To develop a mobile app that allows capturing and editing of photographs, performs image transposition and projection of a protractor with 360° axis markings, and permits accurate visualization of programmed alignment for the positioning of toric intraocular lenses (IOLs).  In this prospective case series study, a codesign methodology was chosen to develop the Eye Axis Check application. After app development, measurements were obtained and comparisons were made between manual marks and toric IOL alignment without and with the app in 30 eyes that had undergone cataract surgery with toric IOLs. The mobile app was made available to 15 ophthalmic surgeons in different cities to assess its usability.  The users approved the developed application for its ease of use and utility. The mean difference between the markings made manually and those made with the app was 1° , and the mean difference between the IOL position and the assessment made by the app was 3° . Upon comparison of the agreement between the app measurements and the manual measurements for the IOL angle, no significant differences were found, and an excellent concordance (0.997) and a strong positive linear correlation (0.995) were observed.  A mobile app for preoperative planning and intraoperative toric IOL alignment was developed and revealed to be useful and easy to use. Treatment of corneal astigmatism is an important factor in cataract surgery, since residual astigmatism may compromise a patient's uncorrected visual acuity after surgery. It has been estimated that 30% of patients with cataracts have more than 0.75 D of corneal astigmatism, that 22% have more than 1.50 D, and that 8% have more than 2.00 D [Ophthalmic applications are making the smartphone a medical tool, and there are more than 342 eye-care applications available. From 2009 to 2012, there was a 9-fold increase in the number of surgical applications available on smartphones [This study aimed to develop a mobile app to verify the marking of eyes planned for cataract surgeries with toric IOLs and to aid in the visualization of correct IOL alignment.The study was carried out in accordance with the protocol number 62660116.3.0000.5049, approved by the Research Ethics Committee of Christus University Center (Unichristus), and the ethical principles that govern the Declaration of Helsinki.The work was divided into three stages: development and creation of the mobile app, realization of the study with a series of surgical cases in which the application was used and the results were documented and analyzed, and evaluation of the usability of the application as indicated by different surgeons in their responses to a validated questionnaire.XY axis. It is even possible to take a new photograph of the eye to see if the implants are correctly positioned.The measurement process is based on a previously taken reference photograph of the eye at the 0–180° position and on subsequent comparison of the implant. The positioning of the photograph is guided by a bubble-level system that uses the inclinometer available on the hardware of the smartphone to obtain a properly aligned image. Even so, there is the option to make subsequent adjustments in the markings by making use of a line that can be moved and rotated in the Clicking on the IOL Module option during phacoemulsification with toric IOL implants takes the user to a screen with three new keys: “Surgical Planning,” “IOL Position Photographing,” and “IOL Axis Analysis”; in addition, a tutorial is available through the “Tutorial” key in the upper right corner.Clicking on the Marking 0°–180° key opens the next screen, which allows the user to photograph the 0°–180° markings already made in the patient's eye with a manual marker . When selecting “Photograph Marking,” the user should be positioned in front of the patient with the 0°–180° marking already made in the eye. After the patient's eye has been photographed with the 0°–180° markings, the “Adjust Marking” screen allows the user to adjust the photograph, so it overlays the markings made in the patient's eye . The appK1) and the steepest axis (K2) of the cornea are also recorded. In addition, the user can see a simulation of the surgical plan in a graphical format when the proper surgical planning data and patient information are recorded .When the patient is on the surgical table, a second marking is made that refers to the position of the axis of the lens with a Mendez ring; alternatively, according to the routine of the surgeon, this may have already been done with one of the various manual markers on the market. The surgery is performed, the toric IOL is implanted as planned, and a photograph of the TV monitor coupled to the surgical microscope chamber is acquired by clicking “Photograph IOL Position”; this again accesses the camera of the device, and the mobile protractor and bubble level can be referenced to guarantee the correct alignment of the hand at the moment of the photo .There is an option to save to the camera roll or print the image. In the upper left corner, there is another small circular key with the shape of an intraocular lens, selection of which allows the user to verify the markings against the surgical plan by overlapping the IOL images, incision positions, and corneal meridians from the surgical planning stage. This step completes the target alignment of the axes for intraocular lens implantation.t-test for paired data was used to compare the two methods.IOL angle measurements were performed on 30 eyes. A Individuals underwent cataract surgery with toric intraocular lens implantation by the same surgeon at the Ceara Vision Institute from March to October of 2018 with the due consent of the institution and after free and informed consent was provided by each participant in the study.The inclusion criteria included cataract and regular astigmatism of more than 1.25 diopters. Subjects with cataract who had irregular astigmatism or regular astigmatism of less than 1.25 diopters and those who refused to sign the informed consent form were excluded from the study.The app was used, measurements were obtained, and comparisons were made between the manual marks and toric IOL alignment without and with the app. Manual marking was performed using conventional toric marking tools .The mobile app was made available to 15 ophthalmologic surgeons in different cities. Through a usability test, the study aimed to determine whether the participants could verify the alignment of the marks before and during cataract surgery with implantation of toric lenses to correct astigmatism.There are different standardized questionnaires available in the literature to evaluate the responses of participants of usability tests that are capable of assessing the quality of different characteristics of a system. Our questionnaire was a modified form of the Technology Acceptance Model (TAM) implemented by Davis in 1986 . This quIn this test, answers to the following questions were determined: if the app for measuring the alignment of markers preoperatively and intraoperatively via mobile phone was viable; if the results obtained with the mobile device were comparable to those obtained with traditional methods; if the markings were unaffected; if the time needed to carry out verification with the app was a limiting condition for its use; if the developed system presented good levels of usability; if there were good levels of usefulness for clinical practice; and what the positive aspects, negative aspects, and suggestions for improvement to the presented app were.The questionnaire was sent online to participants using the Google Forms template, through which it was possible to access real-time responses.r) analysis. The agreement between the manual and the app method measurements was also evaluated by the Bland–Altman graphical method.The measurements of the IOL axis made with the app and by the manual methods were initially analyzed with the Shapiro–Wilk test. With regard to descriptive statistics, the mean and standard deviation were calculated, and nonparametric methods were used for statistical analysis. Comparisons of IOL axis measurements between the app and the manual methods were performed using the Wilcoxon test for paired data. The intraclass concordance coefficient (ICC) and its 95% confidence interval were used to evaluate the agreement between the manual and app axis measurements. The degree and direction of the linear correlation between the manual and application method measurements were, in turn, evaluated by Spearman correlation coefficient . GraphPad Prism software version 6.00 for Mac  was used to implement statistical procedures and for graphing.In all analyses, a significance level of 5% was considered to indicate statistical significance . The ICC calculation was based on a two-factor model in which both factors were random: the 30 participating cases for IOL implantation and the 2 measurement methods (random two-factor model).The degree of agreement between the measurements obtained by the two methods was evaluated by the intraclass correlation coefficient (ICC). The ICC values showed excellent agreement between the measurements of the IOL angle  values showed a strong positive linear correlation between the measurements obtained by the two methods for the toric IOL angle .The degree and direction of the linear correlation between the measurements obtained by the two methods were measured by Spearman correlation coefficient analysis. The Spearman coefficient . These findings indicated that the agreement between the measurements obtained by the two methods was very good .Thirteen of 15 colleagues who tested the Eye Axis Check app answered the usability questionnaire. Two colleagues reported that they had not had the opportunity to perform toric IOL implantation in a timely manner.The questions evaluated the utility of the application as perceived by the participants, and the answers are summarized in A meta-analysis in 2016 of 13 randomized clinical trials concluded that toric lenses were more effective in reducing astigmatism than monofocal lenses in patients who underwent cataract surgery with or without the use of intraoperative relaxing incisions [Inaccuracy of measurements of the eye obtained during preoperative examinations, inaccuracy of the orientation of the intraocular lens relative to the desired or calculated target and, to a lesser extent, rotation of the intraocular lens postoperatively are the main causes for the appearance of residual astigmatism . If the Toric lenses have different optical powers for different meridians, so they must be correctly aligned to neutralize corneal astigmatism . There aP < 0.001). The toriCAM application for smartphones could improve the accuracy of preoperative marking methods for toric intraocular lens alignment [In a prospective randomized study, 22 participants were randomly allocated into two groups to compare the methods for toric intraocular lens marking (both free-hand and slit-lamp), and subsequently, the values obtained were compared to those obtained with the toriCAM application. The mean absolute error of all markings prior to toriCAM adjustment was 3.18° ± 2.22°. This was reduced to 1.28° ± 1.34° after use of the application  under protocol number BR 512017001573-2 (Eye Axis Check).However, this study has some limitations. In the initial model of the proposed app, some features could have made the application more complete. For example, the lack of ability to store images for successive patients from the same surgical day and the lack of ability to connect the application to another device that could do so forced the users to delete each case before adding another. This deficiency has been mitigated by the possibility of saving the images to the camera roll of the smartphone or printing them. Nevertheless, the scope of the application, enabling access to the calculators of the main intraocular lens manufacturers, and the diversity of language options in a single application, including Portuguese, English, and Spanish, enrich and will tend to broaden interest in the application. In addition, it is possible to create a surgical plan for a procedure; the plans can be printed, taken to the surgical center, and overlaid at the end of the measurement, enabling assessment of the result. Similar to the case in the tests carried out by the developer, the literature has shown misalignment of toric lens axis markers created with manual markers during cataract surgery .In the case series, the data obtained by the app presented a minimal standard deviation from the target axis of the intraocular lenses relative to the manual 0°–180° reference mark. When the Wilcoxon test for paired data was applied, no single set of data presented a statistically significant difference between the two methods. However, the findings had important clinical relevance, since 3 degrees of IOL deviation cause an approximate loss of 10% of astigmatism correction .r) values revealed a strong positive linear correlation between the measurements obtained by the two methods for the IOL angle. The degree of agreement measured by the Bland–Altman graphical method between the markings made with the application and the manual method with respect to the IOL angle were very well correlated.The Spearman coefficient (Through a usability test, it was finally demonstrated that the participants of the study could verify the alignment of their markings preoperatively and intraoperatively in the context of cataract surgery with toric IOL implantation, indicating that the application is useful in phacoemulsification surgeries with toric IOL implants.Eye Axis Check, a mobile app for preoperative planning and intraoperative toric IOL alignment, was developed and revealed to be useful and easy to use. The usability test demonstrated good acceptance of the device by different surgeons participating in this study. Errors in both the 0°–180° marking and the IOL angle, when present, were detected by the application. In addition, assessment of the application did not reveal any statistically significant differences between the application-assisted markings and the manual markings relative to the 0°–180° reference marks.


Scientific know-how is currently being mobilised worldwide at full speed to better understand the medical mechanisms of COVID-19 propagation and to develop a suitable vaccine. The technological options for working from home, digital coordination and virtual learning are currently experiencing a completely new push. At the same time, the economy is moving towards a crisis situation that threatens to dwarf the 2008/2009 financial crisis. Companies and freelancers are facing a dramatic challenge—in maintaining supply chains and production, but especially in dealing with collapsing demand. At the same time, a mix of policy measures for short-term economic stabilization is emerging, which again exceeds the scope of emergency measures taken after the financial crisis.Politically and institutionally, the state intervenes at the national and regional levels in ways never practiced before: entry bans, bans on events and assemblies, business closures and even curfews. The demands on the political leadership especially in open and democratic societies are immense. This is due to the fact that the Corona crisis in particular requires an enormous amount of solidarity. 80% of the population, who have only minor health problems to fear from the virus, show solidarity with 20% in particularly vulnerable population groups. The fabric of values in our societies is facing a major test—especially if emergency measures are to last for a long time.The examples outlined above show that the Corona crisis challenges the ability to shape the future in a special way. The Wuppertal Institute’s guiding framework for a “Zukunftskunst”, a future literacy, associates technological with economic, political and cultural changes and thus also provides orientation in the current crisis. Presumably there has never been more demand for “Zukunftskunst” in politics, economy and society than there will be in the coming weeks and months Fig. .Fig. 1ThOne thing must not be forgotten: The Corona crisis is hitting the world at a time when a large number of enormous challenges have to be solved. This applies to the correct handling of the growing number of refugees and the elimination of social inequalities as well as, from an environmental policy perspective, to coping with the consequences of climate change and mitigating further changes in the climate. In addition, there are questions such as how to manage the transition to the digital age and how to close material cycles by means of increasingly circular forms of the economy—examples of long-term trends in which everyone (currently) finds themselves. In all areas, massive investments and a proactive design of the associated, sometimes massive, structural changes are required.foremost on health care. The aim is to contain a global Corona pandemic and avert hundreds of thousands of deaths. That is why health protection measures are currently so important.In the coming weeks, the focus will undoubtedly be first and economic consequences have to be absorbed in the short term with appropriate instruments. These include the measures that have now been adopted by many countries, such as the short-time working allowance, easier access to credit, tax deferrals and state guarantees, as well as direct payments to affected groups, such as the assumption of rental costs, compensation for loss of production costs or income. This must ensure that companies remain capable of acting and can contribute to the economic recovery after the crisis.At the same time, the massive long-term crisis management and refers to the aspects that are related to the economic and structural need for action resulting from the effects of the Corona crisis. These range from economic stimulus packages to revive the economy to fundamental structural adjustments, for example in the design of global value chains or a crisis-proof development of social security systems. It is important to think about this third phase at a very early stage, while keeping a firm eye on other global transformation challenges such as climate change. Early planning and a holistic perspective can avoid some of the failures in dealing with the consequences of the financial and economic crisis of 2008/2009.The third phase is Against this background, it is important not to lose sight of the long-term challenges for the future when dealing with the Corona crisis. Three phases are likely to characterise the management of the Corona crisis see Fig. :In the cThis paper is intended to provide the first building blocks for this third phase. It was published in German on 20 March 2020 by the Wuppertal Institute. Comments and contributions to the discussion are welcome.If economic stimulus packages are launched as a follow-up to or accompanying the Corona crisis, it is important that these are developed with a direct focus on the future and that the funds spent are not distributed without explicit targeting. In other words: clear criteria are needed to which the measures can be aligned. Whereas, in accordance with the phase concept , but most of the mechanisms apply to all industrialised countries that have been struggling to meet their climate targets.2 emissions or the CO2 equivalent emissions in the years 2018 and 2019 considered here. CO2 equivalent emissions include not only CO2 emissions but also emissions of other greenhouse gases—such as methane and nitrous oxide—which, for the most part, have a much greater impact on the climate than CO2 as a greenhouse gas. In Germany, emissions fell by 6.3% last year alone. In absolute terms, emissions fell by 54 mio. t CO2e between 2018 and 2019 and were still at 804 mio. t at the end of the year. The majority of 51 mio. t of CO2e can be traced back to the energy industry sector, again due to a combination of three effects:2 certificates—partly as a result of adjustments to the rules in the European Emissions Trading System, i.e. the market stability reserve,a significant increase in the price of COa sharp drop in natural gas pricesand an intensifying discussion on how to shape the phase-out of coal-fired power generation .In climate protection, there is still a clear gap between objectives and reality. This is true regardless of the recent significant reduction in COOverall, this led to a displacement of coal-fired power plants in the electricity mix in favour of natural gas power plants and renewable energies. In 2019, we dealt with an extremely good wind and sun year, so that the contribution of renewable energies to electricity generation increased, although in contrast to previous years  only a smaller increase in capacity was recorded.Overall, German greenhouse gas emissions fell by 35.7% between 1990 and 2019. If the potential effects of the Corona crisis are taken into account, it does not appear unrealistic that a significant reduction in emissions in 2020 would lead to a reduction of 40% or more compared to 1990 and thus to formally achieve the national climate protection target for this year. For the potential effects to be expected from the Corona crisis are already clearly perceptible after just a few days.Which energy-economic and climate-political effects of the Corona crisis are to be expected or are already obvious? First and foremost, industrial production is declining drastically, as evidenced by entire plant closures in the automotive industry. This reduces industrial energy requirements which can be seen very clearly in the electricity demand, which in turn leads to reduced emissions in the provision of energy/electricity. Initial experience from Italy and France shows that, as a result of the very drastic, but nevertheless necessary, measures taken at the beginning of March, the demand for electricity fell by 10% (France) and 20%  compared with the reference values from previous years. Incidentally, this is also in line with experience gained during the financial market and economic crisis in 2009. In Germany, the effects have been less severe so far, but here too there is already a tendency for demand to fall, with corresponding effects on the electricity price, which fell by around a third within a few days on the Leipzig Power Exchange (EEX) in mid-March (the figures apply to short-term futures contracts). In addition, mobility-related emissions have also been reduced, for example as a result of the increased transition to the home office, even though clear figures are still missing. Is climate protection on the right track and can everyone sit back and relax? The clear answer is no, for several reasons:The Corona effect will hopefully remain a one-off effect, and there will probably even be a catch-up development with increased emissions if it is possible to quickly limit the spread of the virus and gradually return to normality.2 certificate prices in both years, winter months with extremely mild temperatures, and a pull-forward effect on the closure of coal-fired power plants.Even the sharp declines in greenhouse gas emissions in 2018 and 2019 cannot be sustained and repeated as often as desired. These are partly due to one-off effects or would require great political courage to repeat on a similar scale. This is because a decline on the scale of 2019 has not yet occurred in Germany outside the economic crisis of 2009. These one-off effects include a five- to sixfold increase in CO2 emissions have not fallen but have actually risen since 1990.And thirdly, there is a strong imbalance between the sectors that contribute to mitigation and others for which there is a clear need to catch up. The latter applies to the building sector but even more so to the transport sector. While emissions in the building sector have increased by 4.4% from 2018 to 2019, the increase in the transport sector was only 0.7%. It should not be overlooked though that the transport sector is the only sector where COthe future will require more rather than fewer measures, a high degree of continuity and extensive investment. There is therefore a strong case for an economic stimulus package by the EU, the German federal government and the German federal states in the aftermath of the Corona crisis  to 50 or even 55%. It is hardly conceivable that this can be done without adjusting the national German target. To this extent, the conversion of steel production to hydrogen-based (green) production processesthe entry into a hydrogen economy as a whole,the successive but consistent closing of material cycles within the framework of a circular economy,the electrification of transport the complete change to an entirely renewable power/energy supplyand the consistent use of digitisation as an enabler for the central transformation arenas of our time .However, the measures must go far beyond this and state investments, especially in the industrial sector, must be used to make the various sectors  ready for the future. This includes among other thingsBut when, if not now—in times that are extraordinary for the economy anyway—should be a very good opportunity to accelerate and proactively accompany the transformation processes that are necessary anyway?There is no question that this will bring about further massive structural changes in our economic cycles (including those induced by the Corona crisis). It is time, otherwise there is a great danger that one crisis will be replaced by another massive global crisis—the climate crisis. We can already be sure that the climate will continue to change and that we will have to get used to higher temperatures in Germany as well. On the basis of new forecasting models based on statistical estimates, the German Weather Service expects that by 2029 it could become 1.5 to 2 ℃ warmer on average in Germany than the average of the last three decades. But we still hold the key to action. It should be used for the benefit of the climate and ultimately also for the benefit of German industry, which can take on a pioneering role, to position itself for the future through climate protection and climate adaptation measures and thus also to firmly establish itself in the climate protection markets of the future.to the reflection of consumption and behavioral patterns,the reduction of vulnerabilities through globally networked value chains in central production areas andthe crisis-proof provision of products and services of general interest and basic services, such as goods for the health system.In view of the long-term transformation challenges, it is also important to seize the opportunity to learn further lessons from the Corona crisis. This applies:Already in the first weeks of the crisis new forms of digital work and digital learning are gaining considerable importance in practice—we are also learning how they can be integrated into everyday life in the long term.The crisis also shows under which conditions people are prepared to make considerable adjustments and show solidarity. All of this will improve our understanding of societies in comprehensive transformation processes and will also be helpful for the climate debate.However, it is also clear that technical and economic systems must become more robust. This applies, for example, to the resilience of infrastructures (e.g. energy infrastructures), which form the backbone of our society. The Corona crisis shows how vulnerable many of our production processes are, which have to be closed down or scaled back, among other things, because the supply chain is no longer available as a result of disappearing imports. One of the central questions will be to what extent and how quickly regional production structures can be established and how the economy and society as a whole can become more resilient. In the infrastructure sector, one possibility is the expansion of renewable energies, which are almost always highly decentralised, and the possibility of coupling them with battery systems and thus building up self-sufficient systems at least partially. This must be combined with reinforcement measures in the electricity grid and the integration of intelligent systems (smart grid).In the context of the Corona crisis, one also becomes acquainted with new behavioral patterns, or appreciates previously known but not yet widely used options. This is especially true for the home office, which suddenly becomes the norm for many. Associated with this is a significant reduction in traffic volume , which at the same time contributes to climate protection and to improving air quality in cities. The latter, incidentally, has a dual significance, since according to statements by the European Public Health Alliance (EPHA) and others, the Corona virus is particularly dangerous for people with pre-existing conditions, and those are often related to poor air quality in cities.Firstly, it will clearly be a major challenge for many companies to reinvest and get the economy going after such a significant economic shock. But dealing with the economic and financial crisis at the time has shown that this is not the case: With wise political support, a faltering economic system can be quickly mobilised again. This is why the measures announced by the German Federal Government (and similarly in many other countries) are important and right.Secondly, even during the period of the economic and financial crisis, there was a significant reduction in greenhouse gas emissions, but the measures and government incentives implemented thereafter led to such a strong rebound effect that emissions rose even more sharply thereafter. This is something that must be avoided in this case.It is to be hoped that, on the one hand, the Corona crisis will be overcome quickly and that as few people as possible will suffer as a result. At the same time, there is a chance that some of the newly learned patterns of behaviour will continue to exist and may have a positive effect in several respects in the future—also in preparation for further pandemics, which cannot be ruled out. With the right orientation of aid measures after the end of the Corona pandemic, the central course can be set for making the state, economy and society more resilient and at the same time taking important steps towards solving the other major transformation challenges, for example through low-carbon investments. Two lessons can be learned from the 2009 economic crisis:In view of the initially limited investment opportunities due to the economic crisis, it is also important to bear in mind that many climate protection measures do not primarily depend on investments, but are rather related to behaviour and lifestyle. Especially with regard to this form of climate protection, many learning effects can be taken away from the crisis.


This article accompanies the study presented in Triulzi et al. (2020) [1]. It briefly describes and makes available the data on functional performance for 30 technology domains, their patent sets, the measurement of patent centrality and the method to estimate the yearly technology performance improvement rate (TIR) that underly that study. Some of this data (performance time series and the lists of patents for 28 domains) has been collected by other authors for previous studies but were previously unavailable to the public. Measurements of patent centrality and other patent-based indicators for the 30 domains, and for 5.259.906 utility patents granted by the United States Patent and Trademark Office between 1976 and 2015 are novel data contributed by Triulzi et al. (2020) [1]. Here we organize, describe and make available the collection of data in its entirety. This allows anyone interested to replicate the study or use the method to estimate the improvement rate of a given technology for which patents can be identified. For a detailed description of the data and methods see Triulzi et al. (2020) [1]. Furthermore, it provides carefully selected patent sets for 30 technology domains and a variety of indicators that can be used to predict technologies’ improvement rate or for empirical studies of technology evolution along defined technological trajectories.•This data is of interest to scholars and practitioners studying technological change. It can also be used for pedagogical purposes in courses on technology monitoring and intelligence and econometrics of technological change.•Patent centrality measurements for 5.259.906 USPTO granted patents can be used to estimate TIRs for technologies for which we do not have reliable time series of their performance evolution, following the method described in Triulzi et al. (2020) •The data can also be used to test alternatives predictors of the technology improvement rate, using those tested in the papers Triulzi et al (2020) •and use the same scientific principles, as opposed to commonly used classification systems that only rely on one of the two definitions.The added value of the patent data provided, compared to patents retrieved for given technology classes  is that our data is grouped in technology domains, whose definition includes artefacts that achieve the same function 1http://dx.doi.org/10.17632/f4fj887y67.1All .csv and .xlsx files described in this paper are available in Mendeley Data repository at 1.1In 2 of the linear fit on a log-linear plane, as a measure of the goodness of fit of the exponential hypothesis, and the estimated TIR coming from patent data. The latter is obtained using the method briefly summarized in Section 3.2 of this document and explained at length in Triulzi et al. (2020) 1.2Finally, 2Patent sets for the 30 technology domains were used to compute several patent variables, which, in turn, were tested as predictors of the technology yearly improvement rate (TIR). Each variable was computed in its raw form and in a normalized form. They were then included as independent variables in a regression that estimated TIRs. The full description of the methods used can be found in Triulzi et al. (2020) 2.1https://www.patsnap.com/). Then, basic information on their filing and grant year, classifications and their citations (made and received) were downloaded from Patentsview (https://www.patentsview.org). We then removed from the list re-issued patents, applications and non-utility patents. After that, we computed raw and normalized versions of the variables described in all the variables computed publicly available, in case users would like to experiment with them.2.2For each variable included in the file “Domains_patent_info.csv”, for each technology domain, we computed the mean value including only patents granted up to that year. We then performed a Monte Carlo Cross-Validation exercise in which we sampled randomly half of the 30 domains (creating a training set), trained a regression with that single variable as predictor of the improvement rate and then tested the performance of the regression to predict the improvement rate for the testing set of the remaining half of the domains. We did this for all years up to 2015. This exercise allow determining that two centrality variables were the predictors that ensured the most accurate estimation of the improvement rate and the least reliable on the domains included in the training test or the period of time for which the mean patent variables were computed. Finally, we estimated the full regression coefficients when including all data at disposal  and selecting the best predictor only. That regression, combined with data in the file “All_patents_info.csv”, can then be used to estimate the improvement rate for technology domains for which we only have patent data and no empirical observation of their functional performance. The estimating equation and its coefficients can be found in Triulzi et al. (2020) The authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the work reported in this article.


This paper describes the theory and development of Take it personal! an indicated prevention programme aimed at reducing substance use in individuals with mild intellectual disabilities and borderline intellectual functioning.The process of the development of Take it personal! followed the steps of the Intervention Mapping protocol. Take it personal! is based on the theory that personality traits are an important construct to understand substance use (14–30 years old). A small modelling study was conducted with six adolescents to examine the feasibility, user‐friendliness and potential effectiveness of the intervention.The results showed that the intervention has good feasibility and user‐friendliness. Post‐intervention evaluation of frequency, binge drinking and problematic use indicated that use was lower than at pre‐intervention.Take it Personal! can be a promising preventive intervention designed to reduce substance use in individuals in this target group. A larger scale study is needed to draw further conclusions. The secondary aims of Take it personal! were to decrease the intention to use alcohol, cannabis and/or illicit drugs in the future and to decrease internalizing and externalizing behavioural problems. Intervention Mapping (IM) was used to guide the development of this intervention.IM is a useful tool for theory and evidence‐based development of health promotion interventions  with MID‐BIF and severe behavioural problems  in the general population  and cognitive behavioural therapy (CBT), which have been proven to be effective in decreasing alcohol and drug use among non‐disabled adolescents  psycho‐education, (ii) behavioural coping skills and (iii) cognitive coping skills. At the start, the intervention focuses on psycho‐education addressing the participants' personality profile and related problematic coping behaviour, like substance use or aggression. Psycho‐education was adapted to the level of intellectual functioning by using games, visual support and the use of daily life experiences. The confident (the role of the confident is explained in the following paragraph) has a supporting role by bringing up these daily life experiences. In this phase, the participants will become familiar with their personality profile and learn to deal with their personality through exercises. Daily life experiences and subsequent physical, cognitive and behavioural reactions will be analysed. Moreover, they will set individual goals, which they will encounter during the training. The participants will identify personality‐specific thoughts that lead to problematic behaviour. For example, the intervention aimed at adolescents with the personality profile “Impulsive” will focus on thinking before taking action. Simultaneously, the participants will be trained to use cognitive restructuring techniques to counter such thoughts. They will be asked to edit a personalized “changing plan” to deal differently with their problematic and risky behaviour. Table The intervention will involve five group sessions and six individual sessions spread across 6 weeks. Individual sessions will last 30 min, and group sessions will last 45 min . During the individual sessions, participants may invite a confidant for support. The confidant is someone from the professional network of the participant (e.g. a caregiver), who has an explicit role in establishing the transfer of training to everyday life situations. The design of the intervention with individual sessions and group sessions was specifically modified for this target group. Personality‐targeted interventions for adolescents without MID‐BIF only comprise group sessions . Participants received either the impulsive behaviour intervention or the sensation seeking intervention, and all participants were associated with a treatment centre for their behavioural problems in the Netherlands. A pre‐test (2 weeks before the intervention) and a post‐test were conducted (2 weeks after the last session) to measure potential intervention effects. To measure feasibility and user‐friendliness, participants and trainers were asked to fill in questionnaires 2 weeks after the last session.Based on the SURPS . The average level of intelligence  of the participants was 70.2 (SD = 6.4) with an IQ ranging from 58 to 77. Three participants were diagnosed with ADHD, with one having a co‐morbid conduct disorder. Two participants were diagnosed with attachment disorder and one with symptoms of depression. Therapists were a psychologist and psychomotor therapist who had received specific training on Take it personal! prior to the start of the study, including training in CBT, MI and the theoretical background of the intervention. A pre‐test was conducted 2 weeks before the start of the intervention and a post‐test 2 weeks after the last session.Seven adolescents with MID‐BIF with severe behavioural problems placed in residential care were invited to participate. Based on the SURPS  parts well. The trainers reported that involvement of a confidant  during the individual sessions was of great value for the transfer to the daily life of the participants, as the trainers indicated. The adjustments that were suggested after a careful evaluation of the intervention with the trainers lead to changes that were in line with the underlying theory of the intervention. The main adjustment included increasing the trainer's and counsellor's awareness of the importance of discussing substance use in both the individual sessions and group sessions, and skipping an individual session during week five to avoid repetition. In week five participants, there is now an optional individual session or contact by phone to repeat this week with their personal changing plan.3.2Table 3.3Post‐intervention evaluation of frequency of alcohol and drug use, binge drinking and problematic alcohol and drug use indicated that level of use was lower than at pre‐intervention (see Table 4The IM protocol was utilized to develop Take it personal! intervention based on theory and the results from other research that were expected to improve the likelihood of effectiveness of the intervention. The use of the IM protocol increased our understanding of the mechanisms underlying the effectiveness of Take it personal!. Evaluating the programme with a small modelling study was part of the process of the IM protocol (Bartholomew et al., With regard to potential effectiveness, this modelling study revealed that a number of participants were able to reduce their use of alcohol, cannabis and illicit drugs after the intervention. Given methodological constraints, we were not able to establish whether this change was associated with the intervention; therefore, a larger scale study is needed to draw conclusions about the effectiveness of Take it personal!.Several limitations need to be acknowledged regarding the use of IM and this study. First, IM provides a rather static picture, while developing an intervention is a dynamic and constantly changing process. Nevertheless, the intervention was developed based on sound systematic theory and evidence. Second, only a small number of participants were included in this study, making it difficult to draw conclusions. Besides, because of this small group of participants it is only generalizable to a limited extent. Third, questionnaires to assess the feasibility and user‐friendliness of the programme were bespoke questionnaires developed for this study, and therefore, there is no information about the reliability, validity and other psychometric aspects of these questionnaires. Last, information about substance use as well as the user‐friendliness of Take it personal! was obtained by self‐report questionnaires. Future research could include additional parent‐ or staff‐reported assessments in order to avoid potential self‐report bias. Concluding, Take it personal! can be a promising indicated preventive intervention designed to reduce substance use in individuals with MID‐BIF. Although, a larger scale study is needed, to draw firm conclusions about the effectiveness of Take it personal!The authors declare that they have no competing interests.


Many species of bacteria swim through viscous environments by rotating multiple helical flagella. The filaments gather behind the cell body and form a close helical bundle, which propels the cell forward during a “run”. The filaments inside the bundle cannot be continuously actuated, nor can they easily unbundle, if they are tangled around one another. The fact that bacteria can passively form coherent bundles, i.e. bundles which do not contain tangled pairs of filaments, may appear surprising given that flagella are actuated by uncoordinated motors. In this article, we establish the theoretical conditions under which a pair of rigid helical filaments can form a tangled bundle, and we compare these constraints with experimental data collected from the literature. Our results suggest that bacterial flagella are too straight and too far apart to form tangled bundles based on their intrinsic, undeformed geometry alone. This makes the formation of coherent bundles more robust against the passive nature of the bundling process, where the position of individual filaments cannot be controlled. Many large eukaryotic cells, particularly in plants, set up helical flows to enhance chemical transport within the cell4 and some viruses also take this shape5. Prokaryotes too have learnt how to assemble blocks of proteins into a helical structure and put it to good use9. Indeed, many species of bacteria are able to propel themselves through the viscous medium they inhabit by exploiting an apparatus known as flagellum, whereby a relatively rigid helical filament is actuated by a specialised constant-torque rotary motor12. In the case of multi-flagellated bacteria, the filaments are swept behind the cell body and rotate together in a coherent bundle, which leads to an interval of straight swimming called a “run”13. To change swimming direction, at least one motor must switch its sense of rotation, upon which the associated flagellum will leave the bundle and generate an imbalance of forces. The subsequent reorientation of the cell is called a “tumble”14.There is arguably no complex geometrical structure more central to biology than the helix. Two helical strands of nucleic acid spiral around each other to form the blueprint of life15, and from there onwards both the counter-rotation of the cell-body and hydrodynamic interactions between the filaments contribute to the synchronization and formation of the bundle22. Computational studies have investigated the effect of the number of flagella on the motility of the cell23, and the role played by polymorphic transformations24 and mismatched motor torques25 in the bundling and unbundling process. Experiments using scale models have provided further insights into the bundling mechanism27.This run-and-tumble behaviour lies at the heart of bacterial motility. It is known that the initial stage of bundling is enabled by an elastohydrodynamic instability of the hook28. However, the cell has no control over the exact position of individual filaments whilst bundling, so it is intriguing that a passive process can reliably lead to ordered bundles. One potential problem is the helical geometry of the filaments, which may tangle around each other, like the intertwined strands of DNA. Yet neither experiments, nor computational studies have reported cases of tangled bundles. Despite the helical structure of flagella and the stochastic fluctuations in the torque applied by motors, it appears that tangling is always prevented thanks to a combination of hydrodynamic interactions between the filaments, their elastic deformations, and the shape and arrangement of flagellar filaments over the cell body. In this paper we aim to isolate and better understand the effect of one of those agents – what can geometry on its own, without the mechanics, tell us about the issue of tangling?Evidently, the ability of a multi-flagellated bacterium to bundle and unbundle its flagella is crucial for its mobilityN ≥ 3 parallel helices cannot be physically interlinked if no pair of helices is intertwined. Therefore, it is sufficient to consider the pairwise tangling of flagella within the bundle. Under the quasi-steady assumption, we establish the theoretical conditions under which a pair of rigid helical filaments may tangle, and then compare these constraints with experimental data collected from the literature. Our results suggest that bacterial flagella are too straight and too far apart to form tangled bundles based on their intrinsic, undeformed geometry alone.In this article, we show that the geometrical constraints imposed by the intrinsic helical shape of bacterial flagella are incompatible with the formation of tangled bundles, therefore increasing the robustness of the bundling process. The underlying assumption of this study is that the dynamics is quasi-steady, so that we may neglect elastic deformations and focus on the kinematics that can be achieved with the filaments in their intrinsic helical shape, as if they were perfectly rigid. Inspired by experimental observations, we consider the proximal to distal coming together of the filaments as they are being swept behind the cell body see Fig.  and we a29. He examined two parallel identical helices of helical amplitude r, and found that they are intertwined (or tangled) if the distance between the helical axes is less thanπ), is greater thanIn 1977, Robert M. Macnab published the first study discussing the geometry of bundles of helical filamentsIn this case, as we scan the two filaments along their helical axes  = , whose components are given with respect to the lab frame {ex, ey, ez}. The two vectors spanning the plane orthogonal to the helical axis are e1 = eθ and e2 = eϕ(ϕ). This setup is illustrated in Fig. ϕ, the inclination angle θ, and the phase χ.In order to describe such behaviour, we begin by introducing the parameters that allow us to represent non-parallel helices. Since the hook is much shorter and much more flexible than the filament, we model the flagellum as being anchored to a fixed location by a universal point joint. We assume that the helices are tapered near their anchoring point, meaning that the helical amplitude entclass1pt{minimad. In the kinematic perspective, where we are only interested in the space occupied by the filaments at each moment in time, we can adaptively change our frame of reference {ex, ey, ez} such that the anchoring points remain fixed and the direction ex is always given by the line between the two anchoring points, despite the cell-body counter-rotations that may be observed in a stationary frame. Henceforth it is assumed that we are in a frame where the anchoring points, and hence the distance d, are fixed. Suppose we wanted to bring the two flagella from a configuration where they are not intertwined  into a tangled bundle. Intuitively, the easiest way to achieve this is to arrange the helices symmetrically about the midline between their anchoring points at every step of the way, because this gives them space to circle around each other and intertwine, without blocking each other’s way. This can be achieved by placing one helix in the configuration  and the second in the configuration , so that the helices are an image of one another under a rotational symmetry through angle π about the midline between their anchoring points, as illustrated in Fig. z-axis, and the helix is anchored to a point in the xy-plane at a distance d/2 away from the origin along the x-axis. Despite having zero thickness the vertical line has material properties, i.e. the filament cannot cross this line, because it would have to cross through its mirror image filament on the other side of the midline.Now consider a pair of filaments anchored to two fixed points separated by a distance s, ϕ) indicating the contact point and the azimuthal angle over which the helical axis is inclined. In keeping with experimental observations illustrated in Fig. s, slides up from the proximal to the distal end of the helix. As this happens, the portion of the helical filament below s will gradually envelop the vertical line, until we reach a deadlock . At a certain critical height scrit, not only will the outside of the filament be in contact with the line at scrit, by design, but the inside of the filament will also make contact with the line at height scrit − p. Since the vertical line has material properties, any further increase of s will lead to an overlap, so we cannot go beyond this point. This constraint is a consequence of the helical geometry of the filament and applies equally well to a helix of constant amplitude, so we start by deriving the threshold in the case of a perfect helix.Since we want to determine the threshold where tangling is no longer possible, we must look at the limiting case where there is only enough space to tangle if the helical filament is touching the line of zero thickness, as seen in Fig. ϕ at which the helical axis is inclined, by taking a cross-section in the plane spanned by ez and e2(ϕ)∧ez, which we call the “focal plane”  =  going through the origin, which explains our choice of focal plane. If we impose the further condition that the filament is tangent to the line at s − p as well, we can determine the critical point scrit(ϕ), and the critical incline angle We may calculate the critical point analytically, as a function of the azimuthal angle see Fig. . Recall z-axis is d′(ϕ) = d cos ϕ/2, and the projected distance between the filament centreline and the helical axis is r′(ϕ) = r cos ϕ′, where ϕ′ = sin−1(d sin ϕ/2r) is a measure of the offset between the focal plane and the axis of the filament. The only quantity that requires careful consideration is the horizontal distance z-axis. It can be shown that, for a small filament thickness rε and major axis z-axis. The tilting of the ellipse away from the vertical direction is partly due to the inclination angle θ applied to the entire helix, and partly due to the offset ϕ′ between the focal plane and the helical axis, the latter effect being enhanced by the amount of sloping in the filament, as measured by ψ . All these factors combined lead to a horizontal distance of approximatelyz-axis.The resulting geometric problem is sketched in Fig. The multiple lengths in the problem can be linked together through the similarity of triangles ΔABB′ and ΔACC′, from which we deriveθ = θcrit dependent on ϕ, for which we can solve in the limit of small thickness The first part of Eq.  will onlsing Eq. , to findThen, by rearranging the second part of Eq. , we obtaϕ, s) coordinate space, as shown in Fig. ϕscrit(ϕ) = scrit(π).This condition restricts trajectories in  trajectory of the filament due to interactions near the anchoring point. The theoretical threshold for tangling from Eq.  = scrit(π). As we do this, we must continuously decrease the phase χ, for which we have the exact solution p above some arbitrary point s0 + p/2, the point s0 will loop around the vertical line once . This is because the incline angle s > s0, so the vertical line already lies inside the cylindrical envelope of the helix up to the point s0. Meanwhile, the point s0 revolves around this cylindrical envelope once every time the phase π, which happens each time the contact point s covers an interval of length p.Beyond the case of helices with constant amplitude, tapering imposes further constraints on the  with a tapered helix that is anchored to a fixed point. Then every time the contact point goes up by one helical pitch, the filament would have to intersect the vertical line. This is because the bottom end of the anchored helix is fixed relative to the vertical line, but there exists some point s0 higher up the filament which loops around the vertical line once. Since the filament is a continuous curve between these two points, it must intersect the vertical line in the process. These intersections can be determined numerically, with results shown as dotted orange lines in Fig. Suppose we wanted to follow the same strategy  in such a way as to avoid hitting any physical constraints. We may work our way up between the sloping lines shown in Fig. ϕ-periodic domain until we reach the constraint s = scrit(ϕ) . The maximum height up to which two helices can tangle around one another is found numerically to be ϕ* is a consequence of tapering. This threshold depends on all the parameters in our model, namely the geometry of the flagellum described by , and the distance, d, between the two anchoring points.In order to complete tangling up to the highest possible point along the helix, we must navigate the coordinate space , the helix angle. The coordinate space  can be divided into two regions where the pair of filaments may or may not tangle, according to whether the theoretical threshold, send. The boundary between these two regions depends on d/L, the distance between the anchoring points relative to the length of the filaments, which is our control parameter.We start by considering a single cell of fixed dimensions, and we allow for isometric variations in the shape of the helical flagellum . Any helical filament of fixed length d/L, we note that the expected minimum distance between any two flagella on a bacterium will depend on the size of the cell body and the number of flagella. Modelling the cell body as a capsule  of length, l, and width, w, we compute the expected minimum distance between any two rotary motors, dmin, by simulating 10,000 random arrangements of N motors on the cell body sampled from a uniform distribution over a capsule (this sample size is sufficient to make our estimate for dmin accurate to within 1%). The expected minimum distance is then scaled by the mean length of a flagellum reported in the literature. Our theoretical predictions for a single cell, using the average cell body size and average length of flagella for the bacterial strain E. coli AW40514, are shown in Fig. In order to choose realistic values for E. coli AW405 quoted in the literature, which is between three and four flagella13. From the phase space we also deduce that the semicoiled form is the most susceptible to tangling. Finally we note that, at a typical number of three or four flagella13, all four polymorphic forms lie in the region where the intrinsic geometry of the flagellar filaments should not allow the formation of tangled bundles.The four most common polymorphic forms, depicted in Fig. l, and widths, w, with means and variances taken from the literature. For each of these cells, we compute the expected minimum distance between any two rotary motors, dmin, by randomly placing N motors on the cell body, distributed either uniformly or according to a known asymmetric distribution3144, and averaging over 10,000 realisations. The flagellar filaments attached to these motors have a given geometry  corresponding to one of the bacterial polymorphic forms found in nature, but their length is a random variable, sampled either from an experimentally measured distribution32 or from a log-normal distribution if only the mean and variance are available in the literature. For each simulated cell we compute the theoretical threshold, We now consider stochastic variations in the shape of the cell body and the length of flagella, but keep the helical shape of the filaments constant. We model the cell body as a capsule, as before, and we generate a sample of 500 cells with independent normally distributed body lengths, 43, are shown in Fig. Escherichia coli, Salmonella typhimurium and Bacillus subtilis . For our theory, we use the two most common polymorphic forms that the bacterial flagellum can take, namely the left-handed normal form used in runs (circles) and the right-handed semicoiled form used in tumbles (triangles)41. The empty symbols represent an estimate based on a non-uniform arrangement of molecular motors over the cell body, according to distributions reported in the literature for Escherichia coli and Bacillus subtilis44 . These estimates are always slightly lower than those for a uniform distribution, because the effective distance between flagella is reduced when the molecular motors are crowded towards one pole of the cell, which makes tangling more likely. However, the relative difference between the two estimates is very small because the asymmetry in motor distribution is not very pronounced.Our theoretical predictions, based on parameter values taken from the literature13, but they are so slender that the corresponding theoretical thresholds are much higher than for normal and semicoiled flagella, as evidenced in Fig. Remarkably, we find that the theoretical thresholds in Fig. 45. In the current study, our kinematic model for tangling allows us to examine whether the number of flagella could be linked to the robustness of bundling. By comparing the thresholds from our theoretical model with the real number of flagella counted in experiments, we deduce that the intrinsic geometry of flagellar filaments should not allow the formation of tangled bundles. This is consistent across the four most common polymorphic forms of the bacterial flagellum, and across three different strains of Escherichia coli and one strain of Salmonella typhimurium for which we could test a consistent set of data. We note that in the case of Bacillus subtilis, the geometrical constraints identified in this paper and presented in the last column of Fig. 38, which is equipped with fewer flagella. In contrast, the wild-type and highly-flagellated strains of Bacillus subtilis can have up to forty flagella with only a slight increase in cell body size (less than 50%), meaning that the constraints imposed by the intrinsic geometry of flagella are not sufficient to rule out tangling. The thresholds predicted by our model for the wild-type strain DS954038 were of approximately nine normal flagella or thirty curly flagella, compared to experimental measurements of twenty-six derived from a basal body count44.The number of flagella is a fundamental control parameter for multi-flagellated bacteria, and its connection to bacterial spreading and speed of locomotion has been previously investigatedEscherichia coli and Salmonella typhimurium, we can formulate our conclusion either in terms of the helical geometry of the polymorphic forms, which appears to be too slender to allow tangling  away from the true location of the molecular motor, which is fixed. When the filaments are being swept behind the cell body, the effective distance between the proximal ends of the filaments could be reduced, making it easier to form a tangled bundle.26 and computations21. This kind of wrapping is made possible by the elastic deformation of the filaments and is different to the left-handed tangling considered in this article, which is the only one allowed by the left-handed intrinsic geometry of the normal flagellum29. Simulations have shown that, if hydrodynamic interactions are switched off, the bundle comes apart because the filaments are not geometrically interconnected due to the right-handed wrapping19. In this article we have focused instead on the tangling which arises from the intrinsic geometry of the filaments  because it is the one that hinders the continuous actuation of the filaments during a run and the dispersal of the filaments during a tumble.Hydrodynamic interactions play a very important role in the formation of stable bundles since they favour the synchronization of flagella, leading to helical filaments rotating in phase with one another. The clockwise rotation of normal flagella, together with the counter-rotation of the cell body, lead to a right-handed wrapping of the filaments inside the bundle, as seen in experiments14. The qualitative difference between the kinematics that leads to tangling and that of real flagella is a further argument for the robustness of the bundling process.Our kinematic model for tangling is based on the idea that the set of hydrodynamically feasible paths is a subset of all possible geometries of motion. Thus, we have shown that hydrodynamics is not essential to prevent tangling in the quasi-steady regime – geometry imposes sufficient restrictions to avoid the formation of tangled bundles. If we relax the quasi-steady approximation, the set of possible geometries of motion will expand greatly since the shape of the filament could undergo arbitrary elastic deformations. Then tangling will (obviously) always be theoretically possible within the set of all possible geometries of motion. It will therefore be necessary to identify the filament kinematics that is also dynamically feasible, given the background flow conditions and the input of the rotary motors. Such a wide range of dynamic conditions is computationally inexhaustible, which is where our model can provide a stepping stone for further studies and narrow down the search. Based on the intrinsic geometry of the filaments, we have identified the kinematics that leads to tangling (see Supplementary Video 47 but also sufficiently slender to avoid tangling.Our results bring a new perspective on the ability of multi-flagellated bacteria to passively form coherent, tangle-free bundles of flagella that can be continuously actuated during a run and easily taken apart during a tumble. At one extreme, we know that straight flagella could not intertwine, but they would also not be able to propel the cell forward in a viscous fluid. It appears that the polymorphic forms most commonly adopted by bacterial flagella are sufficiently coiled to be efficient propellersSupplementary Video S3Supplementary InformationSupplementary Video S1Supplementary Video S2


This increased pressure is known to correlate with decreased treatment efficacy and potentially with tumour aggressiveness and therefore, accurate noninvasive estimates of tumour pressure would be of great value. We present a proof-of-concept method to infer the total tumour pressure, that is the sum of the fluid and solid parts, by examining stiffness in the peritumoural tissue with MR elastography and utilising nonlinear biomechanical models. The pressure from the tumour deforms the surrounding tissue leading to changes in stiffness. Understanding and accounting for these biases in stiffness has the potential to enable estimation of total tumour pressure. Simulations are used to validate the method with varying pressure levels, tumour shape, tumour size, and noise levels. Results show excellent matching in low noise cases and still correlate well with higher noise. Percent error remains near or below 10% for higher pressures in all noise level cases. Reconstructed pressures were also calculated from experiments with a catheter balloon embedded in a plastisol phantom at multiple inflation levels. Here the reconstructed pressures generally match the increases in pressure measured during the experiments. Percent errors between average reconstructed and measured pressures at four inflation states are 17.9%, 52%, 23.2%, and 0.9%. Future work will apply this method to  Increased interstitial fluid pressure (IFP) is caused by factors such as vessel leakiness and interstitial fibrosis which lead to a buildup of fluid and reduced drainage3. Elevated solid pressure originates from the proliferation of cancer cells and growth of the tumour4. Both increased IFP and solid pressure lead to decreased efficacy of treatment and there is some evidence that these correlate with poor prognosis, due to promotion of tumour progression and increased invasion5. IFP is able to be measured invasively by wick-in-needle1 and the solid pressure of tumours has been measured after extraction2, but clearly noninvasive measurement of IFP and/or solid pressure would be of immense value.Tumours often exhibit both increased fluid and solid pressure relative to surrounding tissueet al.2 by observing the expansion of excised tumours. In many instances this force will cause nearby tissue to deform. For example, a nearly spherical and well separated tumour exhibiting high pressure would compress nearby tissue radially and stretch it circumferentially. As tissue exhibits nonlinear response to strain, these deformations will lead to significant changes in the stiffness of the tissue near the tumour. The magnitude of these changes in stiffness will then scale with the total pressure of the tumour (the sum of fluid and solid parts) and so measurement of these stiffness changes represents a pathway towards inferring the tumour pressure noninvasively.Such an approach is proposed here, using measurements of material properties in peritumoural tissue to infer tumour pressure. Increased fluid and solid pressure lead to the tumour pushing on surrounding tissue, which has been shown by Nia 8. Typically, the patient is subjected to single frequency vibrational waves from an external transducer while in an MR scanner. Through phase-contrast imaging, images of the wave motion are constructed. A stiffness reconstruction method is then responsible for solving an inverse problem using these wave images to create an image of the tissue stiffness (most often the shear modulus)9. Recent work has introduced an MRE reconstruction method that accounts for stiffness bias due to large deformation10. This latter approach is extended here to account for and utilise the effect of the tissue deformation due to tumour pressure. The stiffness in the vicinity of the tumour is reconstructed while incorporating radial scalings of an assumed deformation field. The scaling which most reduces the presumed biases is chosen as the correct scaling. Finally, an analytic formula based on the nonlinear material law relates this scaling to an overall tumour pressure. The method is herein applied to both simulation and phantom data.To measure tissue stiffness in the peritumoural tissue, magnetic resonance elastography (MRE) is used. MRE is an established magnetic resonance imaging (MRI) based method to estimate tissue stiffness based on imaging the propagation of shear waves11. Another approach used by several works is dynamic contrast enhanced MRI where fluid flow velocity at the tumour surface is estimated by examining contrast agent over time14. This velocity can then be used to estimate IFP by assuming or estimating hydraulic conductivity and related parameters16. Alternatively, this velocity can be used as a stand-in for IFP as strong correlation has been shown in some cases17 and recent work showed it may be a prognostic factor in cervical cancer18. An MR elastography method was published that reconstructs images of fluid pressure and hydraulic conductivity distributions in addition to tissue stiffness19; however, results were limited to a single numerical simulation and high errors were reported. Ultrasound elastography techniques have recently been applied to solid stress and tumours, however these have mainly focused on an analysis of the stress or stiffness inside the tumour23. In contrast to the above methods, the method presented here estimates a related but different parameter - total tumour pressure - by analysing stiffness in the tissue surrounding the tumour.Some previous research has investigated noninvasive approaches to tumour pressure measurement within the MRI and elastography domains. Early work showed that T1 and T2 relaxation times do not correlate with IFP measured by wick-in-needleThe goal of the method presented here is to infer total tumour pressure by examining the stiffness of the tissue surrounding the tumour. There are three main components making up this method: (1) a stiffness reconstruction that accounts for nonlinear stiffness bias due to deformation, (2) a method for determining the correct scaling of the deformation prescribed to the tumour, and (3) a conversion between the deformation scaling parameter and pressure. These three components are presented in turn in this section, followed by a discussion of the simulations and phantom experiments used to validate the method.26, however many reconstruction methods, including the method27 extended here assume isotropy and incompressibility. This results in the following linear time-harmonic viscoelastic equations governing the wave behaviour, v are the complex-valued wave displacements, ρ is the tissue density , ω is the angular frequency of the transducer, and p is the complex hydrostatic pressure. The complex-valued shear modulus is denoted storage modulus or elasticity and G″ is the loss modulus or viscosity. The complex-valued steady-state displacements, v, and pressure, p, are related to their real-valued time-dependent counterparts by G∗. Briefly, the method here computes a value for G∗ at every voxel of the wave image data using a moving local finite element mesh and assuming G∗ is locally homogeneous.Various approaches to elastography and stiffness (shear modulus) reconstruction have been researched including work on differing material assumptions32. Subject to such deformation, stiffness can rarely be thought of as a single parameter. Most generally, stiffness is represented by the 4th order elasticity tensor relating the 2nd order stress and strain tensors. While in many cases stiffness can be reduced to fewer parameters, large deformation of isotropic tissue will result in at least some apparent anisotropy in stiffness as, for example, compression (and therefore softening) in one direction will lead to tension (and therefore hardening) in another direction. As described in Capilnasiu et al.10, the shear waves will generally observe the stiffness component corresponding to the propagation direction . So in a simple case of orthogonal deformation and wave propagation the interaction may be well understood. In complex scenarios, however, the resulting stiffness values are much harder to interpret. If the standard MRE reconstruction mentioned above is applied in these cases, then biased results are expected due to the waves observing a combination of multiple stiffness components. These complexities, however, can be fully accounted for if the biorheology of the tissue is known.Unlike the linear wave theory utilised above, tissue is generally considered to have a nonlinear response to large deformationThe main model considered here for a pressurized tumour is an inflating sphere. As a spherical or some approximately spherically shaped inclusion inflates within tissue the surrounding tissue will stretch in the circumferential direction and compress in the radial direction. Assuming the tissue is reasonably homogeneous and isotropic before inflation then this will lead to anisoptropic stiffness in the region with increased stiffness in the circumferential direction and decreased stiffness in the radial direction. In an idealized case of shear wave propagation in a single direction across the entire domain we can predict the three dimensional pattern of increased and decreased stiffness bias that is reconstructed. This will lead to apparent softening in front of and behind the inclusion and a ring-like zone of increased stiffness around the inclusion, facing the wave. This is illustrated in Fig. et al.10, used to extend the stiffness reconstruction method from Fovargue et al.27, is able to reconstruct the unbiased intrinsic stiffness of a deformed material given the macroscale deformation and nonlinear material law as input. This method is constructed in a mathematically rigorous manner using a perturbation analysis relating the two scales defined by v and u, the small scale wave displacements and the large scale deformation, respectively. The analysis leads to the following set of equations governing the wave behaviour et al.10 assuming the fractional derivative parameter is 1. Further, F = ∇ u + I is the deformation tensor, S is the second Piola-Kirchoff (PK2) stress tensor and is the sum of elastic, Se, viscous, Sv, and hydrostatic, Sp, parts. Depending on the form of S, different approaches to reconstruction may be considered. If we know the deformation that caused the apparent anisotropy and hence biases, then this approach may be used to reconstruct the unbiased intrinsic stiffness of the material, thereby undoing the effect of the deformation.The method from Capilnasiu μe is the intrinsic shear modulus of the material in the absence of macroscale deformation. This gives the elastic PK2 stress tensor S is considered to be negligible and ∇FSe is μe is a constant multiple of all terms in μe is the same as on the frequency dependent μe is simply replaced with Here, a neo-Hookean material law is assumed, giving the following strain energy function into Eq.  giving tet al.27 only with v.In order to maintain features of the reconstruction method that contribute to increased robustness we must solve for a scalar  stiffness. If the waves are processed differently for the elastic and viscous parts of the stiffness then these features are lost. Therefore we choose to scale the waves corresponding to the viscosity in the same way as the waves corresponding to the elasticity. Changes to viscosity due to deformation is outside the scope of this article and further we assume that any effect on the elasticity due to this choice is negligible. So, the equation which the reconstruction solves is then et al.10, the deformation field considered here is spatially variable, and so the value of ∇ v at each voxel is modified by the corresponding value of F = I, but in the presence of actual deformation then the result will match the standard version of the reconstruction and will show biases due to deformation. However, if the correct deformation field is inserted then the reconstruction will recover the intrinsic unbiased stiffness, thereby undoing the effect of the deformation (in our case due to the pressurized inclusion).As opposed to Capilnasiu Using the stiffness reconstruction described above, we wish to find a macroscale deformation field which mimics the effect of the pressurized inclusion on the surrounding tissue. Our assumptions are that the surrounding tissue is nearly homogeneous and that the deformation introduces apparent heterogeneity in stiffness due to nonlinear effects. Therefore the deformation which most reduces this heterogeneity will be considered to be the correct deformation. To limit the possible choices we only consider scalings of a spherical deformation. The assumption is further justified in that most tumours grow in an approximately spherical way and that as objects inflate they tend towards a more spherical shape.33, where R0 is the radius of the uninflated tumour and r0 is the radius of the tumour after inflation. In other words, r0 represents the real size of the tumour, whereas R0 represents the theoretical size of the tumour if all fluid and solid pressure were removed. We define a radial variable, r, corresponding to the inflated state, and a radial variable, R, corresponding to the uninflated state. Incompressibility then implies α, so that α = 0 corresponds to no inflation (or zero pressure) and α = 1 corresponds to inflation from a point, α < 0 would imply a negative pressure, or pulling of instead of pushing on the surrounding tissue. Knowing r0 and the center of the tumour, c0, and assuming a value of α allows the construction of the deformation field. At a point x that is a distance r from c0, the magnitude of the radial deformation field is given by x−c0. Scalings of this deformation field can be constructed by varying the value of α. Considering the example shown in Fig. α = 0 and an elimination of the biases when α = αtrue. Furthermore, α < 0 would lead to an increase in the magnitude of the biases and α > αtrue to an inversion of the biases.The family of deformation fields considered here are defined by an incompressible thick spherical shell modelα is considered to be the one that most reduces the heterogeneity of stiffness in the surrounding tissue. This is measured from the standard deviation of the reconstructed stiffness, r0. This is to balance being as close as possible to the inclusion but avoiding including α value which minimizes the standard deviation of The correct scaling of α we use an analytic model of an inflating sphere to calculate the pressure. Equilibrium equations, and assuming a neo-Hookean material law, give the following for determining the radial stress33pinc is the pressure in the inclusion. Noting that α then by μe, and the value of α found by the method described above. As this portion of the method does not rely on frequency, it is appropriate to use the intrinsic μe of the material and not From entclass1pt{minima34.Computational simulations are used to verify and test the method. These consist of two main parts: (1) a nonlinear solid mechanics simulation governing the expansion of a pressurized inclusion and (2) a linear wave simulation in the same domain to model the vibration during elastography. Both simulations are executed in CHeart, a finite element software specializing in the multi-physics of fluid and solid mechanics36. Several additional spherical inclusions of varying initial size  are also modelled. This group of simulations was limited to 50 load steps (2.08 kPa) as the larger radii subject to the highest pressures led to problematic levels of deformation of the computational mesh. For all simulations, the domain is modelled as a neo-Hookean solid with μe = 1.5 kPa and with several boundary nodes fixed in place to restrain the simulation. The background stiffness is chosen to be near that of some real tissue, specifically breast (0.87 kPa37), brain (1.2–2.1 kPa38), and liver (2.0 kPa39), as these organs may be the most likely application of the method in future work. The finite element meshes are composed of approximately 210,000 to 230,000 tetrahedral Three inclusion shapes are modelled: a sphere, a bumpy inclusion, and an oblique egg-shaped inclusion. The inclusions (modelled as voids) all begin the inflation simulation at approximately 4 mm radius and are situated in the center of a cube domain with edge length 50 mm. Over the course of 60 load steps, the internal pressure of the inclusion is incrementally increased from 0 to 2.5 kPa. The higher end of this spectrum should be approximately in the range of total tumour pressure for real tumoursG∗ = 1.5 + i0.2 kPa. These simulations took approximately 8 hours each using 64 cores on the same HPC machine. The result of the wave simulation is extracted from the well-resolved unstructured finite element mesh (in the configuration from the desired inflation load step) onto a coarser uniform grid to represent a typical image formed from MR elastography (1 mm isotropic resolution). Figure The steady-state wave simulations are run on the same meshes as used for the inflation simulations. A portion of the boundary has Dirichlet type boundary conditions set to induce waves, where all displacement components are initialized. The wave frequency is 100 Hz and μL of water added into the balloon. Higher resolution images, used to estimate the inclusion position and radii, were also acquired in each state with 0.89 mm isotropic resolution. The higher vibrational frequency used here of 210 Hz, compared to human applications (~50 Hz), led to significant attenuation of the waves away from the transducer and balloon. Therefore, all processing of the wave data was limited to approximately the half of the phantom closer to the transducer to ensure correct alignment and orientation of the data, as lack of wave data can disrupt these calculations.A set of three phantom experiments were performed to further validate the method, using an expanding balloon catheter to model a pressurized tumour. The balloon catheter was inserted into an approximately cube-shaped 8 cm plastisol phantom (a different phantom was made for each experiment). Five MRE scans were performed at 210 Hz for each phantom, with 2 mm isotropic resolution. These five scans corresponded to five states: one uninflated state and with 100, 200, 300, and 400 μe = 11.2 kPa. While the frequency, inclusion pressure, and background stiffness are all higher than would be expected in vivo, their relative contributions mimic tissue.The fluid pressure was measured at each inflated state during the MRE experiments. As the balloon itself also contributes to the pressure, the fluid pressure was measured outside of the phantom as well (again at each state and after the MRE experiments) and these values were subtracted from the total fluid pressure to give only the pressure due to the restriction from the phantom. Replicate measurements were also made again, both inside and outside the phantom, but not during scanning. Mean measured pressure and radii values for each inflation state are included in Table α, to pressure, the relationship defined by Eq.  and R0 (from load step 0) are calculated as the average distance from the center of the mesh to all mesh nodes making up the inclusion surface. Then α is found from Eq.  at load step 40 (1.6667 kPa) at the center slice. The reconstructed stiffness in a cross section of the ROI is also shown. A plot of standard deviation of α is shown as well. Here, α is incremented by 0.05 for illustrative purposes, but for other results α was incremented by 0.01. The α and pressure calculated for this data set  are also indicated in Fig. Wave images were extracted at every 10 load steps corresponding to incremental pressure increases of 2.5/6 ≈0.417) kPa from 0 to 2.5 kPa for the simulations comparing shape . Deformation parameters, 17 kPa frn0, n0] where n0 was approximately 5%, 10%, and 15% of the maximum wave amplitude in the ROI for calculating stiffness variation. For cases with noise, Gaussian smoothing with 3 pixel support and σ = 1 pixel was applied after noise was added to mimic reality. Figure Tests were also run on all data sets with added random noise on all six components of the wave data. The noise was drawn from a uniform distribution from [−Pressure was reconstructed for all five inflation states for each of the three experiments. The same Gaussian smoothing was applied to the wave data as for the simulations. The stiffness variation ROI was constructed in the same manner, however, depending on the inflation level there was not always enough slices to cover the entire spherical shell in the slice direction, so as many as possible were used. For the phantom data, an additional step of smoothing the reconstructed stiffness was also applied, so that the variance calculation was more influenced by larger scale variation due to the inflation and less by small scale variation often seen in experimental data.μL inflation. All elastogram images from the phantom experiments are included in Supplementary Material. Figure μL is missing as the balloon popped and one measurement for 100 μL was discarded as post-analysis revealed the initially recorded pressure was not stable over time potentially indicating a leak. Table μL case . The 100 μL case is not significantly different from the 0 μL case (p = 0.72).Figure α-pressure relationship . This presumably affects the egg shape as well, however, as it is overestimated for small α it then appears to become closer for larger α.Good agreement is seen for the hip (Eq. ) as dispα. Also, the magnitude of the deformation is dependent on radius, and so small radii will have less effect on stiffness which may lead to a stronger dependency on the homogeneity assumption and therefore more variability in the resulting pressure. This is clear too, in the results for the spherical inclusion with the smallest radius as it clearly suffers the most with added noise. We also note an overall tendency for the pressure to be overestimated for these smaller radii inclusions in the presence of noise. The background stiffness and tumour pressure range of the simulations were chosen to be in the expected ranges of real tissue and tumours. There is a scaling relationship between tumour pressure and tissue stiffness, in that for the same amount of strain (deformation of the tumour), the pressure and tissue stiffness will positively correlate, and so the simulations inherently cover a wider range of values at least in terms of recovering pressure.Pressure reconstructions from the numerical examples match the true pressure very well for zero and low noise cases and for all inclusion shapes and sizes as seen in Fig. μL inflation was the largest inflation where we could guarantee that the phantom material would not tear.As seen in Fig. 27, although there is a slight increase in time over the original method due to re-scaling the wave derivatives. Stiffness reconstructions using this method typically take on the order of 10s of seconds, simply scaling with the number of voxels in the data set. Likewise, the computational effort of the pressure reconstruction scales with the number of desired α values. For example, the pressure reconstruction in its current MATLAB implementation for a phantom data set takes about 15 minutes if α is incremented by 0.01 from −0.2 to 1. In this work, the stiffness reconstruction was typically restricted to a bounding box surrounding the ROI, however this could be further restricted to the exact voxels comprising the ROI. Moving forward, the time can be substantially and straightforwardly reduced, if need be, as the sweep of α values is trivially parallelizable.The computation of pressure is inexpensive as the underlying stiffness reconstruction utilises a local moving window and a direct least squares solvein vivo pressure data will be expected to be more difficult to estimate, coming from factors such as stiffness variability due to noise, inherent heterogeneity, or data-model mismatch. Robustness of the method could be increased by collecting more data through typical routes to improve wave image quality or by collecting multiple data sets with differing wave sources. The latter could then require the α reconstruction process to find the α which minimizes the stiffness variance of multiple data sets, as these would have different k-vector directions and therefore different stiffness biases surrounding the tumour. For now, we assume any potential future in vivo data would conform well to the assumptions that the tumour is nearly spherical in shape, well-embedded but clearly delineated from surrounding tissue, and that accurate values for the tumour center and radius can be found. Understanding the effects of straying from these assumptions is left for future work. While the volume of tissue affected by the deformation is small, relative to the whole organ for example, MRE should be able to accurately reconstruct stiffness values, at least for approximately the ratios of tumour size, deformation magnitude, wavelength, noise, and pixel size described here. Previous work has shown accurate stiffness reconstructions of small inclusions of a similar size (in terms of pixels per wavelength) as the affected area here42.Generally speaking, future in vivo studies could be better suited in two ways however. First, in vivo data will not have the same catheter hole, as the phantom does, and so the tumour will be more properly embedded in the tissue. Second, the tumour will support shear waves. The worst case here is represented by the simulations where the tumour is replaced with a void which creates a very sharp discontinuity in the wave data and affects the stiffness reconstruction near the boundary. Similarly, the balloon in the phantoms is filled with water and therefore does not support shear waves, creating a less noticeable but extant discontinuity. We also note that some version of this method may be applicable to ultrasound elastography, however it is only directly applicable to a 3D image stack of 3D displacement data.Possible future ex vivo and animal studies as well as application to in vivo patient data.This paper presented a proof-of-concept method to infer tumour pressure noninvasively using stiffness measurements from MRE and the application of nonlinear biomechanical models. Essentially, the pressure is found from undoing the presumed stiffness biases resulting from the large scale deformation caused by the outward push from the pressure. The method was tested on simulated pressurized inclusions with results matching well with true pressure when varying pressure level, inclusion shape, initial inclusion size, and added noise. Phantom experiments were run with catheter balloons inflated to multiple levels and pressure was reconstructed from the resulting MRE images. Here the mean pressure over several experiments generally matched the behaviour of the experimentally measured pressure. This method offers a potential way to measure an important biomarker noninvasively. Future work includes further validation via Supplementary Information.