Amine Boumaza
email: amine.boumaza@loria.fr

Promoting Reproductive Isolation Through Diversity in On-line Collective Robotics

We present a behavioral diversity selection scheme that favors reproductive isolation to promote the learning of multiple task in on-line embodied evolutionary robotics (EER). The scheme estimates the behavior of the controllers without the need to access the agent experience, respecting thus the online, distributed properties EER. Reproductive isolation is assessed through coalescence trees and task specialization is tested on a concurrent foraging setting.

Motivations

It has been shown that evolving specialized behaviors in Embodied Evolutionary Robotics (EER) requires reproductive isolation, and tailored selection operators [START_REF] Montanier | Behavioral specialization in embodied evolutionary robotics: Why so difficult[END_REF][START_REF] Haasdijk | Combining Environment-Driven Adaptation and Task-Driven Optimisation in Evolutionary Robotics[END_REF]. The fact that agents spread their genetic material without any barriers does not help the conservation of specialized skills. One way to limit mating encounters and the preservation of learn skills is trough geographical isolation (Allopatric speciation) where contact and genetic exchange between agent is limited. If reproductive isolation is a requirement to behavior specialization, in this study we ask the following question: can this isolation be enforced in other ways than geographically? Indeed, there exists in nature some evidence that behavioral separation can be promoted through sympatric speciation; situations where multiple species share a single environment and exchange genes but reproductive barriers maintain species distinct [START_REF] Maynard | Sympatric speciation[END_REF].

In this study, we propose to explore this idea for promoting isolation. Agents share the same geographical region, and the addition of tailored selection methods ensures the isolation needed for specialized skills to be preserved. Our goal is to verify the following hypothesis: promoting diversity favors reproduction isolation, and thus favors the emergence of specialization. To that end, we propose a selection scheme that promotes diversity by selecting solutions based on their originality in the behavioral space. The selection scheme respects the distributed nature of EER, it operates locally on the agents and uses generic behavioral descriptors measure.

Methods

We use a modified version of minimally Environment-driven Distributed EA (mEDEA) [START_REF] Bredeche | Environment-driven Embodied Evolution in a Population of Autonomous Agents[END_REF] to which with we add a selection operator. We considered a concurrent foraging task in which agents have to collect items randomly placed in the environment. There exist two types of items (red and black) and agents are rewarded one unit of fitness every time they collect one item regardless of its type. When picked, an item of the same type is randomly placed in the environment. This task has been extensively studied in the context of task specialization and of diversity preservation [START_REF] Haasdijk | Combining Environment-Driven Adaptation and Task-Driven Optimisation in Evolutionary Robotics[END_REF][START_REF] Hart | Evolution of a functionally diverse swarm via a novel decentralised quality-diversity algorithm[END_REF]. Collecting one type of items or the other is considered a distinct task, because agent perceive the types of items trough different sensors.

The selection scheme we propose selects solutions at the agents level by choosing the genome that has the most different behavior from other genomes in the agent's list. It can be considered as an instance of Novelty Search [START_REF] Lehman | Abandoning objectives: Evolution through the search for novelty alone[END_REF], without the archive. Since agents live specific experiences depending on their encounters (obstacles, other agents, etc.), it is difficult to generalize a behavior measurement outside from the situation that it was measured in. We propose to estimate the behavior of the genomes regardless of the experience of the agents the originated from. Since the goal is to identify the most "different" behavior in the selection pool, we propose to simulate behaviors and measure their difference on random sensory data. The difference in the outputs will be the basis for the selection criterion.

To be more specific, let us consider a typical agent of the swarm, let it be a. We note L a = {x 1 . . . x µ } the set of genomes collected by agent a during its lifetime. The selection scheme aims at selecting one genome x ∈ L a that has the most different behavior to replace the current active genome of a. At each selection step, agent a generates ι k with k = 1, . . . , K "fake" inputs s.a. ι k = Uniform(0,1)

|s| , where |s| is number of sensors and [0, 1] is the range of values they can take. All neuro-controller in L a are presented the same "fake" sensory data, as if they experienced the same situation. For each input ι k , we compute the "would be" output o i,k = C i (x i , ι k ) of each controller in L a , where C(x, ι) computes the output of the neuro-controller with weights x on input ι. The behavior of genome x i is then defined as the concatenation of its controller outputs from all inputs or: B(x i ) = {o i,1 , o i,2 , . . . , o i,K }, which represent a vector of K × |e| elements, |e| being the number of effectors each agent has. The agent then selects the genome with the most different behavior defined as the behavior that has the largest average distance to all others or: x = arg max x∈L a 1 |L a | y∈L a B(x) -B(y) . To assess if the diversity selection scheme promotes isolation, we compare a purely objective selection method (number of items) with the above diversity selection method (novelty only).

Results and discussions

One way to measure if reproductive isolation occurs is to inspect the population dynamics. We take a gene perspective where at each generation, we record the dissemination of the genes between agents and track their descendants. We then extract the corresponding coalescence tree which synthesize the genealogy of the last surviving genomes. This tree is constructed from the last generation up to the first where, at each step lineages are merged whenever two or more genomes share the same parent (a coalescence event).

The most recent common ancestor (MRCA) is the genome that all the surviving genomes (those that form the last generation) descend from and its height (Time to MRCA) in the tree is a good indicator of genetic closeness, since it is related to the number of generations and thus to the number of mutations between the MRCA and a current population. The larger it is, the farthest apart are the genomes in the population, the smaller it is, the more its descendants are related. We measure also, the length of the branches of the coalescence tree as it is related to of how much history genomes share. Genome would share the least history if they come from a common ancestor far back in time and then evolved along distinct lineages i.e. higher reproductive isolation.

Behavioral diversity

Objective based To assess if reproductive isolation is favored by diversity, we compare both instances on the basis of the coalescence measures we described above. If we inspect the left of Figure 1, it is clear that the objective based instance has the lowest TMRCA. On the other hand, in the diversity selection instance, there was no MRCA! This is indicated by the flat box-plot at the value 500 (the number of generation). This reflects the fact that in this case there were distinct lineages that coexisted since the start of the simulation that never coalesced. In parallel, if we look at the branch length, we notice that the higher values are those for diversity selection indicating that the end-survivors of those instances share the least genetic history. The difference is statistically significant (p-value < 10 -4 , 64 runs). To illustrate the above results Figure 2 shows coalescence trees from typical runs from both instances. To measure if both behaviors (specializing on one item type) are present in the swarm, we measure the histogram of the ratio of collected black and red items by each agent. When all agents collect both items indistinguishably, this histogram is centered around 0.5. On the other hand, when agents favors one color over the other the histogram is spread toward the edges. Figure 3, clearly shows that the diversity selection scheme create diverse behaviors on all the spectrum. We notice also that there is a number of agents that collect only items of one type (on the left or the right edge). On the other hand objective based selection create the least diversity most agents collect equally red and black items. The difference is statistically significant (p-value < 10 -4 , 64 runs). We proposed the idea of favoring reproductive isolation without geographical constraints through the use of a diversity selection scheme and tested the hypothesis on a concurrent foraging task. The results suggest that it is the case. Furthermore, we introduced a procedure that allows estimating behavioral distance on board the agent, and we argue that it provides sound measurements of the behaviors independent of the agents' experiences, which in the case of EER is not accessible.

Behavioral diversity Objective based

Behavioral diversity Objective based

Figure 1 :

 1 Figure 1: TMRCA (left) and lineage branch length (right).

Figure 2 :

 2 Figure 2: Coalescence trees of typical runs

Figure 3 :

 3 Figure 3: Histogram of red/black across the population.


Stéphanie Thiéry
email: stephanie.thiery@icn-artem.com

Didier Fass1
email: didier.fass@loria.fr

Cybersecurity risks and situation awareness: Audit committees' appraisal

Keywords: Cybersecurity Awareness, Board of Directors, Audit Committee, Safety by Design, Cyber-resilience

The issue of cybersecurity has become a challenge for companies and boards of directors. Cybersecurity is not only an IT topic but a risk extended to all operations of the companies. Indeed, cybersecurity potentially has an impact on financial reporting quality, this attribution being one of the duties of audit committees. Using Endsley's model, our exploratory study seeks to determine the levels of cyber situational awareness of audit committee members, how they comply with it and if this appraisal matches the steps identified within the model.

1.

Introduction Cybersecurity is nowadays a significant topic within organizations since the last 25 years, assets of companies have evolved from physical assets to the digital [START_REF] Nacd | Larry Clinton, Director's Handbook Series[END_REF]. Intangible assets valued according to international standards are particularly sensitive to internal or external manipulation and attack. However, taking cyber risk into account mainly covers the IT (internal IT) technical risks. The human and organizational factors aspects are neither clearly known nor clearly identified, in particular by decision-making bodies such as Board of Directors. Thinking the company as an integrated system "critical security" and the risks inherent to its field of activity are a theoretical and practical issue.

If the explicitly described missions by regulation were discussed in the literature, only few studies related to cyber-attacks management exist at board level [START_REF] Higgs | The Relationship Between Board-Level Technology Committees and Reported Security Breaches[END_REF] or, specifically, at audit committee level. Thus, the literature on boards and audit committees has not operationalized the examination of this risk by governance institutions. Indeed, the criticism of organizational data is a well-known issue of actors who are responsible for, as indicated by [START_REF] Rahimian | Estimation of deficiency risk and prioritization of information security controls: A data-centric approach[END_REF], since the developed model in their study allows to take into account the data owners', senior management's and legal experts' point of views to give a framework to data security assessment. Authors also recommend an implication of internal audit and information technology functions [START_REF] Steinbart | The influence of a good relationship between the internal audit and information security functions on information security outcomes[END_REF].

However, these works do not consider the direct appropriation of this issue by governance institutions as board of directors or audit committees. Yet, regulation seems to have integrated the topic, requiring firms to perform a cyber-risks assessment, with associated costs and consequences or a description of occurred cybersecurity issues including their costs and consequences [5]. Clark and Harrell [6] however highlight that if SEC current recommendations (disclosure of data breach issues) became obligations, directors of public companies could incur lawsuit risks, in addition to the decrease of share price. For this reason, Lunn [START_REF] Lunn | Strengthened Director Duties of Care for Cybersecurity Oversight: Evolving Expectations of Existing Legal Doctrine[END_REF] indicates the questions directors should ask in case of cyber-attack in order to protect their responsibility if the latter was engaged. He advocates to consider some factors in their monitoring role: existence of monitoring process of cyber risks, probability and consequences of loss related to cyber-attacks, existence of consequences which may adversely affect human lives or the survival of organization or implementation of action plans to mitigate cyber risks. Recommendations are given in order to limit directors' responsibilities, such as training directors to cybersecurity issues or recruiting directors having an experience in this field. Von Solms [START_REF] Solms | Towards a cyber governance maturity model for boards of directors[END_REF] takes up an assessment model of board maturity in terms of cybersecurity device review. This model allows an assessment of cyber governance knowledge within board members, giving insights on their understanding of the issue and the implementation degree of cyber governance. However, if this model contributes to the self-assessment of the directors' actions, it seems that it does not exist any study building a state of directors' competences and received information (particularly of audit committee members) in terms of cybersecurity. To our knowledge, the appraisal of audit committee members on the review of cyber risks has not been investigated in the literature: are audit committee members aware of issues related to cybersecurity? There are still unanswered questions regarding the audit committee functioning process in general [START_REF] Gendron | Getting Inside the Black Box: A Field Study of Practices, « Effective » Audit Committees[END_REF] and, specifically, as for cyber issues and those process issues remain neglected by researchers. In order to answer our previous question, we favored a field study and a qualitative approach. This leads us to determine if audit committees address significant cybersecurity topics and / or face cybersecurity breaches. Our work in progress seeks to determine if audit committee members are aware of the issues linked to cybersecurity, in order to improve both cyber-resilience and safety by design decision-making.

2.

Cybersecurity awareness and human factors at board level Management and production information systems and digital informations, especially if they are strategic assets for the company, are safety-critical. Consequently, the impact of deficiencies of cybersecurity can have global consequences: loss of intellectual property, risks of legal or regulation-linked penalties, reputation loss, costs to restore clients' confidence and to give explanations to authorities [START_REF] Kpmg | Cybersecurity -What does it mean for the board ?[END_REF]. To prevent that systemic risk, one needs to be able to estimate related human factors such as situation awareness and processes responsible for maintaining it. Three categories of main components impact cybersecurity at each organizational levels of the socio-technical system : technical risks / factors, human risks / factors and organizational risks / factors. Misunderstanding or underestimation of cyber-risks is thus a danger for the company that must be dramatically considered at board level. Because cyber risks are not only virtual but actual, taking into account this serious danger is a question of situation and risk awareness depending on knowledge, cognitive bias or emotional states which participate to the perception of the risks and which influence decision-making and control process [START_REF] Endsley | Toward a Theory of Situation Awareness in Dynamic Systems[END_REF] [12] [START_REF] Damasio | Descartes' Error: Emotion, Reason, and the Human Brain[END_REF].

Just like aeronautics, i.e airplane piloting and air traffic control, enhancing cyber situational awareness at board and audit committee levels is a major issue. Thus, board of directors seem to be considering the topic since, according to NACD 2016-2017 public and private company governance surveys, 81% of surveyed boards address cybersecurity issues during meetings and that 51% of respondents claim that cybersecurity should be considered at audit committee level. In order to evaluate the cyber situation awareness of audit committees' members, we favored Endsley's framework [START_REF] Endsley | Situation awareness analysis and measurement, chapter theoretical underpinnings of situation awareness[END_REF] and its three levels. This enables us to assess the perception, the comprehension and the projection of the audit committee's members.

3.

Directors' appraisal of cyber issues 3.1. Method used, Data collection and analysis Our collection of empirical material is driven by our exploratory study. We both rely on invaluable observations of audit committee meetings, interviews with audit committee members and participants, publicly available reports and internal documents. Interviews lasted, on average, between 60 and 120 minutes and on-site observations around 150 minutes each.

First, we reviewed publicly available documents (10-K reports) to gain understanding on how organizations formally report on audit committees' appraisal of cyber issues. We next got closer to the field and supplemented our empirical material, with an source of data constituted by on-site observations of two audit committee meetings. Furthermore, we carried out 27 semi-structured interviews with audit committees' members but also with individuals who attend the meetings, such as partners of audit firms and chief audit executives. Interviews are a relevant data collection mechanism, complementary to observation-based material [START_REF] Yin | Case Study Research Design and Methods[END_REF]. Having completed on-site observations with, first, documentation and, second, interviews was a powerful tool in order to help us gathering evidence of their appraisal of cyber risks and cyber issues. Table1. Content Analysis (66 listed French firms) 3.2. Level 1 SA -Perception: Disclosed cyber-awareness to the public and individual returns of experiences Listed firms communicate and disclose both their internal control concerns and their risk assessment. Being part of the most important emerging risks, cyber issues are disclosed within the 10-K reports. This is confirmed by the content analysis we achieved on our 2015-2016 annual reports of French firms. On 66 firms for which we examined the audit committee reports, 18 made explicitly reference to a review of cyber risks (table1). Out of our 2 on-site observations and 27 interviews conducted, only one on-site observation and three interviewees mentioned and analyzed cyber issues. This is far more less than the 51% of firms supposed to address cyber risks at the level of audit committee [START_REF] Nacd | Larry Clinton, Director's Handbook Series[END_REF]. Hence, according to our field work, some audit committee members highlighted a basic perception of cyber situation awareness : " we have an extremely high risk (…); on particular points with can be presented and studied in depth by the audit committee".

Level 2 SA -Comprehension

However, it seems that only 54% of global organizations have carried out an assessment related to fraud or economic crime. In particular, less than half of firms have achieved a vulnerability assessment related to cyberattacks and only 30% have implemented an action plan [START_REF]PwC's Global Economic Crime and Fraud Survey[END_REF]. Furthermore, for members of audit committees and, more generally, for boards, "cyber" is new for many directors, and is certainly far from intuitive" [START_REF]The Corporate Governance Advisor[END_REF].

As our interviewees stated : "we have to perform regular checkup and that, basically, we acknowledge that some persons may have non-restricted accesses to the system (…) This must be the subject of a presentation and in-depth study while audit committee meetings".

Level 3 SA -Projection

Mostly our field work highlights that directors are first "cyber-risks aware" and that they intend to get a specific overview of the main cyber issues, using ever specialists or governmental agencies in order to help them appraise and improve cybersecurity: "we asked specialists and ANSSI in order not to waste time". Moreover, our interviewees assess that, in order to be compliant with the main internal control frameworks (COSO, COBIT), they target some specific levers of control, such as control environment (the 'tone at the top' and human knowledge and skills) and control activities (Segregation of duties): "we need to train our people to improve their cyber awareness and secure their accesses and behaviours(…) specifically we must disseminate this cyber awareness through operational middle management and their teams".

4.

Directors' appraisal of cyber issues Annual report should disclose the risks including cyber issues if it happened but only if they are material. This means that without any material effect, cyber issues are not always revealed to the public. Our analysis confirms that this disclosure is not obvious and depends on the knowledge, expertise and will of the boards. Nonetheless, our exploratory study highlights that, when audit committees tackle cyber issues, they follow Endsley's process and that they both embrace, appraise, evaluate and disseminate the issues. Our preliminary analysis should be of course deepened with archival data in order to validate this fieldwork evidence, but our work underscores requirement and impetus for improving board cyber situation awareness.

Firms

  , Dassault Systèmes, Engie, Essilor, L'Oréal, Renault, Saft, Sanofi, Technicolor, Total (14 firms) Endered, Essilor, Saft, Valeo (4 firms)


Didier Fass

Bruno Levy

Pierre Perez

Dominique Méry

Virtual environment design as automated "physiological" counter-measures in extreme environment: from intensive

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Title: Virtual environment design as automated "physiological" counter-measures in extreme environment: from intensive care to human space flight.

Authors: Didier FASS (1), Bruno LÉVY (2), Pierre PEREZ (2), Dominique MÉRY (3) (1) ICN Business School and Mosel Loria UMR CNRS 7503, University of Lorraine.

(2) Service de Réanimation Médicale Brabois, CHRU Nancy, Pôle Cardio-Médico-Chirurgical, 54511 Vandoeuvre-les-Nancy, France ; INSERM U1116, Faculté de Médecine, 54511Vandoeuvre-les-Nancy, France ; Université de Lorraine, 54000 Nancy, France.

(3) TELCOM Nancy and Mosel Loria UMR CNRS 7503, University of Lorraine.

How can we model and design virtual environments to prevent, monitor and avoid automatically major human factors and health issues after intensive care long stay and long-term space flight?

Intensive care unit (ICU) and long-term space flight are extreme environments. In both cases it is a risky journey for patients or astronauts that requires life support systems to maintain and protect body integrity, vital functions, sensorimotor and cognitive capacity as stable as possible for post-ICU quality of life recovering or for human outer planet exploration.

To send and make a human living and acting in space, the problem is sensibly different. It is no longer a question of survival but of extension of the domain of life and activity of the person that requires specific life and activity support systems. Artefacts, transport and life modules, and wearable devices (astronaut suits) must be designed in order to maintain: body integrity and physiological functions; sensorimotor and cognitive functions, and the operational capacity of the operator in situation; the physiological functions of the operator in a functional area compatible with the return to planet gravity (different on earth, moon or mars) by avoiding for example the risk of cardiovascular collapse or a transient sensorimotor disability.

Designing reliable, safe and adaptable human-machine in intensive care for every person with a major disease is a challenge for automated monitoring, decisionmaking and medical treatment to maintain the patient alive and allow healing on one side and to avoid complications due to prolonged stay in intensive care. For example both long-bed rest in resuscitation and the absence of gravity during long-term space flights cause neuromuscular deconditioning and loss of muscle strength.

To prevent and avoid complications related to long-term stay in these extreme environment, related to human factors and habitability element as bed rest, sound and light environment, medical treatment side-effects in ICU, food or weightlessness and life support systems design, we propose the use of mutimodal virtual environment as "physiological" counter-measures and monitoring system.

The challenge of these human-system automated body enhancement system, is not so much a question of human-machine communication as of integrating the whole human machine into a coherent system ensuring functional capacity and limiting dysfunctions evolution either directly, either by countermeasure or substitution. It is a question of modelling and simulation correctness. From evidence-based medicine to model-based engineering it is a safety and reliability by design challenge.


Authors: Franck GECHTER(1) and Didier FASS(2)

(1) UBFC -University of Technology Belfort-Montbeliard -LE2I (2) ICN Business School and Mosel Loria UMR CNRS 7503, University of Lorraine Can we define a valid and generic theoretical framework for modeling and simulation based on a co-integrative approach to analyze, model, design and deploy human-machine systems that are reliable, stable and adaptive in this extreme environments?

The development and the more and more intensive usage of devices aimed at enhancing the human operational capacities, implies the design of safety frameworks for the development and the spreading of efficient and reliable human-machine systems. This is particularly mandatory when this human-machine system must maintain a level of operational efficiency in extreme environment applications related to health, defense and aerospace fields. Thus, in these contexts, the main issue is to validate and certified through formal approaches the Human-Systems Integration engineering methods aimed at developing systems that are correct by construction, safe, reliable, and adaptable. The currently developed systems mainly rely on the adaptation capacity of the human. However, the interactions modes tend to thicken the limit between the technical and the biological systems. The currently more and more widespread technologies such as implantable biotechnological nano-systems, ubiquitous artificial intelligence, biomimetic prothesis tends to reinforce this last trend. By the way, this convergence is hard to reach due to the difference in nature of the involved systems. The technical system, generally considered as a Cyber-Physical System (CPS), is mainly developed using a techno-centered approach relying on the regulation loop concept. This involves implicitly to consider the interaction with the human as an additional regulation loop making the Human in-the-Loop approach a natural way of thinking in a CPS context. This reductionist point of view leads naturally to design human-system interaction following a CPS paradigm. However, inter and intra human interactions have not the same nature. According to [Chauvet], these human interactions are non-local and non-symmetric whereas the physical and the cyber interaction are mainly local and symmetric. Even if the spreading of theoretical computer science model focused on emergent properties and self-organisation is increasing, they are still few used in a human-machine system context.

According to this, it is clear that a rethink of artificial system design is becoming mandatory. The considerations on the different natures of interactions naturally lead to the concept of Bio-Cyber-Physical systems [Fass]. The next step is now to define a co-integrative approach for the development and the design of human-machine systems where the human and the machine are no longer considered as independent system that must interact but are design as a whole unique system defined by its own shape, structure and dynamics. Such designed system can then fulfill its function with an extended stability domain and with the ability to adapt to the possibly high variations of the operational constraints. This co-adaptation ability is supported by the whole system including adaptation skills on both sides (Human AND Machine). The goal of this paper is to sketch this approach and illustrates the relevance of the co-adaptation in extreme environments.


Tsiry Andriamananaivo

Guillaume-Anthony Odri

Matthieu Ollivier

Lucas Mattesi

Arthur Renault

Frédéric Rongieras

Sébastien Pesenti

Mathieu Severyns

Contribution of the remaining attachment index in the management of Vancouver B1 periprosthetic hip fracture

Keywords:

Introduction: Implant fixation assessment following Vancouver B1 periprosthetic hip fracture is a major decision factor for internal fixation and/or implant revision. The main aim of the present study was to assess the correlation between radiographic Remaining Attachment Index (RAI) and risk of implant loosening at last follow-up following internal fixation of Vancouver B1 periprosthetic hip fracture. Material and method: A multicentre retrospective study included 50 patients with Vancouver B1 periprosthetic hip fracture with uncemented femoral stem between 2013 and 2019. Preoperative radiographs were analysed independently by 2 senior orthopedic surgeons, distinguishing 2 groups: RAI > 2/3 versus < 2/3. Postoperative and last follow-up radiographs were then screened for signs of complete femoral component loosening. Results: Median age was 89 years (range: 36-99 years). Two RAI > 2/3 patients showed implant loosening (8%) versus 9 RAI < 2/3 patients (36%), disclosing a significant correlation between early loosening and RAI < 2/3 (p = 0.005). Interobserver agreement for both radiographic RAI and radiographic loosening assessment at last follow-up was 98% with kappa correlation coefficient 0.96 [range: 0.88-1]. Conclusion: Remaining Attachment Index < 2/3 in Vancouver B1 periprosthetic hip fracture was a risk factor for early implant loosening after isolated internal fixation. In these often frail elderly patients, first-line implant exchange is to be considered in the light of the risk/benefit ratio. The present results confirm the need for rigorous preoperative radiographic work-up of the remaining attachment area in Vancouver B1 fracture. Level of evidence: IV.

Introduction

Implant fixation assessment in Vancouver B1 periprosthetic hip fracture with uncemented stem is a major decision factor in planning internal fixation and/or implant revision [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF][START_REF] Brady | The reliability and validity of the Vancouver classification of femoral fractures after hip replacement[END_REF]. Loss of stem anchorage is difficult to assess on standard X-ray, whereas complete implant loosening in case of migration with or without osteolysis (Vancouver B2 and B3) is easy to diagnose for a trained observer [START_REF] Rupp | Computed tomography for managing periprosthetic femoral fractures. A retrospective analysis[END_REF]. Conventional CT is systematically artifacted and cannot reliably assess loosening in the remaining attachment area [START_REF] Rupp | Computed tomography for managing periprosthetic femoral fractures. A retrospective analysis[END_REF]. In internal fixation, moreover, intraoperative assessment of implant loosening is rarely performed as the hip approach is extra-articular [START_REF] Chakrabarti | Cable plate fixation for Vancouver Type-B1 periprosthetic femoral fractures. Our experience and identification of a subset at risk of non-union[END_REF][START_REF] Lenz | Plate fixation in periprosthetic femur fractures Vancouver type B1-Trochanteric hook plate or subtrochanterical bicortical locking?[END_REF][START_REF] Lewis | Tangential bicortical locked fixation improves stability in Vancouver B1 periprosthetic femur fractures: a biomechanical study[END_REF]. The 2005 Symposium of the French Society of Orthopedic Surgery and Traumatology (SoFCOT) [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF] recommended a specific Remaining Attachment Index (RAI) to asses residual fixation, RAI > 2/3 stem-length enabling implant conservation and internal fixation. The present study hypothesis was that RAI > 2/3 allows internal fixation without risk of early secondary loosening. The main aim of the study was to assess the correlation between RAI and risk of radiographic loosening at last follow-up following internal fixation of Vancouver B1 periprosthetic hip fracture.

Material and method

Study population

The present multicentre retrospective study analysed radiographs for 64 patients with Vancouver B periprosthetic hip fracture between January 1, 2013 and December 31, 2019. Inclusion criteria comprised: Vancouver B1 periprosthetic hip fracture on isolated internal fixation with uncemented femoral stem. This included 50 patients. Exclusion criteria comprised: Vancouver B2 fracture with complete radiographic loosening (n = 4), Vancouver B3 fracture with periprosthetic osteolysis (n = 4) and Vancouver B1 fracture with cemented stem (n = 6), all of which indicated prosthetic reconstruction according to the most recent SoFCOT guidelines (Fig. 1) [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF]. Preoperative CT was performed (n = 21) to screen for loosening radiolucency in the remaining attachment area (leading to reclassification as Vancouver B2) or osteolysis overlooked on initial radiography (reclassification as Vancouver B3). RAI was measured only in radiographs showing Vancouver B1 periprosthetic hip fracture with uncemented stem.

Assessment criteria

Radiographic analysis was performed independently by 2 senior surgeons. Preoperative radiographs were analysed for all patients with periprosthetic hip fracture, and 2 groups were constituted: B1 fracture RAI > 2/3 versus RAI < 2/3. Postoperative and last-follow-up radiographs were then analysed for signs of complete femoral component loosening (radiolucency > 1 mm at the stem and/or femoral implant migration). RAI was measured as described in the SoFCOT symposium [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF] as A/B ratio on AP view where A is the minimal remaining anchorage height and B is the total initial height (Fig. 2).

Statistical analysis

Analyses used JMP ® software 11.0.0 (SAS Institute Inc.). The numerical variables showed non-normal distribution and intergroup comparison used non-parametric Wilcoxon test for continuous variables [age, body-mass index (BMI), follow-up duration] and Fisher exact test for qualitative variables (gender, ASA score, walking autonomy). Multivariate nominal logistic analysis on gender, age, BMI and RAI > 2/3 identified loosening risk factors, eliminating confounding factors. The significance threshold was set at p < 0.05.

Interobserver agreement on RAI values and on loosening was assessed on kappa correlation coefficient and expressed as percentage.

Results

The 50 patients with Vancouver B1 periprosthetic hip fracture with uncemented stem and isolated internal fixation comprised 25 women and 25 men (sex ratio: 1); median age at fracture was 89 years (range: 36-99 years). Median BMI was 22 (range: 16-34). ASA score was ≥ 2 in 94% of cases (n = 47). Forty-two per cent (n = 21) had Parkinson syndrome and 80% (n = 40) had cardiovascular history. Only 26% (n = 13) were initially able to walk without mechanical or human assistance.

After X-ray and CT analysis, 25 patients were identified as having RAI > 2/3 (50%) and 25 with RAI < 2/3 (50%). Interobserver agreement was 98% with kappa correlation coefficient 0.96 [0.88-1]. The only significant intergroup difference was for BMI, which was greater in RAI > 2/3 (p = 0.017). Table 1 presents patient data.

Postoperative loosening was screened for on at least 2 X-rays at last follow-up [mean: 3 months (range: 1-48 months)]. Interobserver agreement again was 98% with kappa correlation coefficient Fig. 2. Remaining Attachment Index (RAI) is measured as described in the SoFCOT symposium [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF] as A/B ratio on AP view where A is the minimal remaining anchorage height and B is the total initial height (A). X-rays of Vancouver B1 periprosthetic fracture with a RAI less than 2/3 (B) and greater than 2/3 (C). 0.96 [0.88-1]. In RAI > 2/3, 2 patients showed implant loosening (8%) versus 9 in RAI < 2/3 (36%), showing a significant correlation between early loosening and RAI < 2/3 (p = 0.005). At last follow-up, none of the patients with implant loosening after internal fixation of Vancouver B1 fracture required implant exchange (Fig. 3).

Discussion

Two of the present patients with internal fixation of Vancouver B1 periprosthetic fracture with RAI > 2/3 developed implant loosening (8%) versus 9 with RAI < 2/3 (36%), showing a significant correlation between early loosening and RAI < 2/3 (p = 0.005). In the literature, internal fixation is the first-line gold standard in Vancouver B1 fracture [START_REF] Giaretta | Diagnosis and management of periprosthetic femoral fractures after hip arthroplasty[END_REF][START_REF] Pavone | Periprosthetic femoral fractures after total hip arthroplasty: an algorithm of treatment[END_REF], despite loosening rates of 19-29% [START_REF] Moreta | Functional and radiological outcome of periprosthetic femoral fractures after hip arthroplasty[END_REF][START_REF] Finlayson | Outcomes and predictors of mortality following periprosthetic proximal femoral fractures[END_REF][START_REF] Chatziagorou | Surgical treatment of Vancouver type B periprosthetic femoral fractures: patient characteristics and outcomes of 1381 fractures treated in Sweden between 2001 and 2011[END_REF].

In the 2005 SoFCOT symposium [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF], internal fixation of Vancouver B1 fracture was assessed comparing RAI > 2/3 versus RAI < 2/3 in a series of 811 patients. In case of RAI > 2/3, fixation was intact at last follow-up in 73% of cases, versus only 31% in case of RAI < 2/3. Prosthetic reconstruction was therefore suggested in case of RAI < 2/3. However, there was no significant correlation between RAI and subsequent implant revision (13% in RAI > 2/3 and 19% in RAI < 2/3). In the present series, none of the patients with implant loosening underwent implant revision. Population characteristics were comparable to those found in the literature, except for mean age at fracture, which ranges between 59 and 76 years depending on the report [START_REF] Beals | Periprosthetic fractures of the femur. An analysis of 93 fractures[END_REF][START_REF] Parvizi | Treatment protocol for proximal femoral periprosthetic fractures[END_REF], compared to a median 89 years in the present series. This may account for the frequent abstention from secondary reconstruction, due to the major risk of secondary complications in case of radiographic loosening [START_REF] Finlayson | Outcomes and predictors of mortality following periprosthetic proximal femoral fractures[END_REF].

The radiological Vancouver classification is reliable and reproducible [START_REF] Brady | The reliability and validity of the Vancouver classification of femoral fractures after hip replacement[END_REF][START_REF] Younger | Periprosthetic hip and knee fractures: the scope of the problem[END_REF]. This was confirmed in the present study, with 98% interobserver agreement and a kappa coefficient of 0.96 [0.88-1] for both fracture classification and RAI measurement. Although RAI is easy to measure and reproducible, fixation is assessed only on AP view, despite most B1 periprosthetic fractures being spiroid, leading to risk of under-or over-estimation of anchorage. It should nevertheless be stressed that preoperative CT analysis of remaining attachment area, ruling out loosening there, did not diverge from the radiographic analysis in all the present B1 fractures. This confirms the findings of Rupp et al. [START_REF] Rupp | Computed tomography for managing periprosthetic femoral fractures. A retrospective analysis[END_REF], that standard CT does not improve assessment of loss of stem attachment, further indicating the relative non-contributiveness of CT in Vancouver B1 fracture if initial X-ray is of good quality and interpreted by an experienced observer.

In terms of treatment, indications in type A or C fracture are straightforward: internal fixation except in case of demonstrable pre-existing loosening [START_REF] Giaretta | Diagnosis and management of periprosthetic femoral fractures after hip arthroplasty[END_REF][START_REF] Pavone | Periprosthetic femoral fractures after total hip arthroplasty: an algorithm of treatment[END_REF]. In type B, the choice between internal fixation and implant exchange is more problematic [START_REF] Chatziagorou | Surgical treatment of Vancouver type B periprosthetic femoral fractures: patient characteristics and outcomes of 1381 fractures treated in Sweden between 2001 and 2011[END_REF]. In B3 or B2 fracture, where fixation is obviously defective and/or accompanied by osteolysis, exchange is logical, as advocated by Berry [START_REF] Berry | Treatment of Vancouver B3 periprosthetic femur fractures with a fluted tapered stem[END_REF], Ko [START_REF] Ko | Distal fixation with Wagner revision stem in treating Vancouver type B2 periprosthetic femur fractures in geriatric patients[END_REF] and Springer [START_REF] Springer | Treatment of periprosthetic femoral fractures following total hip arthroplasty with femoral component revision[END_REF]. Most series focused on internal fixation for B1 fracture [START_REF] Chakrabarti | Cable plate fixation for Vancouver Type-B1 periprosthetic femoral fractures. Our experience and identification of a subset at risk of non-union[END_REF][START_REF] Lenz | Plate fixation in periprosthetic femur fractures Vancouver type B1-Trochanteric hook plate or subtrochanterical bicortical locking?[END_REF][START_REF] Lewis | Tangential bicortical locked fixation improves stability in Vancouver B1 periprosthetic femur fractures: a biomechanical study[END_REF][START_REF] Zhang | Limited open reduction and double plates internal fixation for treatment of Vancouver type B1 periprosthetic femoral fracture after hip arthroplasty[END_REF], but analysing the remaining attachment area is essential to guide indications and avoid long-term loosening and surgical revision. Exchange, on the other hand, is not without risk, notably of increased implant instability, with rates approaching 10%, and of intraoperative fracture, associated with 3.3-11.6% 1-year mortality [START_REF] Finlayson | Outcomes and predictors of mortality following periprosthetic proximal femoral fractures[END_REF][START_REF] Abdel | Epidemiology of periprosthetic femoral fractures in 5417 revision total hip arthroplasties: a 40-year experience[END_REF][START_REF] Spina | Causes of failure in periprosthetic fractures of the hip at 1-to 14-year follow-up[END_REF]. At the same time, unlike exchange, internal fixation does not allow early weight bearing, which can be of poor prognosis in elderly patients [START_REF] Haddad | Periprosthetic femoral fractures around well-fixed implants: use of cortical onlay allografts with or without a plate[END_REF].

Among B1 periprosthetic fractures, we excluded cemented femoral stems; B1 fracture around a cemented stem breaks the cement mantle or detaches the cement from the bone, inevitably entailing loosening [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF][START_REF] Cassidy | Failed osteosynthesis of cemented B1 periprosthetic fractures[END_REF]. Karam et al. [START_REF] Karam | Periprosthetic proximal femoral fractures in cemented and uncemented stems according to Vancouver classification: observation of a new fracture pattern[END_REF] recently reported equivalent results in fractures around cemented or uncemented implants, and argued that surgical treatment should be the same for both.

The present series had short follow-up, but focused exclusively on last-follow-up X-ray, without attempting to assess morbidity and mortality, as was done in other studies [START_REF] Lindahl | Periprosthetic femoral fractures classification and demographics of 1049 periprosthetic femoral fractures from the Swedish National Hip Arthroplasty Register[END_REF]. Longer prospective radiological and clinical follow-up is needed to assess progression in internal fixation with implant loosening, as suggested by Bates et al. [START_REF] Bates | An international, cross-sectional survey of the management of Vancouver type B1 periprosthetic femoral fractures around total hip arthroplasties[END_REF]. A prospective comparative study of internal fixation versus prosthetic reconstruction in Vancouver B1 fracture with RAI < 2/3 would doubtless finally confirm the 2005 SoFCOT recommendations [START_REF] Bonnomet | Periprosthetic fractures around total hip and knee arthroplasty. Classification of femoral fractures on a prosthetic hip[END_REF].

Conclusion

Remaining Attachment Index < 2/3 in Vancouver B1 periprosthetic hip fracture is a risk factor for early implant loosening after isolated internal fixation. In these often frail and elderly patients, first-line implant exchange should be considered in the light of the individual risk/benefit ratio. The present findings confirm the recommendations of the 2005 SoFCOT Symposium and the necessity of rigorous preoperative radiographic assessment of the remaining attachment area in Vancouver B1 fracture.

Disclosure of interest

The authors declare that they have no competing interest.

Fig. 1 .

 1 Fig. 1. PRISMA flowchart.

Fig. 3 .

 3 Fig. 3. X-rays control showing two cases of early implant loosening after isolated internal fixation for Vancouver B1 periprosthetic fracture with a RAI less than 2/3.

Table 1

 1 Patient characteristics and distribution between groups (RAI > 2/3, RAI < 2/3). Non-parametric Wilcoxon test for continuous variables and Fisher test for qualitative variables.

	RAI < 2/3 (n = 25)	RAI > 2/3 (n = 25)	p

RAI: remaining attachment index; BMI: body-mass index; HBP: high blood pressure.

Acknowledgments

Pr Franc ¸ois Bonnomet and Pr Hervé Thomazeau for precious advice and help, and for having launched the 2005 discussion of the Remaining Attachment Index at the SoFCOT Symposium.

Funding

None.

Author contributions

Dr Odri contributed to statistics; Dr Pesenti and Dr Ollivier, to revision; Dr Andriamanaivo and Dr Rongieras, to article writing; Dr Mattesi and Dr Renault, to radiographic analysis; and Dr Severyns, to project management.


Craig S Carlson
email: craig.carlson@wits.ac.za

Ryunosuke Matsumoto

Koji Fushino

Miryu Shinzato

Nobuki Kudo

Michiel Postema

Nucleation threshold of carbon black ultrasound contrast agent

Most ultrasound contrast agents used in ultrasonic imaging comprise shell-encapsulated microbubbles, whose ingredients have been associated with adverse bioeffects. In this study, we investigated the nucleation behaviour of carbon black dispersion, whose hydrophobic nanoparticles are used intradermally. For a hypothetical, perfectly spherical carbon black particle surrounded by a perfectly spherical gaseous void, we derived a theoretical nucleation threshold of only 1.3× the resting radius. Carbon black particles and aggregates thereof were investigated using high-speed photography during 1.0-MHz sonication. The nucleation threshold found experimentally is lower than the Blake cavitation threshold of 2.0× the resting radius of free, unencapsulated microbubbles. Therefore, carbon black dispersion may be a promising ultrasound contrast agent.

Ultrasound contrast agents typically comprise lipid-or albumin-encapsulated perfluorocarbon gas microbubbles. [1][2][START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF] They are injected during sonography with the main purposes of imaging perfusion processes and detecting tumours. [START_REF] Tano | [END_REF][5][6][7][8] Using acoustic transmit amplitudes sufficiently high to generate asymmetric microbubble oscillations, the presence of microbubbles is subsequently detected by means of so-called harmonic imaging. [START_REF] Kudo | Contrast Harmonic Imaging in the Diagnosis and Treatment of Hepatic Tumors[END_REF][START_REF] Kawabata | [END_REF][11] The encapsulating microbubbles shells and the perfluorocarbon gas ensure a prolonged lifespan of the microbubbles by several minutes to hours. 12,13) Without an encapsulating shell, a perfluorocarbon gas microbubble would dissolve in seconds, whilst a nitrogen microbubble would dissolve in milliseconds. 14,15) The main disadvantage of said encapsulation materials is allergic reactions to them. 16,17) Due to the prolonged lifespan of the microbubbles, caution should also be observed when subjecting people to sudden ambient pressure changes post contrast-agent administration, such as flying or scuba diving. Although the acoustic amplitudes required for harmonic imaging have been considered clinically safe, they may inadvertently generate harmonic response from surrounding tissue and associated unintended bioeffects. [18][19][20] Therefore, there has been an interest in ultrasound contrast agents that are safer in use than shell-encapsulated gas microbubbles and that express harmonics at lower acoustic amplitudes, i.e., amplitudes that do not generate tissue harmonics.

Hydrophobic carbon black nanoparticles have demonstrated harmonic behaviour. 21) As the nucleation of carbon black nanoparticles is transient, 22) we hypothesise that harmful cavitation-related aftereffects must be less prominent when using hydrophobic carbon black instead of a microbubble-based ultrasound contrast agent. However, most carbon nanoparticles are not desirable for in-vivo utilisation.

Carbon black pigment dispersion is allowed to be inserted through the skin by means of needles for cosmetic reasons -the inking of a tattoo. 23) In solid state, it comprises nanoparticles or nanoparticle aggregates with a mode diameter of 0.24 µm and a maximum diameter of 0.97 µm. 24) In solution, a hydrophobic particle takes up its own volume plus a surrounding void. 25) Consequently, in solution, the carbon black pigment dispersion nanoparticles or aggregates thereof were measured to have a mode diameter of 0.29 µm and a maximum diameter of 1.14 µm. 24) In carbon black dispersion, the gaseous void surrounding the hydrophobic solid nanoparticle takes up approximately 20% of the diameter. 24) The linear resonance frequencies of these suspended nanoparticles were estimated to be greater than 15 MHz. 24) In a recent feasibility study, we found that carbon black pigment dispersion under sonication demonstrates transient nucleation. [START_REF] Carlson | Proc. 41th UltraSonic Electronics Symp[END_REF] In this follow-up study, we investigated the nucleation threshold of carbon black pigment dispersion nanoparticles both theoretically and experimentally.

Let us assume a perfectly spherical hydrophobic particle in suspension in an infinite liquid.

Its resting radius including polytropic gaseous void is R 0 , whilst its incompressible solid core radius is R c . The instantaneous surface pressure p s as a function of instantaneous radius R is equal to

p s (R) = p g (R) + p v -p L = 2σR R 2 -R 2 c , (1)
where p L the absolute pressure in the liquid at the bubble surface, p g is the gas pressure inside the void, p v is the vapour pressure inside the void, and σ is the surface tension at the void-liquid interface. If there is no disturbance in the liquid pressure, i.e., if the particle is at rest, p L = p 0 , in which p 0 is the ambient pressure, close to 1 atm.

Following the derivation of the cavitation threshold of a free bubble, [START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF] if buoyancy and

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A c c e p t e d M a n u s c r i p t gas diffusion are slow with respect to a change in ambient pressure,

p g V γ = constant , (2)
where

V = 4 3 π R 3 -R 3 c
is the instantaneous void volume and γ is the ratio of specific heats of the gas. For air, γ = 1.4 is a good approximation. [START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF] Substituting (1) for the gas pressures yields

p 0 -p v + 2σR 0 R 2 0 -R 2 c V γ 0 = p L -p v + 2σR R 2 -R 2 c V γ , (3)
where

V 0 = 4 3 π R 3 0 -R 3 c
is the resting volume of the void. Rewriting V 0 and V in terms of R and reordering gives an expression of the absolute liquid pressure as a function of instantaneous void radius:

p L (R) = p 0 -p v + 2σR 0 R 2 0 -R 2 c R 3 0 -R 3 c R 3 -R 3 c γ + p v - 2σR R 2 -R 2 c . (4)
The function p L (R) has a minimum in point R θ , p θ . If the liquid pressure is lowered below the critical threshold pressure p θ , corresponding to threshold radius R θ , there is no equilibrium for (4), which results in explosive expansion of R.

For microbubbles, R θ ≈ 2.0 R 0 , which is referred to as the Blake cavitation threshold. [START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF] A temporal pressure change ∆p(t) = p L (t)p 0 can be generated by an acoustic wave ∆p(t) = p a sin(2π f t) of frequency f and pressure amplitude p a . For the pressure change to be quasi-isostatic, f must be much less than the resonance frequencies of the suspended nanoparticles. [START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF] Using ∆p(t) as a driving function and following the derivation for an oscillating antibubble, [START_REF] Kotopoulis | [END_REF] the fundamental equation of spherical hydrophobic particle dynamics is found to be

R R + 3 2 Ṙ2 = 1 ρ       p 0 -p v + 2σR 0 R 2 0 -R 2 c R 3 0 -R 3 c R 3 -R 3 c γ + p v - 2σR R 2 -R 2 c -p 0 -∆p(t)       . ( 5
)
Assuming a low driving amplitude, the linear resonance frequency f r of a spherical hydrophobic particle follows to be

f r = 1 2πR 0 √ ρ 3γ p 0 -p v + 2σR 0 R 2 0 -R 2 c 1 -R c R 0 3 - 2σR 0 R 2 0 -R 2 c , (6)
which is similar to the linear resonance frequency of an unencapsulated antibubble. 28) The radial dynamics of antibubbles subjected to higher acoustic amplitudes have shown to be highly nonlinear. 28) Leaving out R c from (6) gives us the linear resonance frequency of a free Solutions of ( 4) and ( 6) were computed using MATLAB ® (The MathWorks, Inc., Natick, MA, USA). It was assumed that p 0 = 1.0 atm, p v = 1.0 kPa, R c = 0.80 R 0 , γ = 1.4, and σ = 0.072 N m -1 . From ( 6) it followed that a particle of outer diameter 2R 0 ≤ 1.14 µm and core size R c = 0.80 R 0 must have a linear resonance frequency f r ≥ 15 MHz. This is more than double the frequency of a free gas bubble of equal size.

The experimental procedure was identical to the experimental procedure described in From each tube, 0.2 mL was pipetted into the observation chamber of a high-speed observation system. 29) The observation chamber was placed under an Eclipse Ti inverted microscope (Nikon Corporation, Minato-ku, Tokyo, Japan) with a CFI S Plan Fluor ELWD 20XC objective lens of 20× magnification and 0.45 numerical aperture. Attached to the microscope was an HPV-X2 high-speed camera (Shimadzu, Nakagyo-ku, Kyoto, Japan), operating at frame rates equal to or greater than two million frames per second. [START_REF] Imai | Proc. IEEE Int. Ultrason. Symp[END_REF] The maximum exposure time corresponded to 0.50 µs per frame. During camera recording, the material was subjected to ultrasound pulses.

A laboratory-assembled single-element transducer produced focussed ultrasound pulses. 29,[START_REF] Imai | Proc. IEEE Int. Ultrason. Symp[END_REF] Each pulse had a centre frequency of 1.0 MHz. It is noted that 1.0 MHz 15 MHz, so the pressure changes in the liquid could be considered quasi-isostatic. The voltage amplitudes of the pulses were varied from 1 V to 5 V, with 1 V increments. In a running wave field, these voltages corresponded to peak-negative acoustic pressures between 0.20 MPa and A total number of 87 high-speed video sequences were recorded during five imaging sessions. Each video sequence consisted of 256 frames. The video sequences were stored on a personal computer and processed offline using the onan.m programme in MATLAB ® . In the first frame of a sequence, the rectangular area of a particle i to be sized was selected manually, after which automated adaptive thresholding was used to measure the particle cross-section areas A i j per frame j. [START_REF] Bradley | [END_REF] The particle radii R i j as a function of time t j were computed from

R i j (t j ) = A i j π .
Particles oscillating out of phase with respect to the incident sound field were classified as non-nucleating, whilst particles undergoing a phase shift during sonication were classified as nucleating.

Figure 1 shows solutions of (4), expressed in ∆p as a function of R R -1 0 . The curves had been particle sizes prior to sonication and during maximum rarefaction. Particles 1 and 2 were observed to nucleate during the third and fourth sonication cycle, respectively. Particle 1 had a maximum expansion of R max =8×R 0 during its first nucleation cycle, whilst particle 2 had a maximum expansion of R max =9×R 0 during its first nucleation sonication cycle. Particle 3, not shown in the frames but represented by the dashed R(t) curve, was observed to undergo volumetric oscillations with an expansion amplitude R max =1.6×R 0 during sonication, 1 2 π out of phase with respect to the incident sound field, but without explosive growth. During subsequent ultrasound pulses, the ink particles that had been involved in this nucleation cycle remained unaffected (not shown). explosive growth, the maximum expansion during the first nucleation cycle was taken for R max , whilst for the remaining particles, the greatest expansion over all oscillation cycles was taken. All but one particle not undergoing explosive growth had a maximum expansion R max ≤ 1.75R 0 . Although the exact nucleation threshold could not be determined, these results confirm that the nucleation threshold is lower than 2× the resting radius.

Only the manually suspended ink particles demonstrated nucleation activity, whereas not a single recording of ink suspended with the ultrasonic cleaner showed nucleation. These results agree with our observations of other hydrophobic particles. 22) Tattoo ink particles were observed to lose part their gaseous shells. Up to five subsequent ultrasound bursts were observed to reinitiate nucleation of the same particle at the same acoustic amplitude. Sonication at a higher acoustic amplitude was also observed to renucleate particles that had stopped nucleating in a lower-amplitude regime.

It is concluded that ultrasonic nucleation of carbon black pigment dispersion nanoparticles is a transient phenomenon. The theoretical nucleation threshold of a perfectly spherical particle surrounded by a perfectly spherical gaseous void is 1.3× the resting radius of the hydrophobic nanoparticle in suspension. This is lower than the Blake cavitation threshold of

3 / 10 A

 310 c c e p t e d M a n u s c r i p t gas bubble for comparison.

Ref. 22 ,

 22 except for the compound under investigation and the camera frame rates. A quantity of 0.50 µL Zuper Black pigment dispersion (INTENZE Products, Inc., Rochelle Park, NJ, USA) was pipetted into a FALCON ® 15 mL High-Clarity Polypropylene Conical Tube (Corning Science México S.A. de C.V., Reynosa, Tamaulipas, Mexico), after which 5.0 mL of 049-16787 Distilled Water (FUJIFILM Wako Pure Chemical Corporation, Chuo-Ku, Osaka, Japan) was added. Tubes were either gently manually shaken for 5.0 minutes, or individually held for 1.0 minute in a 2510J-MT BRANSONIC ® ULTRASONIC CLEANER (BRANSON ULTRASONICS CORPORATION, Danbury, CT, USA) filled with degassed water and operating at a transmitting frequency of 45 kHz. The sonically shaken tubes were used as controls.

1. 0

 0 MPa, equivalent to mechanical indices between 0.20 and 1.0. 3) To avoid a standing-wave situation, we only took the first eight ultrasonic cycles into account. The time between subsequent experiments was at least one minute. The signal fed into the transducer was generated by an AFG320 arbitrary function generator (Sony-Tektronix, Shinagawa-ku, Tokyo, Japan) and 4/10 A c c e p t e d M a n u s c r i p t amplified by a UOD-WB-1000 wide-band power amplifier (TOKIN Corporation, Shiroishi, Miyagi, Japan).

Fig. 1 .

 1 Fig. 1. Quasi-isostatic liquid pressure change ∆p as a function of R R -1 0 , computed for the mode particle diameter (-) and the largest particle diameter (-) of carbon black pigment dispersion. A red dashed line is drawn through the minima, for which R θ R -1 0 = 1.3 holds (--).

Figure 2 Fig. 2 .

 22 Figure 2 shows representative R(t) curves from a high-speed video recording of Zuper Black dispersion particles. The frames were selected from the full video sequence, to illustrate

Figure 3 Fig. 3 .

 33 Figure 3 shows a histogram maximum expansion results of Zuper Black dispersion particles under sonication, normalised by their resting radii. For particles visibly undergoing

7 / 10 A

 710 c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t

Acknowledgements

This work was supported by JSPS KAKENHI, Grant Numbers JP17H00864 and JP20H04542, and by the National Research Foundation of South Africa, Grant Number 127102.

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free, unencapsulated microbubbles. AUTHOR SUBMITTED MANUSCRIPT -JJAP-S1102048.R4

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