10 and it is generally believed that the history of organoids dates back to the 1970s when Howard Greene and his colleagues demonstrated that it was possible to cultivate epidermis-like associations of human keratinocytes and fibroblasts in vitro. 11 According to some authors, the organoid construction technique is even older. Jamie Davis considers it contemporary with the work of Wilson who, as early as 1910, showed that sponge cells could be dissociated and randomly reaggregated to rebuild a viable organism. 1 2 This experiment is important because it shows that cells isolated from an adult organism contain sufficient information to specify a multicellular structure, unaided by external instructions or anatomical structures related to their embryological history, even though we cannot extend it to organs isolated from vertebrates, such as the liver or the brain. This hypothesis and basic method of disaggregation and reaggregation have been used by researchers since the 1950s.

The state of research on organoids

Organoids are research tools; they do not as yet have a therapeutic application, although some are envisaged for the future. We will illustrate their role by presenting some examples of projects conducted by Inserm researchers who were interviewed by the Working Group. Olivier Goureau's team (U968, Vision Institute, Paris) is interested in the production of retinal cells from human pluripotent stem cells for transplantation strategies and to model certain degenerative retinal diseases. Retinal organoids are very useful here because rodents do not present all the characteristics of a human eye. These experiments on organoids should minimize the use of animal models for testing purposes. It is important to stress that while organoids are useful for studying diseases of genetic origin -which they can mimic -they are not always useful for analyzing phenotypic phenomena, making them of limited value in understanding the mechanisms of a multifactorial disease such as age-related macular degeneration (AMD). The case of the retina is interesting for another reason: in order to treat blindness, three promising and alternative technologies are likely to be available: gene therapy, microchip implants and organoid cell transplantation. How will we choose?

The project coordinated by Jean-Charles Duclos-Vallée (U1193 Inserm Paris-Saclay University) is aimed at bioconstructing a transplantable liver from human induced pluripotent stem (iPS) cells. The liver is constructed in blocks, which involves producing organoids and connecting them to the biliary and vascular trees.

The potential utility of organoids is primarily clinical, to avoid transplantation from donors and thus compensate for the shortage of grafts. It is also envisaged to develop a functional extracorporeal purification system with a bioreactor that includes liver cells, which will make it possible to temporarily take over a patient's liver functions -as is already the case with the kidneys 13 -as well as construct a liver on-a-chip to study predictive toxicology.Isabelle Sermet-Gaudelus' team (Inserm U1151 -Institut Necker-Enfants Malades (INEM)) deals with respiratory diseases, including cystic fibrosis. They have become interested in the use of organoids to evaluate innovative therapies for this disease. Indeed, the CFTR protein implicated in this pathology is also present in the intestinal epithelium, and changes in the 13 Unlike the kidney, the liver performs enzymatic activities essential for the assimilation of nutrients and the detoxification of xenobiotics, as well as synthesis functions (albumin, coagulation factors, enzymes, etc.) essential for the body to function properly.

protein's activity can be detected in this tissue. Using biopsies, intestinal spheroidssimple 3D cultures that are inaccurately referred to as "organoids" -have been created in the Netherlands to test correction of the CFTR protein function, which should make it possible to avoid prescribing ineffective molecules with potentially serious side effects. However, it has not yet been well established whether these "organoids" are a good model for diagnosis and the evaluation of therapies despite current enthusiasm. Other models derived from respiratory cells can be envisaged.

These three examples therefore concern the in vitro production of structures that mimic certain organ functionalities. Also, the teams all emphasize that the lack of vascularization and/or innervation of these in vitro-produced models is a limitation that can present serious problems. That is why there have been implantation attempts in animal organs 14 or other biological media, such as lymph nodes; 15 some teams are still working on how to generate vascular networks in vitro (real vessels or artificial oxygenation network by microfluidic system). This illustrates the fact that organoids do not contain all the cell types or certain structures (blood vessels, in particular) necessary for the functioning of an organ observable in situ, but only some of them.

 Organoids are research tools that do not yet have a therapeutic application.  It has not yet been well established that organoids are a good model for all diagnosis and the evaluation of therapies.

 The absence of vascularization and/or innervation is a limitation of these in vitro-produced models.

Ethical issues raised by the use of organoids

A review of the state of research has already raised certain ethical issues: the shortage of grafts for transplantation, the use of animals in research, the allocation of resources in terms of both individual treatment -which therapy to choose in case of blindness? -and the direction of research: not to invest the limited financial resources available in unpromising avenues, even if they are "fashionable". But there are many others. Most of them are not new, however they are an opportunity to bring back to the profession questions that are not only related to the use of organoids but remain open and require ongoing reflection. Here are the main ones which can be seen to concern many fields, such as clinical ethics, institutional ethics and even anthropology: 1. The evaluation of risks, benefits, and safety. The most frequently mentioned benefits of organoids research are: a better understanding of human diseases thanks to the use of human tissue, the possibility to test drugs on a model close to the human organism in real life and, eventually, the ability to repair defective organs 16 -including in the case of brain lesions. Toxicology, pharmacology, and cell therapy are therefore also concerned.Since organoids are often derived from iPS cells, the consent of the donors of the original cells must be obtained -this is also a regulatory requirement. The production of certain organoids could raise some reticence (genital tract, brain) and raises the question of the degree of consent and information given to the donors. It also raises the question of the ownership of the resulting organoids, which can also be sources of profit, as well as their patentability; [START_REF] Bredenoord | Human Tissues in a Dish: The Research and Ethical Implications of Organoid Technology[END_REF] in short, the question of who will benefit from the use of organoids must be asked, as well as the nature of these benefits (financial, therapeutic, etc.). [START_REF] Boers | Organoids as Hybrids: Ethical Implications for the Exchange of Human Tissues[END_REF] The genetic analysis of organoids also raises a major issue of health data protection, particularly genetic data, which must be taken into account at the consent stage, although it is not easy to say how.The ideology of promise: organoids are presented as the source of multiple therapeutic advances. But is this actually the case? Indeed, there seems to be little ethical justification for holding out the prospect of speculative and random benefits. The question here is to ensure the biological and then medical relevance, in order to avoid building an ideology of promise from in vitro findings that have been extrapolated too quickly.

2. The moral status of organoids. [START_REF]Ethical Issues[END_REF] This status concerns organoids either in the sense that they could be regarded as individuals (which could concern gastruloids), or to the extent that they possess properties relevant to the attribution of moral status, such as sentience (which could concern cerebroids). This question of status also arises in the relationship between organoids and their donors, whose cells are the source of organisms with a certain degree of autonomy. However, there have been no studies so far on the value that donors attribute to "their" organoids [START_REF] Bredenoord | Human Tissues in a Dish[END_REF] and we must ask ourselves, especially with regard to brain organoids and gastruloids, how cell donors will perceive the fate of these isolated cells that lead, so to speak, a life of their own -this should also be taken into account when collecting consent. The nature of consciousness and sentience: brain organoids are constructed; could such entities feel pain, or even possess some form of consciousness? If so, their moral status should be assessed accordingly.

3. Insofar as organoids could be obtained by 3D printing, the process would imply a certain artificialization of the living; however, for some people, the distinction between natural and artificial has a moral value. What does "creating living entities" mean in this context? This question is a striking illustration of the paradigm shift that has taken place since living entities have been conceived as a set of parts to be assembled.

The creation of chimeras by xenotransplantation:

to ensure the vascularization and innervation of organoids, the latter can be transplanted into animals -including human cerebroids into the brains of adult animals. 21 Chimeric organoids can also be created, but this is not necessarily relevant to understanding biological mechanisms in humans. It will no doubt also be possible to pair organoids with computers or robots, 22 just like what has already been done with neurons or in the project to build an artificial retina.Animal ethics. Organoids enable the development of alternative methods that are used upstream of or in parallel to animal testing. This represents a potentially substantial contribution to the 3Rs. 2 3 Fewer animals will be used, for example, to test the efficacy of new drugs, since some of this testing can be done on organoids. This is also valid for toxicologyespecially since many drugs on the market reveal hepatotoxicity that does not show up in animals, as André Guillouzo points out. Insofar as organoids can be used in organ transplantation, animals will also benefit, since the project to breed genetically modified animals for the purpose of transplanting their organs into humans (the project to develop xenotransplantation) could be abandoned. 24 , "Human Tissues in a Dish", p. 2. The 3Rs are: refine, reduce and replace. This means that animal research must strive to reduce the stress on the animals (refine), reduce the number of animals used and, if possible, replace the use of animals with other methods. 24 J. Loike and R. Pollack, "Develop Organoids, not Chimeras, for Transplantation", The Scientist, August 23, 2019,https://www.the-scientist.com/news-opinion/opinion--develop-organoids--notchimeras--for-transplantation-66339 .

interesting to note that the term "sacrifice" is sometimes used for organoids after they have been used in an experiment, just as it is for animals.

As can be seen from this list, the ethical issues can be grouped under the following two headings:

A. What norms and rules should be applied when researchers work on organoids?

B. What is the moral status of organoids?

The first directly concerns our behavior as moral agents, while the second relates to the nature of moral patients. A moral patient is a being towards which moral agents have moral obligations; 25 the question then is whether or not organoids are moral patients (organs are not moral patients, but just objects or things). This issue is raised for cerebroids, as we have just seen, and gastruloids.These questions relating to the ethical rules and statuses applicable to organoids could be usefully clarified and supplemented by the legal questions that accompany them. At this stage, there are no legal norms governing them and it may be difficult to determine with certainty who is the owner or custodian of this biological element obtained from a culture of human body products and to which legal category they belong: that of tissues and cells, that of organs, that of gametes in the case of ovarian organoids, etc.? This exercise, which is necessary in order to identify the rules applicable to the sample (from a living or deceased person), to the consent of the initial donor, and to the use that can be made of it, is all the more difficult since our norms do not precisely define the concepts that already exist. There is, for example, no legal definition of the organ.

The elements collected within this Memo will make it possible to enrich these legal reflections, which will undoubtedly emerge.

In this Memo, we are essentially limiting our reflection to the issue of consciousness, which specifically concerns the cerebral organoids, on which one of our interviewees, Frank Yates, a teacher-researcher at Sup'Biotech, is working with the aim of better understanding degenerative diseases (ethical issue no. 4). But first, we would like to say a few words about the paradigm shift mentioned above (ethical issue no. 6) and the ideology of promise (ethical issue no. 3), which concerns all research conducted on organoids -and even well beyond that -as it is linked to the transition to the clinical setting.

25 T. Regan, "The Case for Animal Rights", London, Routledge, 1983, p. 151-156.

A paradigm shift

Life, or more precisely being living, this property that characterizes certain natural beings manifesting self-organization, autonomy, ability to react, reproduction, evolution, and metabolism, 26 has long been considered as something

given. Biotechnology has made it a construction, even a creation. As regards the embryo, for example, "this was commodified at the early stages of development and has become a quasi-object to be manufactured, tested, deconstructed into biobricks from which to derive the totipotent cells that have changed not just reproductive biology but the relationship to the individual body". 27 We observe the transition from a natural order to an artificial one, namely an engineering of the living state, which is morally problematic for some in that it denotes an inappropriate attitude on our part. Thus, says Jürgen Habermas: "My particular concern is with the question of how the biotechnological dedifferentiation of the habitual distinction between the 'grown' and the 'made', the subjective and the objective, may change our ethical self-understanding as members of the species" 28 and Mark Hunyadi specifies: "The frontier between the natural and the artificial

[…] offered a solid grammar to our spontaneous understanding of the world. But if life itself becomes an artifact [...] then a frontier hitherto taken to be fixed is crossed, producing instability, creating uncertainty". 29 Beyond the ethics, biotechnologies and philosophy of life that they convey 30 raise anthropological questions: what conception of ourselves and humanity do they raise and imply? 31  What moral value should be given to living entities conceived as sets of parts to be assembled?  We observe the transition from a natural order to an artificial one, namely an engineering of the living state, which is morally problematic for some in that it denotes an inappropriate attitude on our part.  Currently, there are no legal norms governing organoids that would allow, among other things, to determine with certainty who is the "owner" or "custodian" of this biological element.

The ideology of promise

We have seen that although organoids are essentially a research tool at present, certain therapeutic applications are envisaged. For example, the bioconstruction of liver tissue for liver purification, the restoration of retinal function, the provision of rapid tests for cystic fibrosis treatment and, more generally, the repair of various types of organs and the availability of large numbers of histocompatible grafts. What should we think of the therapeutic prospects related to organoids, as well as the promises and hopes they raise? How can we move from an ideology of promise to an ethic of promise?

The language used by scientific research, for structural reasons of funding, is unfortunately becoming increasingly narrative and utopian, contrary to its epistemological and hypothetical approach that must be prudent. Science must guarantee a critical approach with the exercise of vigilant control over its own prospective advances, pledging not to promise anything that cannot be confirmed.

For this, a broader approach is needed, which encompasses the human and social sciences, and promotes an open dialogue between science and civil society.

The ideology of promise is also fueled by patients: their demand is very strong, and even if it concerns research for the time being, it is not always easy to convey this when communicating with the public. Likewise, clinical trial subjects, when they suffer from the disease to which the research relates, tend to harbor hopes that are not justified by the trial methodology: this is referred to as therapeutic misconception. 32

 Science must guarantee a critical approach with the exercise of vigilant control over its own prospective advances, pledging not to promise anything that cannot be confirmed.

Cerebroids and consciousness

A cerebroid is a 4 mm-diameter globule of which some of the developmental aspects, the electrical activity of neural networks in particular, appear similar to those of the brain of a 19 to 24-week-old fetus. 33 Anatomically, we know that many animals possess nociceptors, 36 but we do not know the nature of the relationship between nociception and feeling -except in humans, for whom we have a decisive element of aid to understanding: language.

However, since animals have a set of physical manifestations typical of pain in humans (frozen posture, cries, raised hairs, sweating, etc.), while we do not know their feelings, we can by analogy detect their suffering. 36 Animals and humans have nociceptors, which allow them to detect and respond to any stimulation that could be dangerous for them. Nociception does not need the brain (the spinal cord reflexes are sufficient) and can exist without pain (pain can also exist without nociception, as in fibromyalgia).

In the case of consciousness, we encounter the same difficulty. There is also a semantic obstacle: "consciousness" has many meanings. In particular, its use by psychologists and physicians is not at all the same. Among the former, it is generally the clarifications proposed by Ned Block that are referred to. This author distinguishes four meanings of the word: phenomenal consciousness, access consciousness, self-consciousness, and monitoring consciousness. [START_REF] Block | Some Concepts of Consciousness[END_REF] Phenomenal consciousness consists in the subjective experience of what happens to us and of what we do, in short, in feeling -it is therefore present in the experience of pain -;

access consciousness includes all the representations we have, such as our thoughts or desires, representations that can be used by our executive system (decisions, actions, etc.); self-consciousness designates the representation we make of ourselves and monitoring consciousness is the reflexive consciousness, i.e. this second ordercapacity of being able to examine what is happening in our mind.

Neurologists use a different classification when talking about states of consciousness in coma patients. As Éric Racine points out:

It is important to understand that the clinical approach to consciousness as a neurological concept is different. [...] Clinical approaches to consciousness typically consider it a two-fold concept defined by wakefulness and awareness. First, wakefulness is basically equated to arousal; wakefulness consists of mechanisms that keep 'the patient awake and which relates to the physical manifestations of awakening from sleep'. Second, awareness refers to 'the content of consciousness or the awareness of self and environment', including psychological functions such as emotions, thoughts and sensory experience." [START_REF]Pragmatic Neuroethics[END_REF] Another tradition, also prevalent among neuroscientists, is inspired by William James. The taxonomy of consciousness thus remains a complex and debated subject; 39 therefore, the question of whether organoids are conscious presents as vague and, in the end, poorly-formulated. Hervé Chneiweiss pertinently states that: "The fundamental question actually lies in our vocabulary. What do we mean by the terms 'emotion' and 'consciousness'?" [START_REF]Des cerveaux libres et heureux[END_REF] The part and the whole What then of the assertion that cerebroids could possess some form of consciousness or sentience, in short, something like a mental life? Many authors consider the question seriously and mention the study that revealed electrical activity in cerebroids similar to that seen in the brains of fetuses at 19-24 weeks. 43 On a very general level, it cannot be ruled out that an entity made up of neurons possesses mental states, given the existence of relationships of correlation and even causality between the mind and the brain. During the course of evolution, consciousness gradually emerged, when there was a nervous system capable of supporting it. The same is true in the history of each of us: an embryo does not think, a child does. 44 Whatever metaphysical position we adopt, monistic or dualistic, materialistic or spiritualist, we must agree on the existence of these causal relationships, which also mean that a brain that is too damaged becomes incapable of thought and consciousness. 45 Thus, the hypothesis that cerebroids might experience pain is a thought experiment, based on the idea of the emergence of consciousness: if pain is a brain activity, future and complex organoids could hypothetically experience it (function emerges from structure).

However, we cannot draw any major conclusions from this general observation, for we must be careful to bear in mind that electrical activity as such cannot be equivalent to consciousness or sentience. More fundamentally, it seems very problematic to attribute the properties of a whole to its parts. This is already the case of the organs themselves: if we want to be precise, we must say that an The same is especially true of cerebroids, particularly since many of them only replicate a particular region of the brain, and not the brain in its entirety; [START_REF]Transplantation of Human Brain Organoids[END_REF] for instance, only two types of cells are found: neurons and astrocytes. But even with regard to whole brain organoids, it should be pointed out that it is not just because their volume is only 1/1'000 of a mouse brain and 1/1'000'000 of that of a human being, or that they have no mature neural networks and so are unable to interact with their environment 47 that they do not possess consciousness, but because they are not functioning organs within an organism. Thus, if it is true that "no one knows how many neurons it would take for a distinctively human thought to emerge", 4 8 it is because the question does not make sense.

Consequently and more precisely, it is very important, in the case of cerebroids, to distinguish between organization, activity and function. Current data show that cerebroids acquire an activity and it is not impossible that, as we gain knowledge, we would be able to create more complex organizations, such as a circuit between two organoids -some teams are currently developing fused organoids, also referred to as "assembloids". 4 9 This should not be enough to create a function. This observation is enlightening when we draw a parallel with the brain activity of people in a state of coma or minimal consciousness. These patients maintain brain activity (otherwise they would be declared dead) and yet certain lesions mean that they can never regain consciousness, understood here as the ability of an awake person to say "I".

The search for reliable markers indicating the presence or absence of consciousness is an open problem, as is the reliability of the detection mechanisms used. [START_REF] Sawai | The Ethics of Cerebral Organoids Research[END_REF] A recent contribution by Lionel Naccache and his colleagues at Pitié-Salpêtrière Hospital sheds particular light on this question and by analogy on the issue of "conscious cerebroids", suggesting that there are not two states of our brain, conscious and unconscious, but different degrees of consciousness -in the sense that neurologists understand this term. [START_REF] Demertzi | Human consciousness is supported by dynamic complex patterns of brain signal coordination[END_REF] This research is based on analysis of the functional activity that allows us to associate different regions of our brain.

According to their hypothesis, in contrast to static descriptions of brain function, consciousness relates to a dynamic process: a "consciousness network". They compared healthy individuals and patients suffering from disorders of consciousness (coma, vegetative state, minimally conscious state). They looked for a pattern in which they could recognize brain regions that activate together and those that function in opposition, one activating when the other switches off. They then observed that the brains of patients in an altered state of consciousness showed a pattern of low coherence between the different brain regions: those that should have activated together no longer did so and those that should have activated when others switched off did not do so either. The alteration of consciousness thus seems to be marked not by inactivity of brain regions but by the loss of ability to be active together. These findings show that consciousness is based on the brain's ability to maintain coherent dynamics and that it is the coherence of the interactions between the regions of our brain that supports our presence in the world, their specific synchronization enabling us to be conscious. It would take time before researchers are able to reconstruct a brain that is capable of all this, but success is not inconceivable.

The situation may be different when cerebroids are transplanted into the brains of animals, such as rats or pigs, which have mental states. [START_REF] Yeager | As Brain Organoids Mature[END_REF] Their chimeric brain is then an organ functioning within an organism. It has already been observed that this transplantation normalizes the expression of the genes of neurons, which is altered in in vitro cerebral organoids. 5 3 What will be the moral status of these "humanized" animals, i.e. these chimeras? At first glance, there are no answers to this question. Here we are confronted with a problem that we had raised in the Memo on EMSUs: these chimeras will have to be human enough to be used as a research model and then, if all goes well, in therapy, but not human enough to fall under the protection that belongs to human beings. [START_REF] Mcfarling | Near the Campus Cow Pasture, a Scientist Works to Grow Human Organs -in Pigs[END_REF] Nevertheless, we can already propose some elements of an answer. As Isaac

Chen and his colleagues have shown, it is not plausible to think that a rat brain, which has a number of cells equivalent to just 0.5% of the human brain, can replicate human brain architecture, even if most of its cells were of human origin.

For larger animals, such as pigs and primates, the same authors suggest the use of behavioral tests such as the mirror test. 5 5 Even if the relevance of this test as a measure of self-awareness is disputed, we can see that we will not be without means to approach the question of the moral status of animals with a chimeric brain when the question arises concretely.



The possession of characteristics such as sentience or consciousness is decisive in defining the moral status of cerebroids as that of any individual.



The meaning given to the terms "emotion" and "consciousness" is essential for understanding the moral status of cerebroids.  While electrical activity in itself cannot be equivalent to consciousness or sentience, it cannot be ruled out that an entity made up of neurons has mental states since there are correlation and even causal relationships between the mind and the brain.



Consciousness relates to a "network of consciousness" that is thought to be based on the brain's ability to maintain coherent dynamics. Thus it is the synchronization and coherence of the interactions between brain regions, a condition not currently met by in vitro cerebroids, which allows us to be conscious.



The identification of the means available making it possible to approach the question of the moral status of animals into which human cerebroids will be transplanted must be considered in concrete terms.

  14. M. Munsie & al., "Ethical Issues in Human Organoids and Gastruloid Research", The Company of Biologists, 2017, vol. 144, p. 942. 15. M. Francipane and E. Lagasse, "Maturation of Embryonic Tissues in a Lymph Node: a New Approach for Bioengineering Complex Organs", Organogenesis, 2014, vol. 10/3, p. 323-331.

  3. G. Rossi & al., "Progress and Potential in Organoid Research", Nature Reviews, 2018, vol. 19, p. 671.

  While official terminology refers to the killing of animals following a research protocol, it is

	21 A. Lavazza and M. Massimini, "Cerebral Organoids: Ethical Issues and Consciousness Assessment", Journal of Medical Ethics, 2018, vol. 44/9, p. 608 and A. Yeager, "As Brain Organoids Mature, Ethical Questions Arise", The Scientist, August 1, 2018, https://www.the-scientist.com/features/brain-organoids-mature--raise-ethical-questions-64533 .
	22 A. Lavazza, "What (or Sometimes Who) Are Organoids? And Whose Are They? ", Journal of Medical Ethics, 2019, vol. 45/2, p. 144.
	23 Bredenoord & al.

  diseases such as autism, epilepsy, trisomy 21 or Fragile X syndrome,34 as well as some types of cancer. 3 5 It is also used to evaluate the toxicity and pharmacological effect of new drugs. The idea that cerebroids, or at least those among them that mimic to some extent the functioning of the brain as an organ, might experience pain or possess some form of consciousness is often raised in the literature. Certainly, the use of the term "mini-brains" contributes to this; however, correcting our vocabulary is not enough for the query to disappear.If this possibility makes us stop and think, it is because the possession of characteristics, such as sentience (the ability to feel pleasure and pain) and consciousness are decisive for the question of moral status: a sentient or conscious being is a moral patient and not a thing. As far as humans are concerned, pain is defined by the International

It is very useful for studying 32 P. McConville, "Presuming Patient Autonomy in the Face of Therapeutic Misconception", Bioethics, 2017, vol. 31, p. 711. 33 Lavazza and Massimini, "Cerebral Organoids", p. 607. See also S. Reardon, "Mini-Brains Show Human-Like Activity", Nature, 2018, vol. 563, p. 453 and A. Olena, "Human Cortical Organoids Model Neuronal Networks", The Scientist, August 28, 2019, https://www.the-scientist.com/news-neurodevelopmental Association for the Study of Pain (IASP) as an "unpleasant sensory and emotional

experience associated with, or resembling that associated with, actual or potential tissue damage". It is notoriously difficult to say whether or not a non-human organism possesses sentience and consciousness. In the case of the former, this has long been known, especially in debates on the status of animals. Sentience is in fact a private phenomenon, which cannot be observed from the outside: all that we see and can see are physiological behaviors and reactions, which is sometimes possible to correlate with anatomical particularities, but they do not tell us anything certain about the psychological states that accompany them, or even if they are accompanied by mental phenomena.

  Some neuroscientists work with Ned Block's distinctions when they have ethical questions, 4 1 but they remain the exception. Perhaps we should not use this expression and refer to "mental states" instead? It is not obvious that the discussion is becoming clearer, because on this point too, the debates are not closed: what is a mental state and what are its properties? For example, since Sigmund Freud at least -he echoes this in his book

	Metapsychology -there has been a dispute as to whether unconscious mental states
	exist or whether they are by definition conscious, thus to be distinguished from
	most cerebral states. 42

  42 S. Freud, Métapsychologie, Paris, Gallimard, 1940. 43 The analogy was revealed by an algorithm, the reliability of which has however been called into question by some authors (H. I. Chen & al., "Transplantation of Human Brain Organoids: Revisiting the Science and Ethics of Brain Chimeras", Cell Stem Cell, 2019, vol. 25, p. 464).44 This is a banal observation and not the assertion that ontogeny recapitulates phylogeny. 45 A causal relationship between two events does not imply that they are of different or the same nature; thus the fact that the mind and the brain interact causally is compatible with their identity. See J. Searle, Minds, Brains and Science, British Broadcasting Corporation, 1984, chap. 1. isolated organ, outside the body, has no function. It is certainly possible to detect functioning in such an organ and study its mechanisms but this does not constitute a true function. For example, the beats of an isolated perfused heart are produced by the electrical and mechanical activity of the cardiac muscle, but this organ only functions as a pump ensuring blood circulation when in relation with the rest of the body. The same is true at the other levels of organization of this organism. At the biochemical level, the oxidation of hemoglobin into oxyhemoglobin by means of the iron present in the molecule ensures the oxygenation function of the tissues only when it takes place in the organism in relation to the other organs. Thus, if we maintain the same rigor, we would say that a brain cannot think, because thinking is a function of the organism as such, when it is situated in an environment that provides it with stimuli through receptors. A brain cannot be conscious of anything, nor can it have the slightest sentience that can be translated at the psychic level.

We shall see in the last section of this Memo that referring to "function" is not, strictly speaking, correct and that it is preferable to use "functioning" or "activity".

Rossi & al., Ibid., p.

and J. Akst, "Tumor Organoids Hold Promise for Personalizing Cancer Therapy", The Scientist, June 15, 2019, https://www.the-scientist.com/notebook/tumor-organoidshold-promise-for-personalizing-cancer-therapy-66093. 6 M. Simian and M. Bissell, "Organoids: A Historical Perspective of Thinking in Three Dimensions", Journal of Cell Biology, 2016, vol. 216/1, p. 31. 7 See also the document by the "Organoids" Research Group of Aviesan's Health Technologies Multi-Organization Thematic Institute, which presents an ontology of organoids. 8 Rossi & al., "Progress and Potential", p. 683.

We often talk about "regenerative medicine", but this expression is erroneous in that it is about repairing defective organs, not regenerating them like a salamander would regrow a limb.


Gil Farkash

Jean-Nicolas Dumez

Lucio Frydman
email: lucio.frydman@weizmann.ac.il

Sculpting 3D Spatial Selectivity with Pairs of 2D Pulses: A Comparison of Methods

Keywords: 3D RF pulses, Spatiotemporal excitation, field inhomogeneities, In Vivo MRS Robust 3D shaping based on spatiotemporal encoding EPI, echo-planar imaging, FFT, Fast Fourier transform, MRI, magnetic resonance imaging, MRS, magnetic resonance spectroscopy, MRSI, magnetic resonance spectroscopic imaging, NMR, nuclear magnetic resonance, PE, phase encoding, RF, radio-frequency, RO, readout, ROI, region of interest, SPEN, spatiotemporal encoding

Enhancing the specificity of the spins' excitation can improve the capabilities of magnetic resonance. Exciting voxels with tailored 3D shapes reduces partial volume effects and enhances contrast, particularly in cases where cubic voxels or other simple geometries do not provide an optimal localization. Spatial excitation profiles of arbitrary shapes can be implemented using so-called multidimensional RF pulses, which are often limited in practice to 2D implementations owing to their sensitivity to field inhomogeneities. Recent work has shown the potential of spatio-temporally encoded (SPEN) pulses towards alleviating these constraints. In particular, 2D pulses operating in a so-called hybrid scheme where the "low-bandwidth" spatial dimension is sculpted by a SPEN strategy while an orthogonal axis is shaped by regular k-space encoding, have been shown resilient to chemical shift and B0 field inhomogeneities. In this work we explore the use of pairs of 2D pulses, with one of these addressing geometries in the x-y plane and the other in the x-z dimension, to sculpt complex 3D volumes in phantoms and in vivo. To overcome limitations caused by the RF discretization demanded by these 2D pulses, a number of "unfolding" techniques yielding images from the centerband RF excitation while deleting sideband contributions -even in cases where center-and side-bands severely overlap-were developed. Thus it was possible to increase the gradient strengths applied along the low bandwidth dimensions, significantly improving the robustness of this kind of 3D sculpting pulses. Comparisons against conventional pulses designed on the basis of pure k-space trajectories, are presented.

Introduction

Achieving accurate excitation selectivity of complex 3D volumes can be an important aid in magnetic resonance spectroscopy (MRS), imaging (MRI) and spectroscopic imaging (MRSI) studies. By improving localization, voxels with arbitrary 3D shapes enable spectral measurements of organs or tissues with higher specificity [START_REF] Weber-Fahr | Short-echo-time magnetic resonance spectroscopy of single voxel with arbitrary shape in the living human brain using segmented twodimensional selective radiofrequency excitations based on a blipped-planar trajectory[END_REF][START_REF] Snyder | Three-dimensional arbitrary voxel shapes in spectroscopy with submillisecond TEs[END_REF], as well as improved estimations of relaxation rates [START_REF] Qin | Quantitative T2 measurement of a single voxel with arbitrary shape using pinwheel excitation and CPMG acquisition[END_REF], diffusion coefficients [START_REF] Partridge | Diffusion-weighted MRI: influence of intravoxel fat signal and breast density on breast tumor conspicuity and apparent diffusion coefficient measurements[END_REF] or chemical concentrations [START_REF] Christiansen | In Vivo Quantification of Brain Metabolites by 1H-MRS Using Water as an Internal Standard[END_REF][START_REF] Mekle | MR Spectroscopy of the Human Brain With Enhanced Signal Intensity at Ultrashort Echo Times on a Clinical Platform at 3T and 7T[END_REF]. Most localized studies rely on either selective excitation [START_REF] Bottomley | Spatial Localization in NMR Spectroscopy in Vivo[END_REF] or outer volume suppression [START_REF] Mlynarik | Localized Short-Echo-Time Proton MR Spectroscopy With Full Signal-Intensity Acquisition[END_REF]. Both radiofrequency (RF) manipulations usually sculpt a single spatial axis at a time, thereby defining relatively simple shapes. More finely-tuned volumes and shapes can be excited by relying on so-called multidimensional RF pulses [START_REF] Qin | 2D Arbitrary Shape-Selective Excitation Summed Spectroscopy (ASSESS)[END_REF][START_REF] Bottomley | Two-dimensional spatially selective spin inversion and spinecho refocusing with a single nuclear-magnetic-resonance pulse[END_REF][START_REF] Rieseberg | Two-Dimensional Spatially Selective RF Excitation Pulses in Echo-Planar Imaging[END_REF]. Initially developed on the basis of single-shot k-space scanning ideas associated with Echo Planar Imaging (EPI), such strategies are commonly used for achieving 2D spatial/spatial and 2D spatial/spectral selectivity. Volume selectivity with k-based 3D RF pulses has also been reported in ex-and in vivo studies [START_REF] Saekho | Small Tip Angle Three-Dimensional Tailored Radiofrequency Slab-Select Pulse for Reduced B1 Inhomogeneity at 3 T[END_REF][START_REF] Yip | Advanced Three-Dimensional Tailored RF Pulse for Signal Recovery in T2*-Weighted Functional Magnetic Resonance Imaging[END_REF]. These 3D RF pulses, however, are usually long, which makes them highly sensitive to chemical shift offsets and B0 field inhomogeneities. Parallel transmission techniques that shorten these pulses, are therefore necessary for sculpting even simple 3D shapes [START_REF] Snyder | Three-dimensional arbitrary voxel shapes in spectroscopy with submillisecond TEs[END_REF][START_REF] Schneider | Inner-Volume Imaging In Vivo Using Three-Dimensional Parallel Spatially Selective Excitation[END_REF]. Still, as parallel transmission can be of limited availability or constrained by specific absorption rates (SAR) [START_REF] Zelinski | Specific Absorption Rate Studies of the Parallel Transmission of Inner-Volume Excitations at 7T[END_REF], exciting complex 3D shapes remains an important open challenge in in vivo MR. This work explores a number of strategies to target complex shaped volumes, based on concatenating pairs of 2D RF pulses. Our attention is focused on alternatives to k-based methods that use 2D spatiotemporally encoded (SPEN) pulses. SPEN progressively combines the spins' time evolution with their position along a spatial dimension. While initially devised for acquiring multidimensional NMR and MRI data in a single scan [START_REF] Ben-Eliezer | High-definition single-scan 2D MRI in inhomogeneous fields using spatial encoding methods[END_REF][START_REF] Tal | Single-scan multidimensional magnetic resonance[END_REF][START_REF] Frydman | Principles and Features of Single-Scan Two-Dimensional NMR Spectroscopy[END_REF][START_REF] Shrot | Spatially-Encoded NMR and the Acquisition of 2D Magnetic Resonance Images Within a Single Scan[END_REF][START_REF] Frydman | The Acquisition of Multidimensional NMR Spectra Within a Single Scan[END_REF][START_REF] Chamberlain | RASER: A new ultrafast magnetic resonance imaging method[END_REF], recent work has shown SPEN's potential for selective 2D excitations. Compared to their k-based counterparts 2D SPEN pulses can have, under the right conditions, an enhanced robustness vis-à-vis field heterogeneities and chemical shifts [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF]. Besides their use to selectively excite 2D shapes of arbitrary form, such pulses have also been used to impart arbitrary phases that will compensate for 3D inhomogeneities [START_REF] Snyder | MRI by Steering Resonance Through Space[END_REF][START_REF] Tal | Spatial encoding and the single-scan acquisition of high definition MR images in inhomogeneous fields[END_REF].

Multidimensional RF pulses are usually executed as nested loops, where "fast" spatial excitations are looped within a progressive, slower sculpting. This approach is associated with two features that may limit their applicability. One relates to the discreteness of the "slow" axis sculpting: acting somewhat like a DANTE pulse [START_REF] Morris | Selective excitation in Fourier-transform nuclear magneticresonance[END_REF][START_REF] Freeman | Spin choreography: basic steps in high resolution NMR[END_REF], its gapped nature may result in undesired excitation replicates. The other relates to the duration of this "slow" axis sculpting, which makes it sensitive to chemical shift misregistrations and B0 inhomogeneity distortions. It was recently shown that, by addressing spins sequentially via the combined action of magnetic field gradients and frequency-swept pulses, SPEN can alleviate both of these constraints [START_REF] Ben-Eliezer | High-definition single-scan 2D MRI in inhomogeneous fields using spatial encoding methods[END_REF]. 2D pulses exploit this by performing a SPEN-based sculpting along the "slow" axis, while retaining the regular Fourier encoding -which is less susceptible to distortions due to its higher associated gradients-along the orthogonal direction. Given the good results observed with this approach [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF], the question arose whether this robustness could suffice to enable arbitrary 3D excitations.

As an initial step in this direction, this study explores the sculpting of 3D shapes by the concatenation of 2D pulses, possessing one spatial axis in common. Our proposals involved pairing either SPEN-or kbased 2D pulses, including an excitation/refocusing pair, or two refocusing 2D pulses transmitted after a pulse has excited one or more chemical sites in the sample (Figs. 1a,1b). As spins outside the arbitrary planar patterns excited/inverted by these pulses can be crushed by appropriate gradients, complex 3D patterns at the intersection of these 2D shapes will be selected. While the 3D selectivity of this scheme for SPEN-and for k-based pulses was comparable in simulated scenarios, the SPEN-based design performed consistently better in ex vivo and in vivo tests and experiments. The reasons for this, as well as further options to improve the robustness and expand the flexibility of this approach, are discussed.

Theoretical Background

Before explaining their use in sculpting 3D shapes, it is convenient to briefly review the SPENbased RF pulses used in our experiments. As the x-axis was chosen to be the "slow" dimension of the 2D pulses (Fig. 1) we shall assume that, following excitation, a frequency-swept refocusing pulse of duration T180 is applied in the presence of a gradient G !"# x #. Spins will then accrue a phase [START_REF] Tal | Single-scan multidimensional magnetic resonance[END_REF] φ !"# (x) = (-

(%& !"# ) $ ( !"# * x ) + ,γG !"# (T !"# + )*+ %,!"# ,-. ( !"# */ x + 0ΩT !"# - *+ %,!"# ,-. $ ( !"# 2 (1)
where W is a site-specific frequency offset associated to chemical shift or field inhomogeneity effects, O /,!"# is the initial frequency for the RF sweep, R !"# is the RF sweep rate and x denotes the spin's spatial position, as determined by the swept pulse and by the encoding gradient 𝐺 !"# 𝑥 #. 2D SPEN-based pulses harness this point-by-point manipulation by breaking it into a train of discrete gradient blips, and inserting in-between these blips RF pulses acting while activating a second, orthogonal y-axis gradient.

The shape of these pulses is then tailored so as to perform a selective spins' excitation/inversion along such an orthogonal axis. The phases of these RF pulses are modulated with a quadratic time-dependence

φ 12 (t) = O /,!"# t + ( !"# 3 $
) + φ # akin to that associated with the frequency sweep leading to Eq. 1, where φ # is an arbitrary initial phase, and the G !"# 𝑥 # gradient is now blipped so as to apply integrated areas of

∆k !"# = %& !"# 4 !"# 5 !"#
per blip, where N !"# is the number of intervening sub-pulses. The main result of this combined RF/gradient manipulation will be the sculpting of a shape in the x-y plane. A consequence of the slow-domain RF discretization, however, will be the periodic replication of this profile along the lowbandwidth direction. This DANTE-like effect, which occurs for both the k-and SPEN-based discretized pulses [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF][START_REF] Conolly | Two-Dimensional Selective Adiabatic Pulses[END_REF], can lead to sideband contributions arising from outside the region of interest (ROI). The spatial separation between these sidebands and the centerband in SPEN-based pulses will be ∆L = [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF]. Therefore, avoiding band overlap requires the number of sub-pulses N !"# to fulfill

)65 !"# %4 !"# & !"#
5 !"# 78 !"# •4 !"# > 1 ⇔ N !"# > BW !"# • T !"# (2)
where

BW !"# = + ',!"# ,+ %,!"# )6
is the chirped pulse bandwidth, with Oi,180 and Of,180 the initial and final frequencies of the RF sweep. For simplicity one can assume that the sweep is centered on-resonance (i.e., W = 0); the bandwidth of the sweep is then equal to ,+ %,!"#

6

. It follows from this that avoiding the appearance of excitation sidebands within the targeted ROI, will restrict the average gradient along the blipped dimension to

G !"# < )65 !"# %(+;•4 !"# (3)
A clear separation between center-and side-band regions thereby limits the gradient that can be applied along the blipped dimension, a feature that when combined with their extended durations makes 2D pulses susceptible to field inhomogeneities and/or chemical shift misregistrations. This is a general feature of 2D RF pulses. One of the advantages of SPEN-based pulses over their k-space counterparts lies in the fact that, under suitable conditions, they allow one to exceed the gradient amplitude limit posed by Eq. 3 without causing leading to overlapping sidebands [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF]. This is made possible by the sum of linear and quadratic phases that follow from the action of a chirped pulse. In order to eliminate the latter and enable a voxel-wide signal acquisition, 2D SPEN pulses add to their RF waveforms a continuous chirped pulse that eliminates the quadratic phases for both the centerband and the sidebands. Following this refocusing pulse a linear term along the spatial dimension x will still remain in the phase of each band; thanks to differences in these linear phases among the different bands, their individual signals can be discriminated -and thereby selectively filtered out -even if their spatial regions overlap. For a readout acquisition this filtering could imply zeroing out all the readout samples, except for those k-values corresponding to the echo being sought. In a spectroscopic or imaging experiment one could then mask out the undesired sideband echoes, and recover solely the centerband's signal [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF].

The present study exploits this feature, described for 2D pulses in Ref. [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF], in order to achieve the excitation of complex shapes in three dimensions. Figures 1a and1b show two ways in which this was implemented, both of them relying on pairs of discretized 2D SPEN-based pulses played consecutively along a shared "slow" dimension. If the encoding gradients, the RF duration and the number of subpulses are equal for both pulses, so will be their quadratic phases; this would give a chance to eliminate these unwanted phase terms, but at the same time it would make the remaining linear phase terms identical for all bands. Multiple excitation bands would then overlap, and it would not be possible to discriminate among them. To overcome this we explored three sideband-suppressing strategies that arise when concatenating two 2D SPEN-based pulses; namely,

• Utilizing equal effective encoding gradients and times, but different numbers of subpulses for the two discretized pulses. This will endow the pulses' centerbands with identical phase and amplitude profiles, but make the sidebands of the first 2D pulse fall in different spatial positions than the sidebands of the second. Indeed, recalling that the separation between excitation bands is ∆L =

!"# <=> $% <=> & <=>
, different number 𝑁 '() of sub-pulses for two 2D SPEN pulses can lead to the elimination of linear and quadratic phase terms from the targeted ROI, but not from non-overlapping sidebands. Instances will arise, however, where sidebands corresponding to different harmonics of the first and second pulses may overlap; for these instances the quadratic phase terms will be cancelled, but unique linear terms will still remain.

Thanks to these residual linear phase terms, the contribution from the side-excitations will still cancel out.

•

Adjusting the RF duration and number of sub-pulses in both discrete SPEN-based pulses so that their replicates are similarly positioned, but their quadratic phase terms are not canceled (e.g., by setting

𝑁 !"# (%) = 2𝑁 !"# (!) , 𝑇 !"# (%) = 2𝑇 !"# (!)
). While this will not achieve the expected elimination of the ROI's quadratic phase, adding a continuous, short swept pulse designed to eliminate the residual quadratic term of the centerband while maintaining linear phase terms for the undesired sidebands, gives the possibility of removing the latter's contribution from the observed images. Indeed, being continuous, such third 180 0 pulse will have no harmonics and thus solely refocus the centerband. A version of such approach is introduced in Figure 1c.

• Another option that could do away with the additional chirp just mentioned consists of following an initial 2D discrete excitation pulse by a 2D discrete refocusing pulse lasting half the duration of the excitation, so as to mutually cancel the pulses' quadratic phases [START_REF] Bohlen | Refocusing with chirped pulses for broadband excitation without phase dispersion[END_REF][START_REF] Tal | A continuous phase-modulated approach to spatial encoding in ultrafast 2D NMR spectroscopy[END_REF][START_REF] Andersen | A simple approach for phase-modulated single-scan 2D NMR spectroscopy[END_REF].

This scenario, as well as analogous ones encompassing chirped excitation and storage pulses, would add distinctive linear phases to the sidebands that would lead to their filtration. Unless making the initial excitation pulse exceedingly long, however, such strategies based on short 2D 180 0 pulses were found to exceed RF peak power limitations. Due to this reason we decided to focus only on the first two of the alternatives described.

Figure 2 presents insight arising from 1D Bloch simulations for the first two of these bandsuppressing strategies, denoted as sequences I and II. Figure 2a shows results from a SPEN-based discrete-pulse simulation of sequence with 𝑁 !"# (!) = 𝑁 !"# ()) . As can be appreciated from the transverse phase profiles, the quadratic phases for all bands will be removed by the conclusion of the second 180 0 pulse (time point B I ). This leads to a constant phase value for both the centerband and the sidebands. In this state the centerband can be disentangled from the sidebands only if these do not overlap -a condition that is broken as G180 becomes stronger (Fig. 2a, right-most panel). Alternatively, the same sequence played out with a different number of sub-pulses (i.e., 𝑁 !"# (!) ≠ 𝑁 !"# ()) , Fig. 2b) yields a clear reconstruction of the centerband with almost no traces of the sidebands. This is caused by the linear phase residuals affecting the sidebands at time point B I , which leads to echoed signals from the centerband but not the sidebands (right-most column of Fig. 2b). A similar unfolding effect can be seen in Fig. 2c upon simulating sequence II, where a third chirped pulse added after the discretized pulses removes the undesired phase terms from the centerband but not from the sidebands (Fig. 2, time point C II ). These relaxation-free simulations, performed assuming a uniform B0 field, indicate that sequence II provides the best elimination of undesired sidebands, yet at the expense of adding a third refocusing pulse. In practice this will make sequence II longer -and therefore more susceptible to B0 field inhomogeneities and relaxationrelated signal losses-than its sequence I counterparts.

It is worth noting that all these sideband-suppressing strategies are not applicable to k-based 2D pulses, since then phases along all bands are constant rather than linear. Thus the limitation determined by Eq. 3 cannot be overcome for these pulses by any of these schemes.

Materials & Methods

Based on these considerations, the performance of SPEN-based and k-space-based pairs of 2D pulses for achieving 3D selectivity, was evaluated. All these experiments were carried out at 7 T using a

Millipede ® quadrature volume probe on a VNMRS ® 300/89 vertical bore microimaging Varian system.

Water phantom experiments were performed by implementing the sequences in Figures 1a and1c, while ex-and in vivo tests were conducted using the slightly modified sequence in Figure 1b. RF and gradient waveforms for the 2D pulses were designed in Matlab ® (The Mathworks, Natick, MA) using homewritten routines. These waveforms were exported into the NMR scanner and clocked out with a 4 μs dwell time. Data processing was also performed off-line using home-written Matlab routines. All experiments started by drawing planar x-y and x-z contours that defined the desired 3D shape.

Appropriate 2D pulses for imparting these contours were computed as described in [START_REF] Dumez | Multidimensional Excitation Pulses Based on Spatiotemporal Encoding Concepts[END_REF], with the "slow" dimension of both the first and second 2D pulses chosen as the 𝑥 axis. This was also chosen as the acquisition RO dimension, facilitating the removal of the sidebands' contributions. High-bandwidth, "fast" dimensions were set to 𝑦 for the first 2D pulse and 𝑧 for the second 2D pulse. For 2D SPEN-based pulses each sub-pulse along the "fast" dimension was calculated as a 1D Fourier transform (FT) of the corresponding row in the targeted spatial shape, and its amplitude was modulated by a WURST timedomain profile [START_REF] Kupce | Adiabatic pulses for wide-band inversion and broadband decoupling[END_REF]. The frequency sweep along the "slow" (low-bandwidth) dimension was obtained by an overall phase modulation of the train of sub-pulses. For 2D k-based pulses, which covered a blipped Cartesian trajectory in kx-ky and kx-kz excitation spaces, the sub-pulses' RF was computed using 2D

Fourier analyses of the desired spatial patterns. These targeted 2D patterns were smoothed with a 2D

Gaussian kernel, prior to either their SPEN-or k-based RF waveform designs. Both SPEN-and k-based pulses also used a flyback scheme [START_REF] Lau | Spectral-spatial excitation for rapid imaging of DNP compounds[END_REF], whereby RF was only played out during the plateau of the odd k-lines in an asymmetric zig-zag gradient waveform. Such procedure was needed to compensate for eddycurrent timing errors, difficult to correct on the utilized vertical magnet. All 2D refocusing pulses were flanked by crusher gradients. Re-phasing and pre-phasing gradients were also applied on both sides of the second refocusing 2D pulse (simultaneously with the crusher gradients) to account for dephasing caused by the "fast" gradients of the 2D pulses. The 2D pulses used for animal-oriented scans were shorter than the ones used for the in vitro experiments to account for the shorter relaxation times of biological tissues; (13 and 19 ms were the practical ranges for 2D pulses in in-and ex vivo experiments, respectively. In the case of 2D SPEN-based refocusing pulses, the probe's maximal RF handling power (150W, corresponding to a ca. 32 µs hard 90˚ pulse) was used for refocusing. For k-based 2D pulses, this power wasn't high enough to obtain a flip angle of 180 0 at pulse durations that were realistically short for ex-and in-vivo operation; in these experiments, pulse angles of 120 0 were used.

To test the achieved localization, experiments incorporated a 3D k-space multi-scan image acquisition scheme. For the water phantom experiments, each scan had a unique ky/kz phase encoding following a full-volume excitation, while kx was sampled using a conventional GRO readout. A sliceselective excitation pulse and a single phase encoding was also explored in the ex-and in-vivo tests (Fig. 1b). Water tube phantom images were 2D phase-encoded and reconstructed using a 3D inverse Fourier transform (FT); the multi-slice 2D ex-and in-vivo acquisitions were reconstructed using a 2D inverse FT. When needed to be masked, sideband contributions to the reconstructed images were eliminated by zeroing all the x readout measurements except for the 50 central samples. The echo times used were 59-70 ms for the phantom tests, 36-42 ms for the ex-vivo sample and 33ms for the in-vivo experiment.

The most basic of the analyzed phantoms was a 15 mm inner diameter tube filled with CuSO4-doped water. The ex vivo sample was a rat brain immersed in Fluorinert ® , which provides susceptibility matching and reduces field inhomogeneities. In vivo experiments targeted the brain of a mouse. For these experiments, an anesthesia system mixing 1-2% Isoflurane and oxygen gas was fed for respiration through a dedicated nose mask, at ca. 1 L/min. During anesthesia, the respiration signal from a sensor attached to the animal's chest was monitored. A dedicated heating system was also built and used to keep the animal's body temperature stable. Animal protocols and maintenance were in accord with the guidelines of the Committee on Animals of the Weizmann Institute of Science and were approved by this Committee. Prior to all experiments, localized shimming was done with PRESS [START_REF] Bottomley | Spatial Localization in NMR Spectroscopy in Vivo[END_REF].

Results

In general, applying the sequences in Fig. 1 gave images exhibiting several replicas along the readout dimension, here chosen as the "slow" dimension of the 2D pulses. In cases where the excited sidebands did not overlap with the centerband these echoes could be easily discerned and separated, enabling the centerband's ROI reconstruction. Examples of this are illustrated in Figures 3a and3b for carvings of 3D shapes from within a water tube, using k-and SPEN-based pairs of 2D pulses, respectively. In all these scenarios the desired 3D shape was identical: a diamond shape in x-y intersecting with a diamond along x-z. Following these excitations, the selected regions were imaged by 3D MRI acquisitions with full 2D phase encoding. Notice that while of a "grainer", coarser nature than its k-based counterpart, already at this stage the SPEN-based images exhibit fewer distortions from field inhomogeneities and/or eddy currents. Further distortions in the images elicited by the k-based pulses probably arise from RF design errors associated to the use of the small-tip-angle approximation in these large-flip-angle k-based experiments -design errors that will be less important in adiabatic sweeps like those underlying the SPEN-based pulses. As stronger gradients were used and side-and center-band echoes interfered with one another, the ROI could not be reconstructed from these simple experiments. As mentioned,, this complication could be resolved in the SPEN-based sequences by either: (i) applying 2D pulses with a different number of sub-pulses 𝑁 !"# (!) ≠ 𝑁 !"# ()) , or (ii) concatenating a continuously swept pulse to the pair of 2D pulses, even if these had an equal number of sub-pulses 𝑁 (!) = 𝑁 ()) . Either of these strategies led to a separation along the acquisition readout, of otherwise overlapping side-and center-band echoes. For instance, Figure 3c implements the sequence in Fig. 1a on a water tube, while incorporating an unfolding technique based on setting 𝑁 !"# (!) ≠ 𝑁 !"# ()) . This enabled doubling the encoding gradient along the SPEN dimension compared to that in Fig. 3b, affording sharper spatial resolutions along the low bandwidth dimension while remaining free from blipped-related sidebands. We ascribe the better results observed with the SPEN-based pulses in Fig. 3c over their counterparts in Figs. 3a and3b to an increased immunity to B0 inhomogeneities, associated to a doubling of the 𝐺 !"# .

Figure 4 presents additional aspects of these folding and unfolding features, focusing on the properties observed along the SPEN dimension when the constraints set by Eq. 3 on the 2D SPEN gradient G180 for avoiding band overlap, are broken. Shown in Fig. 4a are the results arising upon increasing the amplitude of this slow gradient to G !"# = ?•)@A !"# %(+;•4 !"#

; when using 𝑁 !"# (!) = 𝑁 !"# ()) the overlap between the ROI and two undesired sidebands, is evident. Figure 4b shows how the ROI can be cleaned up while keeping the same G !"# by using 𝑁 !"# (!) ≠ 𝑁 !"# ()) . Figure 4c, collected with a G

!"# = )•)@A !"# (!) %(+;•4 !"#
that is four times larger than the bound in Eq. ( 3), illustrates the selection that can be achieved even when

𝑁 !"# (!) = 𝑁 !"# ())
, by appending a continuous 180˚ adiabatic sweep to the 2D pulses. This band selectivity, however, is achieved at the expense of an additional evolution time that leads to a decay-driven "rounding off" of the targeted shape. the good preservation of hypointense features in the selected regions. Such ex vivo measurements could not be repeated with 2D k-based pulses: RF peak power limitations led to pulse durations that were too long (30ms) for this biological tissue, and to flip angles that were much lower than the full, ideal inversion. These long pulses and compromises in the full inversions, led to very poor sensitivity and to unsuitable images even after prolonged scan times.

Figure 6 presents results arising from the sequence in Fig. 1b, when applied in vivo to a mouse brain.

The manually selected 3D shape was a horse-shoe ROI around the corpus callosum in x-y, and an oval in x-z. The selectivity achieved along all three axes is clearly visible. Anatomical details, however, are more blurred than in the ex vivo results of Figure 5. We tentatively ascribe this to signal decays related to motions that were absent in the ex vivo cases. In addition, there are some weak contributions from sidebands at z=0 and z=0.5cm, positioned in the lower part of the images along the discretized SPEN dimension. Still, the centerband echo was easily distinguishable to filter out most of the sidebands, and delivers a clear view of the selected brain region's ROI. Such results could not be recapitulated when assaying sequences relying on 2D k-based pulses.

Discussion

This study evaluated a number of methods for selecting complex 3D shapes based on pairs of 2D excitation and/or refocusing pulses. While less general than a full 3D RF pulse, these planar manipulations have the advantage of being short while providing a fair amount of spatial selectivity.

Another useful feature is their triggering by a non-coding pulse, which can be easily adapted to spectrallyselective excitations and thus provide an initial degree of chemical shift selectivity. This strategy can be exploited in instances where imaging capabilities are limited as in hyperpolarized 13 C MRS [START_REF] Golman | Real-time Metabolic Imaging[END_REF][START_REF] Day | Detecting Response of Rat C6 Glioma Tumors to Radiotherapy Using Hyperpolarized [1-13C]Pyruvate and 13C Magnetic Resonance Spectroscopic Imaging[END_REF], or when targeting very small objects like lymph nodes by 1 H MRS [START_REF] Pauly | A Linear Class of Large-Tip-Angle Selective Excitation Pulses[END_REF]. The performance of pairs of 2D SPEN-based x-y/x-z pulses was compared to the 3D selectivity achieved with a pair of 2D k-based pulses.

For a water phantom the latter sequence gave more distorted and blurred images, even under relatively homogenous B0 fields. A similar behavior is evidenced by simulations (see Supplementary Material), which evidence that they are largely due to broken assumptions in the small-tip-angle approximation. A feature aiding the SPEN-based implementation of this sculpting, rest on the fact that the gradient along these pulses' "slow" dimension could be significantly increased relative to the limits needed for separating sidebands from centerbands (Eq. 3). To enable the use of these stronger gradients "unfolding" techniques had to be developed; for instance, concatenating different numbers of sub-pulses for the first and second 2D RF shapes. This provided a clean separation between the center-and the side-band contributions; in general, setting the "slow" gradient strength to

G180 = 2 2𝜋! !"# (!) γROI•T 180
, provided the best tradeoff between a higher robustness to field inhomogeneities, versus an ability to fully null the sideband contributions in the final reconstruction.

The advantage of imprinting 3D selectivity with SPEN-based 2D pulses, was especially evident under ex-and in-vivo conditions. For the k-based tests no reasonably complex shape could be sculpted in these scenarios, reflecting an increased sensitivity towards field inhomogeneities, coupled to nonidealities arising when designing k-based 2D 180 0 pulses on the basis of the small-tip-angle approximation. In this respect it was surprising to see how useful this approximation -valid for a smallangle excitation and a magnetization vector starting at Mz -was for the design of the 2D SPEN-based 180 0 pulses. The right selectivity delivered by this Fourier based design was verified by 2D Bloch simulations (see Supplementary Material). The performance of this simple approach remains to be compared against more sophisticated 'inherently refocused' pulses that can achieve large tipping angles [START_REF] Pauly | A Linear Class of Large-Tip-Angle Selective Excitation Pulses[END_REF], and against pulses designed using non-linear Shinnar-Le Roux algorithms that can deliver accurate profiles even for large tip angles [START_REF] Pauly | Parameter Relations for the Shinnar-Le Roux Selective Excitation Pulse Design Algorithm[END_REF][START_REF] Ma | Design of Multidimensional Shinnar-Le Roux Radiofrequency Pulses[END_REF][START_REF] Schulte | Equi-ripple design of quadratic-phase RF pulses[END_REF][START_REF] Balchandani | Designing adiabatic radio frequency pulses using the Shinnar-Le Roux algorithm[END_REF][START_REF] Pauly | Echo-Planar Spin-Echo and Inversion Pulses[END_REF].

While it was satisfying to witness the usefulness of the SPEN-based 3D shaping pulses in tissues, the in vivo selectivity and boundary definition was not as sharp as for the ex vivo experiments. We ascribe this to the stronger motional losses arising in the former case during the relatively long pulses. Indeed, prolonged durations are still a feature associated to the use of these pairs of 2D RF pulses. A better definition should arise if applying the RF on both even and odd encoding gradient echoes; i.e., if working during both positive and negative plateaus of the "fast" gradient waveform. This could shorten the pulses or halve the delays between the sub-pulses, thus shifting the sidebands away from the centerband and enabling a further increase in the amplitude of G180. This was technically not possible in our system due to eddy currents, but may be suitable in better-behaved gradient systems. Other options to shorten the 2D pulses include parallel transmission [START_REF] Katscher | Transmit SENSE[END_REF][START_REF] Zhu | Parallel Excitation With an Array of Transmit Coils[END_REF] and interleaving multiple scans along the fast sculpting dimension [START_REF] Takizawa | A Robust Ultrashort TE (UTE) Imaging Method With Corrected k-Space Trajectory by Using Parametric Multiple Function Model of Gradient Waveform[END_REF]. Such approaches, which so far have been essential to enable k-based schemes to select 3D shapes, could also shorten the total duration of the SPEN-based 2D pulses, albeit at the price of doubling the number of scans and of increasing the required RF power. Finally, in cases where T2 or T2 * degrade too much the sharpness of the in vivo selectivity and image contrast delivered by the sculpting pulses described here, one may also consider the use of sequences involving 2D SPEN pulses that suppress 3D volume shapes outside the targeted shape. When followed by a broadband excitation, the latter could then be used for targeting a preselected ROI.

Conclusions

Exciting complex 3D shapes could be a useful complement in functional, relaxation, diffusion or spectroscopic measurements, particularly in cases were sensitivity is compromised, or partial volume effects are detrimental. This study compared two techniques for achieving complex 3D volume localizations: one based on 2D SPEN-based pulses and the other on k-based 2D pulses. While not completely general, this approach was the most robust among the strategies tested and covers a variety of shapes required to perform flexible tissue localization. In in vitro experiments localization could be achieved by both of the assayed routes, yet in ex-and in-vivo tests, 3D volume selectivity was only delivered by SPEN-based pulses. Factors assisting in this improved performance SPEN's accommodation of stronger encoding gradients along the "slow" dimension, and "unfolding" techniques designed to deliver a clear echo from the targeted ROI while suppressing excitation sidebands. This delivered a tool capable to excite complex-shaped 3D regions in vivo, in a single scan and without parallel transmission. Future research should explore the potential of the ensuing method in physiological investigations, and the incorporation of alternative spatiotemporally encoding strategies. ! !"# (!) = "0$ "'# , for each discrete pulse. The encoding gradients of the discrete pulses were setup so as to have the same total k areas. (c) Results of sequence II, where spins are not fully refocused after the second discrete pulse, but the remaining quadratic phase is removed by a continuous refocusing chirp added after the second discrete chirp. The second and third chirped pulses' durations were 𝑇 "#$ (') =1.33 • 𝑇 "#$ (") and 0.82 • 𝑇 "#$ (") respectively; the discrete pulses had N "#$ (") =128

7.

, N "#$ (') =170 sub-pulses. 𝑁 "#$ (") = 𝑁 "#$ (') = 54. (b) Similar to (a) but upon canceling sidebands with the scheme in Figure 1a, with 𝑁 "#$ (") = 54, 𝑁 "#$ (') = 72. (c) Sideband suppression implemented according to Fig. 1c, where a 180 0 continuously swept pulse is added subsequent to a pair of 2D pulses with 𝑁 (") = 𝑁 (') = 36. In (a)

and (b) the encoding gradient G180 was 0.8 G/cm, i.e. three times higher than the constraint set by Eq. 3. In (c) it was 0.54 G/cm, i.e. twice this limit; these gradient amplitudes correspond to swept bandwidths of 5.8 kHz (a-b) / 3.9 kHz (c). The 2D pulses durations were 𝑇 "#$ (") =𝑇 "#$ (') =27.6 ms for (a-b) and 𝑇 >$ (") = 𝑇 "#$ (') = 𝑇 "#$ (?) =18.4 ms for (c) , where 𝑇 "#$ (?) was the duration of the continuously swept pulse. The total RF irradiation time of the swept pulses in (a,b) and (c) was matched, in the sense that the 2D pulses durations 𝑇 "#$ (") + 𝑇 "#$ (') in (b) was set equal to 𝑇 >$ (") + 𝑇 "#$ (') + 𝑇 "#$ (?) in (c). Sweep rates for (a-c) were 212 kHz/s, the 2D pulses had a gB1,max/2p = 9 kHz and an adiabaticity factor Q = 19.5. The 2D pulses covered a region of 1.7x1.7 cm along the SPEN and Fourier dimensions. A full 3D k-space acquisition similar as in Fig. 3 was done, except for the maximum kz that was here doubled.

Figure 5

 5 Figure 5 displays an analogous set of results, collected on an ex vivo rat brain. These images show, in addition to 3D selectivity, anatomical details that assist in validating the localization and delineation of the targeted tissue. In Fig. 5a the x-y shape was drawn according to the edges exhibited by the corpus callosum in the equator slice (where z=0); Fig. 5b targeted only the left hemisphere of the corpus callosum, while Fig. 5c targeted the right hemispheric part of the corpus callosum. Notice in all images

Figure 1 .

 1 Figure 1. (a, b) Pulse sequences considered for imparting 3D spatial selectivity using pairs of 2D RF pulses. Following a broadband or selective excitation pulse a a 2D refocusing pulse selects a shape in x-y whereas a subsequent 2D pulse selects a shape in x-z. The acquisition that follows is intended for 3D k-space imaging, where each shot acquires a line along kx with a different ky/kz phase encoding (a), or performs a sliceselective excitation (b). The imaging block can be replaced by a FID acquisition for NMR spectroscopy. (c) 3D sculpting strategy suitable for SPEN-based strategies where the excitation/refocusing 2D pulse pair is followed by a continuous 1D swept pulse in order to remove excitation sidebands (see text). (d) Hybrid SPEN-Fourier trajectory in the x/kyspace imparted by the SPEN-based pulses in (a-c). (e) Idem but for 2D k-based pulses. The association of the imaging directions RO,PE,PE' with x,y,z, is arbitrary and for illustrative purposes only.

Figure 2 .

 2 Figure 2. Bloch simulations showing the effects of the SPEN-based sequences I and II, calculated assuming a single (x) spatial dimension. The plots present transverse magnetization phase profiles after the first discrete pulse (left column) and after a full refocusing (middle column) occurring at point B I for sequence I and at point C II for sequence II. The right hand column displays the final spatial magnetization profiles excited, for gradient strengths leading to a strong (red) / weak (blue) band overlap. (a) Results of sequence I acting devoid of unfolding strategies, and arising from an identical number of sub-pulses for both 180 0 sweeps "𝑁 "#$ (") = 𝑁 "#$ (') = 128'. The

Figure 3 .

 3 Figure 3. 3D spatial selectivity demonstrated on a water test tube using the sequence in Figure 1a, recorded under identical, high-resolution shimming conditions (15 Hz full-width-half-height widths measured in PRESS experiments including the relevant voxel). The selected ROI was an intersection of diamonds in x-y and in x-z (illustration in the lower right panel of a). (a) 2D k-based pulse results. (b) and (c) 2D SPEN-based pulses results. G180 was 0.27 G/cm in (a,b) and 0.54 G/cm in (c). G180 led to overlapping center-and sidebands in (c), which were suppressed by setting 𝑁 "#$ (") ≠ 𝑁 "#$ (') . Parameters were equal in all other aspects. For (a) and (b) the 2D concatenated pulses used 𝑁 "#$ (") = 𝑁 "#$ (') = 64; in (c) 𝑁 "#$ (") = 64, 𝑁 "#$ (') = 85. In all cases 2D pulses were 32.8 ms long. The 2D SPEN-based pulses swept over a bandwidth of 1.95kHz in (b) or 3.9kHz in (c), corresponding to a region of 1.7cm along the SPEN dimension, at a sweep rate of R = 59.5 kHz/s (b) or 119 kHz/s (c). Their gB1,max/2p was 9kHz, yielding an adiabaticity factor Q = 𝜸𝑩 𝟏 𝒎𝒂𝒙 √𝑹 = 36.9 (b) or 26 (c). 64x16x256 samples were imaged along ky, kz, and kx respectively, covering a Field-of-View of 2.2cm x 2.2cm x 2.2cm. Ten axial images are displayed -9 for (a) as no data show beyond the 7 th panel-out of sixteen that were acquired.

Figure 4 .

 4 Figure 4. 3D spatial selectivity demonstrated on a water tube with SPEN-based 2D pulses according to the schemes in Fig. 1, with and without unfolding, targeting the same diamond shape as in Figure 3. (a) Sculpting with a pair of refocusing SPEN-based 2D pulses without unfolding:

Figure 5 .

 5 Figure 5. SPEN-based 3D spatial selectivity demonstrated in an ex vivo rat brain. Spin-echo axial images were acquired with the sequence in Fig. 1b using a slice thickness of 2 mm, 64x256 points per slice, an acquisition time T @ = 1024 µs, an acquisition bandwidth of 250 kHz, and a TR of 2 s. (a) Selected volume given by the intersection of a manually drawn callosal ROI in x-y and a tapered diamond in x-z. The left-most image shows a non-selective reference for z = 0. (b,c)Selected shapes involving manually selecting the left and the right x-y ROIs in (a), respectively.(d) Non-selective reference images for experiments in (b) and (c), acquired by turning off the pulserelated gradients. (e,f) Surface rendering (side and top views) of the 3D shape selected in (a). In (a,c) every 2D pulse was 13.8 ms long with 𝑁 "#$ (") = 26, 𝑁 "#$ (') = 36. 𝐺 "#$ was 0.54G/cm, twice the limit to avoid centerband folding. In (b) the 2D pulses were 18.4ms long with 𝑁 "#$ (") = 𝑁 "#$ (') = 36 and centerband unfolding was unnecessary. The 2D pulses swept over a frequency range of 3.9 kHz in (a,c) and 2.9 kHz in (b), covering a region of 1.7 cm along the "slow" dimension at a sweep rate of 283 kHz/s in (a,c) and 158 kHz/s in (b). The 2D pulses had a gB1,max/2p of 9kHz and adiabaticity factors Q=16.9 in (a,c) and 22.6 in (b). Eight averages were collected for (a), 4 averages for (b) and (c). The sample position was slightly different in (a) than in (b-d).

Figure 6 .

 6 Figure 6. 3D spatial selectivity evidenced by the sequence in Fig. 1b, on an in vivo mouse brain. Five spin-echo axial images from z=-0.5 cm to z=0.5 are presented. The left-most image on the top shows a non-selective reference image for the z=0 slice. The desired volume was defined by a manually drawn ROI around the corpus callosum in x-y, and an oval in x-z. The two 2D SPEN-based pulses were 13.8ms long with 𝑁 "#$ (") = 26, 𝑁 "#$ (') = 36 ; this implemented an unfolding of the

Acknowledgments. We are grateful to Amir Seginer for useful discussions and to Koby Zibzener for supporting the experimental setup. This work was supported by the Kimmel Institute for Magnetic Resonance (Weizmann Institute), the Israel Science Foundation grant 795/13, and the generosity of the Perlman Family Foundation.