One consistent finding in the causal reasoning literature is that causal judgments are rather variable. In particular, distributions of probabilistic causal judgments tend not to be normal and are often not centered on the normative response. As an explanation for these response distributions, we propose that people engage in ‘mutation sampling’ when confronted with a causal query and integrate this information with prior information about that query. The Mutation Sampler model (Davis & Rehder,  Causal reasoning is a core facet of human cognition. Dealing with causal relationships in the world and using them to our advantage is a crucial part of our abilities. Causal cognition ties into most  judgments and decisions , after which they are asked to make certain inferences, i.e., compute certain  probabilities. An example of such an inference is “what is the probability of Z (being late for work) given that X (a traffic accident) happened?”. These experiments provide a window into how participants make use of causal information to come to a specific judgment. The current work will focus on using cognitive modelling to understand how people make such judgments using their causal knowledge.The current work addresses probabilistic causal reasoning. An example of this is when someone tries to judge the probability that they will be late for work after hearing on the radio that there has been a traffic accident nearby. To make such a judgment one needs to use their knowledge of a causal system. In this case such knowledge could be represented as Over the last decades so-called causal Bayesian networkssampling approach to cognition proposes that we solve problems by way of first drawing samples, either from memory or an internal generative model, and then generating judgments based on the information in these samples. In this way we can reason about probabilities without the need to explicitly represent probabilities. Often the sampling approach is modelled using Markov chain Monte Carlo (MCMC) processes . The concrete cases here are causal networks instantiated with particular values, i.e., they are particular casual network states . Next, a new state is proposed from the states that differ only in value of a single variable from the current state, i.e., the current state is ‘mutated’. This implements the idea that people tend to only make small adjustments to the cases they are considering currently (Principle 2). Whether the next sample is this proposal state or is the current state is determined by the transition probability. The transition probability is defined by the relative likelihood of the proposal and current state  the starting point of the process is biased  and (2) the number of samples (or ‘chain length’) is limited.Both these factors, limited sampling and biased starting points, lead to a probability distribution that overestimates the likelihood of states where more variables have the same value. That is, it is biased towards prototypical states . Other work on sampling approaches to cognition has shown that using only a limited number of samples can be rational when taking into account costs associated with taking more samples , but a full distribution of responses to an inference. This is in line with the MS being a process-model, since it models the process by which people generate causal judgments it should also produce the variability in responses seen on a variety of tasks rationality of the model, leading us to extend the model using priors in the second part. In the second part we introduce the Bayesian Mutation Sampler and test its distributional predictions. We conclude with a general discussion concerning both the theoretical and empirical advances made in this paper.The nature of the MS as a process-model makes it a useful tool to assess distributional phenomena in addition to the mean phenomena that have been extensively studied ). The experiment is described in more detail in a later section, for now it suffices to note that it used similar methods, including the exact same causal parameters, as Experiment 1A by Rottman and Hastie  as in X1 = 1, Y = 1, X2 = 0] and  to compute the inference based on the relative frequency of these states in the chain. This computation is done using the (Kolmogorov) definition of conditional probability:N stands for the number of samples of that causal state. Now if the required states on the right-hand side of To understand these predictions we have to take a closer look at the mechanisms causing these peaks. Firstly, the peak at 50%. These peaks are due to the MS defaulting to a 50% response for conditional probability queries when the causal network states required for the calculation are not reached at any point by the stochastic sampling process. Throughout this manuscript we will use able see . Let us P, which requires the state A:  and B:  to be visited by the sampler. In the case where state A is not visited, The predicted peaks at 0% and 100% come about similarly as the peak at 50%, however in this case only one of the two required states is not visited. Let us again consider the inference P  , which ruted see . We findLet us now look at the effect of different chain lengths. As the predicted peaks at 0%, 50% and 100% by the MS are all due to certain network states not being visited by the sampling process, the number of samples drawn, i.e., the chain length, determines the size of these predicted peaks. Fewer samples drawn increases the probability that certain states are not visited and so larger peaks are predictedP inference was never computed in 10,000 runs with a chain length of 2. For larger chain lengths these peaks are present as well albeit with a smaller magnitude. Even with a chain length of 48, which is at the high end of the range of chain lengths found previously  the MS predicts responses at 100% for all chain lengths simulated  does directly impact one’s judgment because we can weigh it relative to our prior information . In contrast, the relative frequency approach would be insensitive to the amount of information learned from sampling.Based on the previous theoretical arguments and the problems the MS has with predicting empirical response distributions, we propose the Bayesian Mutation Sampler (BMS) as an account of how people make causal judgments. The BMS is a process-model of causal reasoning combining mutation sampling  to produce a posterior distribution. Subsequently probability judgments are based on this posterior distribution. Following Zhu et al. , we takeFollowing Zhu et al.  we use sβ, β) distributions with values for β as the shape parameters. The Beta distribution is the uniform distribution, assigning equal probability mass to each probability p (from 0 to 1). For β > 1 the beta distributions assign more probability mass to the center of the scale, i.e., probabilities around .5. β < 1 shows the opposite pattern, where more probability is assigned to the extreme ends of the scale. In this way using the symmetric Beta distributions allows the BMS to account for various levels of conservatism.β > 0 the incorporation of the prior moves a response closer to 50% than when just using the relative frequency method. The only symmetric Beta distribution that would not introduce conservatism in this sense is the Beta distribution where all the probability mass is at the extremes of the range, at 0 and 1. Using the Beta distribution is equivalent to using the relative frequency method of forming judgments from samples. This entails that the BMS with β set to 0 is equivalent to the standard MS and so the BMS is a generalization of the MS.For all β, β) distribution as a prior, the expected value of the posterior distribution can be determined without computing the posterior distribution itself. We can compute the expected value directly by adding β as ‘pseudo-observations’ to BMS refers to the estimate of the probability of an event predicted by the BMS, N stands for the number of samples (in a chain of generated samples), and Xi, Y refer to causal variables and x, y refer to their respective states. The β refers to the Beta prior used, where both shape parameters of the Beta distribution are equal to β.By using the Beta probabilistic queries regarding the causal systems. Each of the 3 testing phases consisted of three blocks with different levels of time pressure implemented using response deadlines of 3, 9 and 20 seconds (of which the last one was intended to give participants ample time to respond). Each of these blocks consisted of 27 trials each consisting of a different inference. These inferences were of the form ‘Variable A has value Out of the 43 participants in the dataset, 17 did the study online. The only noteworthy difference between the online and offline study was the response modality; participants in the lab indicated a percentage by moving a joystick while online participants responded by moving their cursor using a mouse or trackpad.We will fit the BMS and MS to each participant and condition  separately, this results in 43 × 3 × 3 = 387 sets of fitted parameters. In this way each set of parameters is fitted to 27 responses on 27 different inferences of a participant.Appendix A) supported this suspicion, but revealed that using a parameter grid search , which is generally seen as good or excellent recovery  and discrete (chain length) parameters. These considerations suggest a discontinuous or at least complex parameter landscape. A parameter recovery study . These simulated responses were then saved in a grid. Each cell of this grid represents the predictions of the model under a particular set of parameters. To compute how closely the simulated responses match empirical responses we use the Probability Density Approximation method  prior would lead to responses only at 50%, we picked β = 100 instead.To make sure that the grid contains the optimal parameters we set a wide parameter range. The chain lengths were varied between , which includes the chain lengths found previously for reasoning tasks  covering a wide range of plausible parameter values and simulated responses using (35 × 21 =) 735 different parameter combinations. While Davis and Rehder  by 21 . Next, we computed the average BIC weights per participant as approximations of posterior model probabilities .As discussed in the P = P), over the presence or absence of variables by flipping responses to the upper half of the response scale  = 1 − P), and over unknown variables  = P(Y = 1|X2 = 1)). In addition, since we did not find significant differences in parameters, we will collapse over response deadline conditions. Finally, we will collapse over the chain and common cause network structures as these have an equivalent underlying normative distribution. We do not use the common effect structure for this analysis nor for the analysis of distributions below, since the small number of observations would lead to unreliable estimates of variability. Collapsing resulted in 7 groups of inferences presented in Appendix B for an overview of all inferences in each group).In addition to mean judgments, another important behavioral index is the variability of judgments . The higher GMD for the MS is expected, because it predicts more extreme responses, increasing variability. Although the average variability of the BMS is higher than the observed variability, there are clear associations between the observed and predicted variability for each inference group  = 14.73, p < .001, BF = 32.5), corroborating this explanation. This effect is not captured in our predictions as we did not model a process by which participants might decide to use different chain lengths.For the ambiguous trials, we observe that the prediction seems to be quite accurate for inference group 2  that is often considered the prototypical uninformative prior. For most participants (79.1%) the mean β is larger than one, indicating they expected answers to be closer to 50%, validating our choice to include values for β > 1  the substantial conservatism observed on this , we find that in 5.94% of cases the best fitting β is zero, the lower bound of the grid. This indicates that in only a small subset of cases the relative frequency method of generating judgments  was used. As could be expected the prior used was not affected by response deadlines  = 1.04, p = .433, BFH1 = 0.036).A summary of fitted BMS parameter per response deadline condition is shown in F = 3.74, p = .121, BFH1 = 0.25). 14.0% of fitted chain lengths reached the maximum value of 70. This reflects that larger chain lengths are more difficult to estimate, since the differences in the predictions of the BMS become increasingly smaller as chain lengths increase (Appendix A). While there is some uncertainty regarding the exact values of the higher chain lengths, the median chain lengths we find are noticeably higher than found by Davis and Rehder , predicts. The two main problems we identified were that the MS predicts a non-trivial number of extreme responses at 0 or 100 %, and that it predicts the bulk of computed responses to be centered near the normative probability. Contrary to these predictions, data indicate that people actually refrain from using the extreme ends of the response scale and that the bulk of their responses tends to lie in between the normative answer and 50%  probabilities and that they incorporate these beliefs into their judgments in Bayesian fashion. Amongst other reasons, we motivated the use of priors by the observation that participants do not provide extreme judgments. That is, we interpret the avoidance of the extremes of the response scale as a rational adjustment to small sample sizes via the incorporation of prior information. However, there are other plausible explanations for the observation that people avoid making extreme judgments. One option would be that people avoid the extremes of the response scale due to a response bias; e.g., participants could be reluctant to express the confidence that a judgment of 0% or 100% might imply . Including such a scaling parameter improves the fit of the MS, but it is still outperformed by the BMS (Appendix C). Moreover, as the use of a (Beta) prior is theoretically motivated the BMS is clearly the favored model.A different approach was used in the original MS paper, where the authors used a scaling factor to map the probabilities computed by the MS to the response scale  in many other domains . However, we know that means often don’t capture response distributions in a meaningful way and that this violates the assumptions of the standard parametric tests  instead of on estimating descriptive effects. Such descriptive effects are often defined using differences in mean response between conditions and tested using standard parametric statistical tools .1 Also known as causal graphical models, graphical probabilistic models, or causal Bayes’ nets.2 The chain and common cause structure had the same causal parameters, with base rates of .5 for all variables. The effects in the network had a probability of 75% when their parent was present and 25% when it was not. In the common effect structure, the two causes combined by way of a Noisy-OR gate Cheng,  with cau3 −10. When the required states for an inference are not visited −10/[10−10 + 10−10] = .5.Davis and Rehder  implemen4 Y = 1 and X2 = 0, an unlikely state.The joint distribution of the causal variables also ties into this, since if there is a network state that has a small normative probability, it will be harder for the sampler to reach as well. This makes it that we observe the largest peaks in 5 One can interpret 50% responses as ‘extreme’ conservatism.6 β visits to all system states in While conceptually different, our approach is computationally equivalent to one which would assign a prior probability to all the possible network states instead of to likely correct responses to queries. That is, if we would add 7 Appendix A).The uncertainty regarding the exact values of higher chain lengths does not affect the conclusion that we found higher chain lengths, since if participants indeed used only few samples  to make judgments, our parameter recovery study indicates we would have recovered those parameter values accurately (Click here for additional data file.


When the microbubbles are exposed to a pulsed ultrasound, the contact angles increase dramatically; the percentage of DMPC molecules desorbed from the bubble surface reaches 70%. Vibration of a single bubble in the radial direction is measured using a laser Doppler vibrometer. The relationship between the vibrational characteristics and the amount of molecular desorption reveals that a larger vibrational amplitude of the bubble around the resonance size induces a larger amount of molecular desorption. These results support the possibility of controlling molecular desorption with pulsed ultrasound.Microbubbles have potential applications as drug and gene carriers, and drug release can be triggered by externally applied ultrasound irradiation while inside blood vessels. Desorption of molecules forming the microbubble shell can be observed under ultrasound irradiation of a single isolated microbubble, and the volume of desorbed molecules can be quantitatively estimated from the contact angle between the bubble and a glass plate. Microbubbles composed of a 1,2-dimyristoyl- The microbubbles used for DDSs are modified chemically so that they can adsorb specifically to the target tissues, and ultrasound excitation can trigger the bubbles to oscillate and release the drug locally. Typical contrast agents used in medical ultrasound imaging are coated with phospholipids or proteins, and a perfluorocarbon gas that is poorly soluble in water is employed to prolong microbubble lifetime in blood vessels10. Understanding the behavior of microbubbles under ultrasound irradiation is important for medical ultrasound imaging techniques because the molecular film surrounding the gas core of bubbles largely affects their vibration and scattering signals, and understanding the bubble dynamics both experimentally and theoretically is an active area of research16. Microbubbles have been proposed for ultrasound-assisted DDSs based on ultrasound contrast agents, which means that the molecular shell plays an important role in drug release11. When a micrometer-sized bubble is subjected to a low-amplitude acoustic pressure field (under approximately 1 kPa in megahertz range ultrasound), it undergoes a spherical vibration (expansion and contraction) mode synchronized with the pressure change. As the sound pressure amplitude increases, nonspherical vibration modes are generated with surface waves propagating on the microbubble surface21, where the vibration mode mainly depends on the relationship between the sound pressure amplitude, driving frequency, and bubble size. A further increase in sound pressure amplitude induces collapse of the microbubble, with a microjet of the internal gas penetrating the molecular film because the bubble cannot maintain its shape due to the violent vibration22. In ultrasound DDSs, local drug delivery can be achieved by exploiting the collapse of microbubbles adsorbed on the target tissues, since the jet flow generated by the bubble collapse can penetrate the cell membrane and release the drug inside the cell through the small pores created 29. However, van Wamel et al. reported that microbubble collapse is not mandatory for sonoporation. The transfer efficiency of drugs into the cells is indeed sufficiently improved in the absence of bubble collapse at smaller sound pressure amplitudes (hundreds of kPa). This implies that the pores are produced during the bubble contraction phase, releasing the drug into the cell in the expansion phase29. These results demonstrate that the quantification and control of molecular desorption from a bubble surface, induced by ultrasonication, are essential, not only to control the amount of drug but also to increase the safety of ultrasound DDSs, as lower sound pressure significantly decreases the risk of tissue damage.In vascular drug therapies, side effects on healthy tissues are serious concerns, and drug delivery systems (DDSs) capable of local drug release have been developed to address this considerable problem. In DDSs using ultrasound, drug- or gene-containing microbubbles with a diameter of several microns are used as drug carriers, injected into blood vessels and transported by blood flow31 by classical ultrasound backscattering methods34 and optical observation using high-speed cameras37, and theoretical modelling allows us to quantitatively evaluate the viscoelasticity of the molecular film38. From the viewpoint of interface engineering, the adsorption and desorption dynamics of the molecular film before and after ultrasonication should be clarified. Kooiman et al. have investigated the distribution of molecules on a bubble surface with fluorescent lipids, using fluorescence microscopy under pulsed ultrasound39, evaluating the desorption of lipids from the bubble via changes in the optical intensity. In our previous work40, the adsorption and desorption of a surfactant from a single bubble were investigated by measuring the change in contact angle of the bubble on a glass plate. Although ultrasound-induced transient desorption of surfactants was successfully observed, the molecules desorbed from the bubble surface to the surrounding medium re-adsorbed immediately because the experiments were conducted using dispersions saturated in surfactant, meaning that the amounts of molecular desorption from the bubble surface could not be estimated quantitatively and this experimental condition was far from that in blood vessels. In addition, the lifetime of the microbubbles is also important for ultrasound imaging and DDS techniques, which depends on not only the molecular density on the bubble surface42 but also that of the surrounding medium. These facts mean that the molecular desorption from a single bubble under ultrasonication can be estimated quantitatively using a surrounding medium with no surfactant. To the best of our knowledge, there are few reports on the estimation of surfactants desorbed from single microbubbles induced by ultrasound, and determination of the temporal changes in the amounts of molecules on a bubble surface is important for vascular ultrasound DDSs. In this paper, we propose a method to measure the amounts of molecular desorption of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) on a bubble surface quantitatively from the changes measured in the contact angle. The relationship between vibrational amplitude and molecular desorption under ultrasound irradiation is also discussed.The effects of a molecular film formed at a gas–liquid interface on the bubble vibration under ultrasound irradiation have been studied43. Here, the contact angle of single microbubbles on a glass plate in water is measured to estimate the amounts of molecules adsorbed on, and desorbed from, the bubble surface. 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), purchased from NOF Corporation, Tokyo, Japan , is used as the surfactant for bubble formation, and a fluorocarbon-enriched gas  is used as the internal gaseous phase of the microbubbles. Figure 3). A bolt-clamped Langevin-type ultrasound piezoelectric transducer  with a resonance frequency of 38.8 kHz is attached at the bottom of the ultrasound cell, so that pulsed ultrasound can be transmitted to the cell filled with liquids. The sound pressure amplitude is measured with a calibrated homemade hydrophone. The ultrasound cell is filled with DMPC dispersions or pure water, and a glass plate with a thickness of 0.15 mm is immersed in the cell for the measurement of the contact angle. Control of the water level in the cell allows constant maintenance of the electric admittance of the ultrasound transducer and the sound pressure amplitude. In this study, we conduct two experiments. Fluorocarbon gas bubbles (without a DMPC shell) in DMPC dispersions with several concentrations (0.1 to 5 mM) are used in the first experiment, and bubbles coated with a DMPC film in pure water are used in the second. DMPC dispersions are used with concentrations ranging from 0.1 to 5 mM, prepared by dispersing DMPC in phosphate-buffered saline (PBS)  using a magnetic stirrer. Polyethylene glycol monostearate  is added to the DMPC dispersions in consideration of future applications in clinical research (e.g. 57 mg of DMPC and 39 mg of PEG are added to 250 ml of PBS for 0.3 mM DMPC dispersion).Surface tensiometry allows us to directly measure the surface tension of a single bubble through optical observation and evaluate adsorption kinetics on the bubble surface in the case of sub-millimeter-sized bubblesIn the first experiment, the ultrasound cell is filled with the DMPC dispersions, and the naked fluorocarbon bubbles are fabricated directly onto the glass plate using a syringe with a microneedle. For the second experiment, microbubbles coated with a DMPC molecular film are fabricated using two connected syringes. For example, a syringe filled with 3 ml of 0.3 mM DMPC dispersion is connected to another syringe filled with 6 ml of fluorocarbon gas and shaken 30 times by hand to create microbubbles with a molecular film. The bubble dispersions are sonicated using an ultrasonic homogenizer  for one minute at 20 kHz, with the vibrational displacement of 108 μm on the tip to form DMPC microbubbles with a radius of 20–440 μm. The DMPC microbubbles are attached on the glass plate in the ultrasound cell using a syringe. The glass plate does not disturb the acoustic field in the cell because the plate thickness (0.15 mm) is much smaller than the ultrasound wavelength . The ultrasound cell is filled with degassed water to prevent exchange of the gas between the inside of the bubble and the surrounding water through the DMPC molecular film.θ can be expressed geometrically asH is the distance from the center of the bubble to the surface of the glass plate, and D is the horizontal diameter of the bubble. The bubble wall (gas–liquid interface) is determined from the spatial gradient of the image brightness. It should be noted that microbubbles are observed with diameters of 20–440 μm, larger than the 1–5 μm bubbles used in clinics, because the image resolution of the high-speed camera is 1.69 μm/pixel. Considering the time constant of the desorption of DMPC molecules, the change in contact angle of the microbubble is measured every 30–120 s. Although the most common observational method for microbubble vibration37, microscopic observation using high-speed cameras requires higher image resolution compared with the vibrational displacement of microbubbles and cannot be used to measure a small vibrational amplitude under low sound pressure amplitude. By contrast, the LDV enables precise measurement of bubble vibration with a small amplitude at the nanometer level15. The sensor head of the LDV is set above the ultrasound cell, and the radial vibrational displacement amplitude of the microbubbles is measured by adjusting the focal point of the LDV to the top of the bubble (the spot size of the laser beam is 1.5 μm). The size of the microbubble is measured through a CCD camera installed in the sensor head (the image resolution is 1.02 μm/pixel). A sinusoidal pulsed signal for 50 cycles with a frequency of 38.8 kHz is input to the ultrasound transducer, and the maximum sound pressure amplitude at the attachment position of the microbubble is controlled to be 20 kPa. All experiments are conducted at 22 °C.The incident light is focused on the microbubbles on the glass plate, with the transmitted light received by the high-speed camera via the long-distance microscope, in order to measure the contact angle between bubble and glass. Figure t = 0 is arbitrary because some time is required to control the focal point of the camera on the bubble after the bubble is attached to the glass plate. Although the contact angle is determined by surface tension, which is almost independent of bubble size, the buoyancy force acting on the bubble distorts it from spherical, resulting in slight differences in contact angle. The contact angle of the bubbles decreases gradually with time for all the DMPC-containing dispersions. The changes in contact angle reach a steady state after approximately t = 1000 s for all concentrations, meaning that the adsorption of DMPC molecules on the bubble surface also reaches the steady state in each dispersion. Higher DMPC concentrations gave a smaller terminal value for the contact angle, indicating a lower surface tension. To estimate the molecular desorption from the bubble surface under ultrasonication, the relationship between the contact angle of the bubbles and the density of DMPC molecules adsorbed on the bubble surface is important. Figure 44.In the first experiment, the DMPC molecules present in the solution begin to adsorb to the surface of naked fluorocarbon microbubbles attached on the glass plate, causing a decrease in the surface tension of microbubbles, and a consequent decrease in contact angle. Figure t = 0 range from 147 to 226 μm. The plots and error bars represent average values and the standard deviations for three trials, respectively, and the right vertical axis indicates the volume of microbubbles normalized by the initial bubble radius at t = 0. In the case of the naked microbubble  are generally used to evaluate molecular density on a gas–liquid interface, and here we evaluate the molecular density on the bubble surface using the DMPC dispersion (mM). This is under the assumption that the amount of DMPC molecules adsorbed on the bubble surface is proportional to the molecular density of the DMPC dispersion under 0.3 mM. Figure 45. In addition, buckling phenomenon, wrinkles, or vesiculation in the DMPC shell were not observed by the high-speed camera under ultrasound irradiation with a small pressure amplitude (20 kPa). This also supports that desorption is the main mechanism for lipid loss (the same trend was observed by Kwan and Borden45 and Lozano and Longo46). In fact, only the spherical and linear vibration of microbubbles was observed by the camera and the LDV. Following ultrasound irradiation, the molecular density decreases continuously and gradually as shown by the results presented in Fig. Assuming that the change in contact angle of the bubble induced by the desorption of DMPC molecules from the bubble surface is sufficiently rapid, that is, if the contact angle changes with the molecular desorption almost simultaneously, the temporal change in the density of DMPC molecules on the bubble surface can be estimated from the change in contact angle via the experimental result in the saturation states shown in Fig. t = 0, giving a maximum sound pressure amplitude of 20 kPa. Although both sound pressure and bubble vibration reach a steady state at approximately t = 0.5 ms (after approximately 20 cycles) in Fig. 47. For 99 microbubbles with radii ranging from 20 to 440 μm, the vibrational displacement amplitudes are measured under the same conditions (50-cycle pulsed ultrasound at 38.8 kHz with 20 kPa). Figure resonance curve), where the vertical axis indicates the vibration displacement amplitude in the steady state, ΔR, normalized by the initial bubble radius R0. The plots indicate values measured by the LDV, with the solid line showing a curve fitted with a Lorentz function23. The resonant bubble radius, in which the normalized vibrational displacement is maximized, is estimated to be 97 μm at 38.8 kHz from the fitting curve. The resonance size of microbubbles can be determined by two factors. The attachment of a microbubble on a rigid wall gives a 10% decrease in resonance radius at 39 kHz23 although a resonant bubble radius at 38.8 kHz in water is calculated to be 84.6 μm using a simplified linear model for bubble vibration under low sound pressure48. In contrast, the molecular film on the bubble surface generally increases the resonance size due to viscoelasticity12. From the fitting curve shown in Fig. Figure 49 implies that the curvature of the gas–liquid interface (bubble surface) may also impact the vibrational characteristics and the lipid desorption rates (intermolecular forces in the lipid shell are dependent on the curvature50). The bubble curvature may also impact bubble stabilization51. Several researchers reported that the composition of lipids adsorbed on microbubbles impact the dissolution process45 . The acoustic response of microbubbles is also affected by the lipids adsorbed on the bubble since the viscoelasticity of the lipid shell changes52. These facts mean that addition of several components on the bubble surface would significantly impact the desorption rates because the vibrational characteristics of the bubbles would be changed. In addition, considering the clinical use of microbubbles as drug/gene carriers, their surrounding medium would impact the desorption rates. If the microbubbles are injected into the blood circulation where nitrogen, oxygen, and carbon dioxide are present, both influx and efflux of the core gas and dissolved gas in blood would occur, resulting in changes in the bubble size53, as well as changes in the desorption rates with time. In addition, the surrounding environment of microbubbles in blood would affect the desorption rate. For, example, an increase of the viscosity of the surrounding fluid would decrease the vibrational displacement amplitude of the bubble and the desorption rate.In this study, bubbles with diameters of 20–440 μm were used. These bubbles are significantly larger than the microbubbles used in the clinic (1–5 μm). The choice of such large bubbles is due to the limited image resolution of the high-speed camera. The fact that the viscoelasticity of lipid-shelled microbubbles changes with the bubble size68. In addition, the same phenomenon is probably observed with smaller microbubbles used as ultrasound contrast agents because the curvature is too large to influence the dynamics of the surfactants at the gas/water interface even in this case54. For controlled drug release, we intend to clarify the relationship between the ultrasound frequency, sound pressure amplitude, and the quantity of molecular desorption in our future work.We propose a method to observe desorption of the shell-forming phospholipid (DMPC) from a single microbubble under pulsed ultrasound. Microbubbles coated with a DMPC molecular film are fabricated, and optically observed using system composed of a high-speed camera, an LDV, and an ultrasound cell to investigate the relationship between molecular desorption and the vibrational characteristics of microbubbles. Change in the molecular density on the bubble surface is estimated from the change in contact angle of the bubble attached on a glass plate. Microbubbles under the resonance condition release significant amounts of surface-adsorbed molecules to the surrounding media: 70% of DMPC molecules are desorbed from the bubble surface by a 50-cycle ultrasound pulse at 38.8 kHz with 20 kPa. The desorption by ultrasonication is not limited to DMPC, and the same effect was observed in the case with other surfactants such as Pluronic F


Crohn’s disease is an inflammatory condition of the gastrointestinal system affecting millions of people globally. As clinicians, we are faced with this disease commonly in the lower and middle gastrointestinal tract. The presentation of this condition is rare in the maxillofacial and oral regions. This case report presents a case where the patient presents with an acute severe infection in the head and neck skin region. Familiarity with this case alerts dentists and physicians to look for signs of inflammatory bowel disease as a differential diagnosis in patients with this presentation. Crohn’s disease is a chronic granulomatous disease that affects the gastrointestinal tract from mouth to anus. There are an estimated 400,000 to 600,000 affected individuals in the United States alone. There is a familial tendency, with siblings of affected individuals having a higher risk to develop this disease . There iThe disease has been associated with the NOD2 gene and its protein . This geA 38-year-old African American female presented from the emergency room for the evaluation of a dental infection. She reported a two-month history of fevers and sweating and a dental infection that was worsening over time. The medical history was unremarkable and the patient’s primary physician had ruled out any other medical conditions. The patient appeared to have an ulcer on the facial skin that was not associated with any pain. In the emergency room, the patient's oral exam was significant for one filling missing on the affected site and sensitivity leading to the diagnosis was “dental infection” with a fistula tract extending intra-orally and facially Figure . The patThe patient subsequently presented to her general dentist and the dental evaluation was negative for any dental etiology.Upon presentation to our office, the examination of her teeth was completely negative. No evidence of dental infection was noticed. The intraoral examination was completely unremarkable with perfect oral hygiene. The facial examination was positive with a large draining abscess. The lesion appeared to have significant extension under the skin with a deep undermining of the dermal layer from the musculature. The patient was subsequently anesthetized and debridement was carried out. Attention was directed to sending cultures and preserving the facial skin.The differential diagnosis on the list included an infection of a skin cyst  and due to the extensive necrosis of skin under the fistula, necrotizing fasciitis was also on differential diagnosis. After culture and biopsy were carried out, the patient was admitted to the hospital for Intravenous antibiotics until possible infection could be controlled.Immediate culture result presented a Staphylococcus infection and no methicillin-resistant Staphylococcus aureus (MRSA) was detected. Three-day hospital admission resolved the acute infection and the patient was discharged with oral antibiotics for one week Figure .The result of the biopsy was significant for fibrocelluar tissue with evidence of acute and chronic inflammatory cells. An abundance of lymphocytes and macrophages were present. A subepithelial granulomatous lesion was also present Figure .Based on these findings, the differential diagnosis included orofacial granulomatosis and Crohn's disease with secondary infection. The patient was referred to her primary physician for a workup. After a colonoscopy and endoscopic evaluation, other lesions were noticed and biopsied in the intestinal tract. The results confirmed the diagnosis of Crohn’s disease.Orofacial Crohn’s disease is not a common condition. Certain ethnicities, such as Jewish heritage (six times more risk) and Europeans  are at a higher risk -9. PatieIntraorally, it may present as a combination problem with dental infection, which may lead to a missed diagnosis, especially if the patient has poor dental hygiene. The signs of this disease include mucogingivitis, mucosal tags, ulcers, cobble stoning of the lining of the cheeks, and swelling of lips. The patients will have lymphadenopathy of the cervical chain usually on presentation ,11.The treatment of the disease includes drug therapy and, in some circumstances, surgery -14. ThisThe treatment usually starts with anti-inflammatory drugs such as 5-aminosalicylates and corticosteroids. The aminosalicylates include sulfasalazine (Azulfidine), which contains sulfa, and mesalamine . These medicines do have side effects such as nausea, diarrhea, and vomiting. The corticosteroids are very effective in reducing inflammation but also have side effects such as moon facies, insomnia, anxiety, hypertension, diabetes, osteoporosis, cataract, and an increased chance of infection. The alternative medication includes immune system suppressors. These drugs include azathioprine (Imuran) and mercaptopurine (Purinethol). These medications are usually used for inflammatory bowel disease. The side effects include liver and pancreatic inflammation and bone marrow suppression. These drugs also increase the risk of infection. Infliximab (Remicade), adalimumab (Humira), and certolizumab pegol (Cimzia) are tumor necrosis factor inhibitors. They are used in children and adults in case other treatment modalities fail. They are provided for severe cases of Crohn’s disease as an alternative to the medication mentioned. Cancer treatment medications, including methotrexate, cyclosporines, and natalizumabs are also used to decrease inflammation and treat fistulas. However, the side effects of these medicines need to be weighed versus the benefits. One of the side effects of Crohn’s disease is infection and fistula formation. These abscesses require antibiotics such as metronidazole and ciprofloxacin to prevent peritoneal infection and spread . SupplemFinally, surgery is the treatment if the disease does not react positively to medication. The surgeon will remove the portion of the gastrointestinal tract that does not respond to medication and reconnect the bowel. However, in the face and oral cavity, the luxury of the resection is less likely. The resection of facial skin could lead to a significant amount of deformity. In our patient, the lesion had extended to the surface and the surgical approach involved the removal of the infected and necrotic skin and subcutaneous skin with the packing of the wound to allow granulation and gradual closure of the facial skin fistula. This patient opted not to have any cosmetic procedures done but facial cosmetic procedures such as Fraxel laser resurfacing combined with chemical peels and micro-needling could be used to minimize the scar and the disfiguring of the facial skin.There are various presentations of Crohn’s disease. Patients may have any of the symptoms mentioned above or any combination of those could be a presentation. A practitioner should be aware of the possible presenting symptoms and be able to manage them accordingly. It is important to realize that usual patients can be responsive to some medications and not to others and combination treatment is very common. In this patient, the presentation was highly unusual due to the disease presenting on the skin side of the face and not an extensive intra-oral component. the patient responded well and is presently managed in a gastrointestinal clinic.


This article provides an innovative approach for verification by model checking of programs that undergo continuous changes. To tackle the problem of repeating the entire model checking for each new version of the program, our approach verifies programs incrementally. It reuses computational history of the previous program version, namely function summaries. In particular, the summaries are over-approximations of the bounded program behaviors. Whenever reusing of summaries is not possible straight away, our algorithm repairs the summaries to maximize the chance of reusability of them for subsequent runs. We base our approach on satisfiability modulo theories (SMT) to take full advantage of lightweight modeling approach and at the same time the ability to provide concise function summarization. Our approach leverages pre-computed function summaries in SMT to localize the checks of changed functions. Furthermore, to exploit the trade-off between precision and performance, our approach relies on the use of an SMT solver, not only for underlying reasoning, but also for program modeling and the adjustment of its precision. On the benchmark suite of primarily Linux device drivers versions, we demonstrate that our algorithm achieves an order of magnitude speedup compared to prior approaches. Modern software is developed by multitudes of developers from all over the world. As a result, the software undergoes frequent minor changes, e.g., bug fixes, introduction of new features, optimizations, refactoring, and so on. The problem of updating software is that this might break existing features—bugs might get introduced. The confidence of correctness can be increased by rigorous verification before a new revision of a piece of software is checked in. Model checking techniques , 2 verifreuse the invested efforts between verification runs. We base our approach on symbolic verification techniques, and in particular bounded model checking (BMC) [function summaries across program changes is useful in BMC when using the so called bit-blasting approach, with the direct use of a SAT solver. However, due to the known complexity of bit-precise encoding it suffers from scalability issues. Using SAT-based function summaries also creates summaries that can be significantly larger than the original formulas, and that are not human-readable, impeding their reuse and maintainability.This work addresses the problem of efficient analysis of a program after it undergoes changes. As a viable solution to this problem, incremental verification is a promising approach that aims to ng (BMC) . The preng (BMC)  has showSMT-based function summaries across the closely-related programs.We present an incremental BMC approach that is based on Satisfiability Modulo Theories (SMT) . Since SFunction summaries are obtained from Craig Interpolants  which plincremental BMC solution aims to maintain and repair over-approximating summaries of all the program functions. Overall, our solution proceeds as follows. First, a program together with safety properties is modeled in SMT, and if properties hold, function summaries are computed. Then once a change arrives, it first determines whether the old summaries for functions are still valid after the change. This validation phase is local to the change and tends to be computationally inexpensive since it considers only the changed function bodies, their old summaries, and possibly the summaries of the predecessors of the changed functions. If this local validation phase succeeds, the new program version is also safe. If local validation fails, the approach attempts to widen the scope of the search while still maintaining some locality, by propagating the validation check to the callers of the modified functions. After each successful validation, any invalidated summaries become a candidate to be repaired and are made available for checking the next program version.Our proposed summary repair approach is to circumvent the deletion of invalidated function summaries and instead attempt to adapt them to the changed functions. Our solution repairs an over-approximating summary of the program function which is coarse enough to enable rapid check but strong enough to cover more changes in an incremental checking scenario. The repair is done via two strategies: the first weakens the invalid summary formulas by removing the broken parts, and the second strengthens the weakened summary by recomputing the corresponding interpolant and adding missing parts. We keep the conjunction of newly repaired summaries for subsequent uses. The refinement procedure accompanies our incremental summary validation algorithm for dealing with spurious behaviors that might be introduced due to imprecise over-approximative summaries.The key idea behind the We implemented our SMT-based incremental verification algorithm with the new concept of summary repair in the UpProver tool. We advocate the necessity to offer various encoding options to the user. Therefore, in addition to the provided SMT-level light-weight modeling and the corresponding SMT-level summarizations supported by our incremental verifier, the tool allows adjusting the precision and efficiency with different levels of encodings. For this purpose UpProver enables the VolCheck , 12), anImprovement over previous own work.  The present work is an extension of [nsion of  publishension of  in a numStructure of the paper.  Sect. We first review symbolic program modeling and interpolation-based function summarization. Then we describe how to compute function summaries and how to apply them while encoding a program.We work in the domain of Satisfiability Modulo Theories (SMT)  where saBounded Model Checking (BMC)  is one oF represents the finite set of unique function calls, i.e., function invocation with a unique combination of a program location, a call stack, and a target function. F also corresponds to the set of functions in the call tree of the unrolled program. We use relations f to all the functions invoked by f, and child. Since each node has at most one parent, we write We write loop-free programs as tuples f, i.e., the logical formula obtained from the SSA form of the body of the function f. Note that partitioned BMC (PBMC) formula [safety query. Typically safe if the safety query is unsatisfiable.Classical BMC of software encodes an unwound program to a BMC formula . First,  formula  is constFunction summary is an over-approximation of the function behavior defined as a relation over its input and output variables. There are different ways to obtain a summary formula, and in this work we use the approach introduced in  for extrA and B, we call the pair binary interpolation instance. An interpolation algorithmI is defined over symbols appearing both in A and B.(binary interpolation) Given an unsatisfiable formula tree interpolants, generalizations of binary interpolants, obtained from a single proof that guarantees the tree interpolation property as defined in the following:Binary interpolation can be generalized so that the partitions of an unsatisfiable formula form a tree structure. We in particular concentrate on tree interpolation property iff  sum when a pre-computed summary substitutes f, and (iii) nondet when f is treated as a nondeterministic function. Since nondet abstracts away the function, it is equivalent to using a summary formula true.The level of approximation for each function sum, as follows:We define three substitution schemes: In this section, we demonstrate summary reuse and summary weakening in our incremental verification approach. Consider two programs in Fig. mentclass2pt{minimmentclass2pt{minimOur approach first performs a bootstrapping verification for mentclass2pt{minimmentclass2pt{minimSummary weakening.  Let us denote mentclass2pt{minimSummary reuse.  During the validation of Since there are no further changed functions unprocessed, the incremental checking terminates, and we simply could conclude that This section presents our solution to the problem of efficient verification of a program after a change. The problem of incremental verification is stated as follows: given the first program Note that we present the incremental verification algorithm instantiated in the context of BMC and SMT. However, the algorithm is more general and can be applied in other approaches relying on over-approximative function summaries.In this section, we first describe the main points of Algorithm 3. Then we describe the important subroutines of the algorithm; (i) an improvement of the algorithm with the summary weakening in Sec. Our approach for incremental verification considers two versions of the program, F to the set of all summaries S. Initially in case no summary exists for f . The algorithm also maintains the set The algorithm maintains a worklist f is not invalid . If so, f. Note that here the substitution scenario inline is used where all function calls in the subtree of f are naively inlined. Later in Sect. The if-condition at line 6 checks whether the summary of strengthening procedure in our approach. If The validation check of pre-computed summaries occurs in 8. The validity of implication f is introduced in f is marked as changed by our difference-checker. In such a scenario, since summary of f is trivially false, the validation check immediately fails, f gets added to f with inlined f generates a summary for f (line 17).Note that if a function Whenever a summary is identified as invalid (line 9), the sub-routine The previous algorithms of incremental verification in , 14 checThe number of top-level conjuncts in a summary formula is a measure of generalizability of the interpolant. In some applications  it In Algorithm 3 once the summary turned out to be invalid (line 9) the sub-routine f is constructed. In this phase f, the summary is used as a substitute for the function body. Then in line 4 the containment of the resulting formula f. In case no conjuncts are left, the function summary is assigned to the weakest possible summary, namely true (line 10) and it is added to the set In line 2 the PBMC formula Once the weakened summary is obtained from Algorithm 4, in Algorithm 3 the check always propagates to the caller  to make sure the new weakened summary is suitable in the subtree rooted at the caller. It can be the case that the weakened summary does not capture the whole relevant functionality of the changed function and needs more conjuncts (strengthening) that can be obtained during the validation check of the caller and interpolation in line 17 of Algorithm 3. Note that in this case even though the check propagates to the caller, it would be still beneficial in the sense that the actual encoding of the function body is substituted with the weakened summary, thus the overall check will be less expensive and still maintains some locality.f are inlined. In other words, the initial substitution scheme was set to In Algorithm 3 line 7 creates the PBMC formula In this section we present an algorithm for creating PBMC formulas in a more efficient way, then we present our solution for refining the abstract summaries on demand. The pseudocode in this section can substitute lines 7 and 8 in Algorithm 3.f, they substitute the actual body of the function calls in the subtree, (ii) while checking the validity of summaries, the infeasible behaviors that are detected during analysis of abstract summaries are refined by an iterative refinement procedure.Algorithm 5 consists of two key points: (i) while constructing the PBMC formula lazy style. Then the PBMC formula The initial over-approximation in Algorithm 5 is set to Then the resulting inline in the next iteration (line 11). If the set is empty, the check fails and the summary is shown invalid. This refinement loop repeats until the validity of the summary is determined.Based on the satisfying assignment the algorithm identifies the set of the summaries used along the counter-example and stores them in k unrolling steps, the algorithm always terminates with the correct answer with respect to k. Notice that in this article, program safety is considered with respect to the pre-determined unwinding bound k. In the remainder of this section, we assume the same k for both old and new programs. In case the user increases the bound for a specific loop, the corresponding function needs to be validated as if changed.This section discusses the correctness of the SMT-based incremental verification algorithm, i.e., given The correctness of Algorithm 3 is stated in the following theorem:Assume the interpolation algorithm for f range over the function calls satisfying f. We first show that the propertiesLet Safety from properties  . Otherwise, the check propagates towards the root of the call tree and eventually may lead to an UNSAFE result. Thus, it suffices to show that the recomputed or repaired interpolants satisfy property (operties  and 8)  Incremenmentclass2pt{minimIn case some change in property  holds. Iproperty . \documeWe instantiate our generic SMT-based incremental verification approach to certain theories of SMT. In particular, we focus on interpolation algorithms that are the low-level primitives in our approach and discuss the requirements they shall fulfill. The theories of our interest are Linear Real Arithmetic  . The intconjunction of inequalities. The algorithm is an extension of A, it tries to decompose the vector of weights (Farkas coefficients) into several vectors. This effectively decomposes the single sum into several sub-sums. If each of the sub-sum still eliminates all A-local variables, the resulting inequalities can be conjoined together to yield a valid interpolant.Recently  introducSince As for the theory of ithm in   that relithm in   graph daFor the propositional part, we use the well-known Pudlák’s interpolation algorithm , which iTree interpolants are used in our incremental algorithm for determining the satisfiability of a first-order logic formula that reuses summaries generated after the unsatisfiability of a slightly different formula is determined. Among the widely used family of interpolation algorithms for The following two lemmas state which found in  where wefined in  have treThe following lemma considers the tree interpolation property of interpolants generated from the same resolution proof in roven in .lgorithm  guaranteIn a purely propositional setting, we rely on the results from , 31 whicPropositional interpolation algorithm introduced by Pudlák  guaranteby construction. Instead the correctness of the algorithm can be preserved by checking for the tree interpolation property on-the-fly. This means that the algorithm can still produce a correct output even if the tree interpolation property is passed by performing real-time checks in verification run.The proposed solution relies on the above lemmas for the correctness of the incremental verification algorithm in the context of bounded model checking. However, the correctness of the algorithm is not solely restricted to the preservation of the tree interpolation property It is worth mentioning that our incremental algorithm with theory This section describes the implementation of our algorithms in the UpProver tool which is a bounded model checker written in C++. UpProver concentrates on incremental verification of program versions written in C. After each successful verification run, it maintains a database of function summaries to store its outputs, which become available as inputs for verification of each subsequent program version. For bootstrapping verification UpProver uses HiFrog standalone bounded model checker . For satThe architecture of UpProver tool is depicted in Fig. Difference analyzer: UpProver performs source code differencing at the level of SSA forms for both the old and the new program to identify a set of functions with code changes. It annotates the lines of code changed between entation . The funCall tree traversal: The call tree traversal guides the check of pre-computed summaries for the modified functions in bottom-up order. It exploits the SMT solver to perform summary validation. When necessary it performs an upwards refinement to identify parent functions to be rechecked using SMT solver or performs summary refinement to refine the imprecise summaries in the subtree.Summary repair: Summaries of SMT solving and interpolation engine: For checking BMC queries and computing interpolants, UpProver interacts with the SMT solver OpenSMT [ OpenSMT . The sol OpenSMT , proofs  OpenSMT , Farkas  OpenSMT , and Dec OpenSMT .Summary storage: UpProver takes summaries RQ 1Is the use of SMT instead of SAT in incremental verification efficient for real-world programs?RQ 2Is reusing function summaries beneficial in incremental verification?RQ 3How does our approach compare with other incremental verifiers?To evaluate our algorithm, we aim to answer the following research questions: Benchmarks and setup:http://verify.inf.usi.ch/upprover.To answer RQ 1, we compare the run time of incremental verification using different encodings. Each point in Fig. The results for benchmarks show the trade-off between the precision and run time of incremental verification. In fact the theories are complementary. This can be contrasted to the plot in Fig. To answer RQ 2 we demonstrate how summary reuse and summary repair benefit incremental verification. To this end we first compare the performance of the tool with and without summary reuse, and then we show how summary repair results in more summaries while the overhead of producing more summaries is negligible.reusing the summary against not reusing it. As opposed to summary-based incremental checking in UpProver that maintains and reuses over-approximating summaries of the functions across program versions, a standalone BMC tool, e.g., HiFrog [The purpose of this section is to compare verification time of , HiFrog  and cbmc, HiFrog , createsreusing the summary of the first version on x-axis, and the running time of HiFrog without reuse on y-axis. The plots demonstrate the performance gains of incremental verification with reusing function summaries against not reusing it. A large amount of points on the upper triangle lets us conclude that UpProver is an order of magnitude faster than the corresponding non-incremental verification for most benchmarks.The plots in Fig. Table uniquely verified programs indicates how many The row The row It is worth noting that we compared the results of UpProver with the expected results of SVCOMP, since most benchmark names indicate the expected result. Out of 2910 pairs of benchmarks, 2794 pairs had both versions classified as safe. However, for the remaining 116 benchmarks, no expected result was provided and they were marked as unknown, thus we are unable to obtain precise numbers for The overall findings from our experiments show evidence for the following key points: precision and performance-gain present a trade-off. UpProver with f, Algorithm 4 first weakens the summary by removing broken conjuncts of the summary. In case the weakened summary is not strong enough, Algorithm 3 (line 17) strengthens the weakened summary by recomputing interpolants for f and conjoining with the weakened summaries. We shortlisted 43 pairs of C programs whose summaries was repaired at least once during incremental verification.In this section, we measure the number of repaired summaries that are generated by two out of the box Figure We can also view the result of this experiment from a different perspective. It can be seen as a way to test how good the interpolants are and how beneficial is the summary weakening. In the summary validation phase in UpProver, the more general interpolants are, the more likely they contain changes of the functions in the new version. Experimenting with Now that we have an estimate of the number of function summaries repaired by In the following, we study the overhead of weakening  which are used to prove equivalence of closely related program versions. To tackle the problem of formally verifying all program revisions various techniques and tools have been proposed for the last two decades [Other techniques for verifying program versions are based on  decades , 45. Exi decades –50. Sinc decades , 52 or c decades . DespiteThe work in  investigA group of related work includes techniques using interpolation-based function summaries certificates of correctness expressing function specifications.The work we find most closely related to ours is eVolCheck , 12, theWe addressed the problem of verifying a large number of programs, in particular, when they are closely related. To avoid expensive full re-verification of each program version and repeating a significant amount of work over and over again, our proposed algorithm operates incrementally by attempting to maximally reuse the results from any previous computations. The key contribution of this work lies in enabling this flexibility by SMT encoding and exploiting the SMT summarization. Having SMT encoding allows for a lot of flexibility when reusing and repairing the summaries leading to the optimization of the whole process which was not possible in the previous SAT-based approach. To achieve incrementality, our algorithm extracts and reuses SMT-based function summaries to over-approximate program functions. It also provides an innovative capability of repairing previously computed summaries by means of iterative weakening and strengthening procedures. Moreover, it offers an efficient way of building formulas and refining them on-the-fly. Through extensive experimentation, we demonstrate that our approach advances the state of the art in incremental verification of program revisions and is significantly more efficient than its predecessor eVolCheck and non-incremental BMC approach.In future, we plan to extend the tool to handle summaries from different theories simultaneously , possibl


Spinal tuberculosis (TB) is a condition that affects numerous people around the world. The incidence of TB prior to the pandemic was decreasing by about 1.8% per year; however, COVID-19 has complicated this incidence rate leading to an increase of 4.5% in 2020 and 2021. Spinal TB is a rare event in all TB patients. The management could be multifactorial including location, severity, and symptom, and this case demonstrates an example of issues to consider in the diagnosis and management of patients. This is a case of a patient presenting with back pain which was subsequently diagnosed as spinal TB. We will review this patient's presentation and consideration for multifactorial opinions in the literature. This literature review demonstrates that there is no one treatment option available. Providers need to tailor treatment to each individual case. This is an example of a case that illustrates that diagnosis of spinal TB is not straightforward and clinicians may have to make a judgment call and treat prophylactically to prevent a poor prognosis. Spinal tuberculosis (TB), also known as Pott’s disease, has been around for at least thousands of years. Percival Pott was the first to describe the case of spinal TB in 1779. However, archaeological analysis of mummies suggests that even Egyptian pharaohs were potentially affected by spinal TB . Mycobacterium tuberculosis can affect the respiratory center in the brain stem leading to significant compromise in the patient's respiratory drive. Spinal TB affects most commonly the thoracolumbar region of the spine [Spinal TB is very difficult to treat, and its location makes it a significant risk to the patient’s health. The involvement of the spinal cord can lead to paraplegia or quadriplegia based on the location of the spinal cord. Spinal cord involvement can cause major neurological deficits according to the level affected. High-level infection byhe spine . The inche spine . It is nhe spine . Early iM. tuberculosis infection, chronic spinal TB presents with severe kyphosis and, in a significant minority of patients, neurologic deficits secondary to mass effect, mechanical instability, and/or stenosis [Spinal TB manifests as an extrapulmonary manifestation of tuberculosis - constituting about half of cases of musculoskeletal involvement . Patientstenosis . The kypstenosis .It has been shown that early diagnosis is the key to management . ComputeThe management of spinal TB has been described extensively. This case however demonstrates the difficulty clinicians face when everything is not straightforward, and suspension of diagnosis may require proactive treatment. The key issue is the location of the lesion  and whether there is neurologic involvement, instability of the spine, and/or presence of kyphosis. Recent recommendations focus on medical management including multiple antituberculosis medications given over a defined period of time.A 52-year-old male presented to a local emergency room in Southern California for severe acute-onset back pain. The patient was playing soccer the day before and woke up the following morning with severe lower back pain that was immobilizing. In the emergency room, he reported severe pain and distress. He was completely asymptomatic prior to this event with negative past medical history. He was a middle eastern male with no habits, and he appeared athletic and in good physical shape. He worked as a sales representative for a store and was married for five years. His blood pressure was stable at 128/67 with a heart rate of 95 and was afebrile on clinical evaluation. The pain was localized to the thoracolumbar spine with no signs of inflammation involving nearby skin. There was no neurologic deficit identified on exam of the upper and lower extremities or trunk. The local lumbar region was tender on pressure and movement, but no erythema was noticed on his exam. The patient was placed on intravenous fluids, and morphine was provided for immediate pain control.Lumbosacral x-ray was significant for small anterior osteophytes at the L5 level. No significant disc space narrowing was noticed. An MRI scan was ordered to better evaluate the questionable soft tissue around the osteophytes. MRI of the spine revealed extensive periarticular enhancement about the right L4-L5 facet of the joint with extension into the epidural space and posterior paraspinal musculature with possible infectious fasciitis Figure . It was The patient was subsequently taken to operating room for imaging-assisted core biopsy surgery. Biopsy of area close to abnormal region next to L4-L5 was done. Result of core biopsy revealed muscle and fibroadipose tissue with chronic inflammation and no caseation necrosis seen in the sample obtained. Immunostains for AE1/AE3, S100, and desmin were negative. SMA and SATB2 showed patchy positivity. CD138 highlighted some plasma cells. CD3 and CD20 highlighted T and B cells. The patient had a history of BCG vaccination, and therefore positive skin test result was questionable. He was subsequently scheduled for a lung scan to rule out pathologic involvement of the lungs, redo of the core biopsy, and culture for abnormal infections such as TB.Over the course of the two months patient followed up with clinical spine surgery team and symptoms had improved. His lung CT scan showed negative result; however, due to previous BCG immunization, the positive skin test was expected. The team felt that a second biopsy and culture at different angle and depth may give better result; however, patient was very hesitant to get it done and decision was made to treat patient conservatively with observation and follow up. He was prophylactically placed on Rifampicin, Ethambutol, Isoniazid and Pyrazinamide for two months followed by Isoniazid and Rifampicin for six months. He was stable on his six-month follow up and was placed on continued observation with repeat MRI scan planned in future.Spinal TB is an uncommon condition seen in less than 1% of TB patients. Being very debilitating, the condition may lead to spinal collapse, precipitating kyphotic deformity. The most involved site is the anterior portion of the spinal column. Destruction of the osseous tissue and abscess formation is the most common finding in spinal TB . It is nManagement of spinal TB is based on medical and surgical treatment. In cases where the lesion is accessible, a surgical approach combined with medical management is the treatment of choice. In cases where the surgical approach is unfeasible or associated with significant possible complications, then medical management using combination antituberculosis medication is considered first . Early dSpinal TB has a favorable prognosis, especially with earlier diagnosis and treatment. There is no definitive recommendation for the treatment of spinal TB. The general consensus seems to be aggressive medical management followed by surgery if the lesion is accessible or if spinal instability exists. In this case, after one attempt at biopsy, the patient was hesitant to get another biopsy due to the location of the lesion. The team decided to proceed with medical management with a combination of Rifampicin, Ethambutol, Isoniazid, and Pyrazinamide for two months and follow up with Isoniazid and Rifampicin for six months. The patient improved on follow-up and was stable and placed on every six months follow-up clinically.Spinal TB is a condition that affects a significant number of people around the world. Understanding this disease and management can be crucial for the prognosis of the afflicted patients. The patients can have a variety of presentations and medical, surgical, or combination therapy has to be deployed to treat each patient individually. The general approach is tailored based on the location of the lesion and medical and surgical teams have to work in a coordinated fashion to treat the patients based on clinical findings. It should be mentioned that organized systemic treatment of the population in highly susceptible countries needs to be considered as a preventative method to minimize the spread of this disease. Even though this is a rare condition in modern countries, immigration and travel can predispose patients to this disease, and practitioners should be aware of this condition and treat it appropriately.


The objective of the Psyche Magnetometry Investigation is to test the hypothesis that asteroid (16) Psyche formed from the core of a differentiated planetesimal. To address this, the Psyche Magnetometer will measure the magnetic field around the asteroid to search for evidence of remanent magnetization. Paleomagnetic measurements of meteorites and dynamo theory indicate that a diversity of planetesimals once generated dynamo magnetic fields in their metallic cores. Likewise, the detection of a strong magnetic moment ( The Psyche mission aims to characterize the structure, composition, geology and origin of the main belt asteroid (16) Psyche  on a 2.15-m long boom, each connected by a harness to electronics units (EUs) within the spacecraft bus Figs. , 5. EachMIT leads the science investigation, operations, ground data processing and trending, DTU designed, built, and calibrated the Magnetometer and leads anomaly resolution, and the Jet Propulsion Laboratory leads commanding. MIT, JPL, and the University of California, Los Angeles jointly developed the level 1 and level 2 Magnetometer science requirements. All four institutions will participate in science operations and data analysis.Most meteorites are samples of planetesimals and many contain NRM records of past magnetic fields on these bodies. The ferromagnetic minerals carrying these records are mainly iron-nickel metals, iron oxides, and iron sulfides. The NRM intensities of meteorites depends on their mineralogy, grain size, history of exposure to ancient fields, and preservation state.The origin of meteorite NRM was debated for decades following its identification in the 1960s. However, it is now understood that some meteorites acquired their magnetic records during or after their formation during the first several Ma to hundreds of Ma after solar system formation  Scholl  has rece) Scholl . XPEEM mEssentially all known IVA irons, IIE irons, and MG pallasites likely cooled too slowly to record a nebular magnetic field, so any NRM would likely be a record of dynamo. Cooling rate studies of IVA irons indicated that their parent body likely lost most of its silicate mantle through impacts occurring early in its history  onboard the European Space Agency’s Swarm mission 2013–)  Figs.  and the z) Figs. . Fig. 8EDTU designed, built, and delivered engineering models and ultimately three Flight Models for the Psyche project. Flight Models 1 and 2 became the pair SU1 and EU1 and the pair SU2 and EU2, respectively. Flight Model 3 is held in reserve at JPL for anomaly resolution and as a backup flight spare.The Magnetometer uses the fluxgate principle for measuring magnetic fields Primdahl . The basThe Psyche Magnetometer’s core consists of 11 wraps of an amorphous magnetic metal ribbon, which is by heat treatment optimized for several magnetic properties  . In principle, the pickup coils could also used for compensating the external field, such that the CDC could be used as a fluxgate magnetometer with excellent performance. However, the nonspherical shape of its pickup coils limits the omnidirectional linearity  that controls all digital functions in the instrument: it produces a highly stable excitation square wave signal with a frequency of 15.625 kHz and a detection signal of frequency 31.25 kHz that are used by the excitation drive and phase detector blocks, respectively. After power on, the instrument operates autonomously. It activates the phase detector with respect to the excitation current in the sensor using the pre-flight predetermined default parameters for the frequency, delay and width, and transmits data at up to 50 Hz.The Magnetometer design incorporates components with high thermal and temporal stability against degassing in space, stresses from changing temperatures, and total ionizing dose from high energy particles. Nevertheless, its performance is ultimately limited by tolerances in the machining processes, electronic parts and assembly of the individual parts and their temperature dependencies. A calibration process has been implemented to correct for these effects. The raw analog-to-digital converter readings from the Magnetometer are transmitted through spacecraft telemetry to ground, where they are converted from engineering units (eu) to magnetic field values (nT) as discussed in Sect. Because conversion from eu to nT occurs during ground data processing, the Psyche Magnetometry uncertainty budget does not depend on the values of the coefficients in o et al. ,b. We alon Sect. .The parameters Offset knowledge as a function of temperature is the dominant term in our Instrument Uncertainty and is specified by a driving requirement for the Magnetometer design Fig. . Both thBased on heritage from the Swarm VFM, the long-term temporal drift of the Magnetometer offset is expected to be exceptionally low  Fig. . The maiThe total masses of each of the two EUs and each of the two SUs including their brackets and harnesses are 0.92 g and 0.9 g, respectively. The length of the intra-harness between each EU and SU is selectable without degrading the performance and for Psyche was required to be 3.85 m for all Flight Models. The masses of each harness and bracket are To mount the SU onto the spacecraft, a carbon fiber reinforced polymer bracket was developed with a finger shape, with one end glued onto the CSC so as not to deform the sensor’s structure during temperature changes. The other end of the bracket has a plate with four holes used to attach the sensor to a Ti node on the boom. The EU has a standard interface with four bolts into the panel of the spacecraft. Attitude transfer from the SU axes to the FS coordinate system was achieved by a reference cube assembly temporarily mounted on each SU. The orientations of the three normal faces of the cube were determined with respect to the SU coil axes following the triaxial coil method of Primdahl et al. . During Upon application of power to one of the EU sides (A or B), that side will connect to the SU autonomously. Each SU was designed to be nonredundant as it does not contain any electronic components. Each EU side contains all resources to operate independently and it is not expected that both sides will be powered on at the same time during science operations. The EU chassis walls are composed of aluminum with side wall thicknesses and top and bottom wall thicknesses of 3 mm and 6 mm, respectively. This provides radiation protection to the EUs at a level that is about 10 times larger than the expected total ionizing dose . Table Using a low-voltage differential signaling (LVDS) electrical layer, the Magnetometer communication features a universal asynchronous receiver-transmitter (UART) serial interface at 115,200 bps with a structure of 1 start bit followed by 8 bits and then a stop bit. Data and commands are organized in packets following the Swarm Packet Utilization Standard (PUS) protocol  payload, latch vales, and traveling-wave tube amplifiers (TWTAs)] and the SUs, minimizing the usage of ferromagnetic and high magnetic permeability materials , reducing current loops , and self-compensation of the fields within a component to minimize magnetic poles . We also ensured that the spacecraft has no conductive paths along which there could be strong thermal gradients that could generate thermoelectric currents during flight  File Delivery Protocol (CFDP) data products for transmission. Science packets include three magnetic field axes and temperature measurements required for calibration and the information to accurately timestamp the measurements. The observations are nominally reported with a frequency of Partially Processed data have been corrected for temperature-dependent scale factors, offsets, non-linearity and non-orthogonality using ground calibration data. The measurements are in physical units  along with internal timing for the instruments are used to time-tag the measurements.Any packets found to be corrupted and/or are otherwise unusable will be flagged either by onboard flight software or by the MIT ground data system and will be rejected from further processing. The ground data pipeline will track the identity and timings of rejected packets. The data pipeline will further scan the data stream to find, report, and resolve, any temporal discontinuities in the data.The absolute time of the start of each packet, Raw data are uncalibrated and in units of eu for each of the three magnetometer axes th order polynomial: The production of Partially Processed data involves converting the three axes from each SU into field vector components. This involves three steps: housekeeping calibration, linearization, and linear calibration. During the housekeeping calibration, the temperature readings for the CSC, CDC and EU are linearized and converted to ft Sect. , and \doThe next step is to apply a linearization algorithm to the Raw measurements: Finally, linear calibration applies the orthogonality matrix, temperature dependent offset vector, and sensitivity matrix to determine the applied magnetic field vector in nT in the orthogonalized sensor measurement frame coordinates . These contributions can then be suppressed by reducing the power in the identified frequencies to the noise level  turn on and off and when subsystems switch between different modes . These changes will be identified in two ways. First, pattern-recognition algorithms can identify rapid field changes in time series of the differenced field like those expected for near-instantaneous changes in the power state of the flight system. The algorithm currently implemented in the data pipeline uses an 0.1 s running average of the differenced field es Sect. . When a The step removal and peak suppression algorithms can be iterated to further clean the data. After these calibration steps are complete—rotation into FS coordinates and suppression of flight system fields and residual instrument offsets—and the final differenced field is determined to be less than then the acceptable noise threshold, the final result is calibrated, cleaned, science-grade data, The Derived data are magnetic field measurements rotated from the FS frame into coordinate frames oriented relative to (16) Psyche’s orbit, a frame rotating with (16) Psyche, and the Sun Fig. : 9\documThe The The The J2E frame is the same as the J2000 Earth mean orbit inertial frame but centered at (16) Psyche’s instantaneous location: The The The The PBF frame is a non-inertial frame centered at the center of mass of Psyche and rotating with the body: The The The The PSO frame is an inertial frame centered at the center of mass of Psyche The spacecraft ephemerides, as well as the ephemerides of solar system bodies are provided by the Navigation and Ancillary Information Facility (NAIF) at JPL in the J2E, PBF, and PSO frames. The data pipeline uses the SPICE toolkit to extract the information in both frames for the spacecraft trajectory and performs conversions of the magnetic field from the spacecraft frame (NAIF name “PSYC”) to the other frames as needed for different products.The PBF frame will be used for mapping the magnetic field with respect to geographical location on the body’s surface, while the PSO frame will be used to map the field with respect to the magnetosphere, which rotates both with the body and with the direction of the incoming solar wind flow. All conversions between the frames are time-dependent and rely on knowledge of the ephemerides of Earth, (16) Psyche, the Sun, and the spacecraft, as well as the spacecraft attitude, as provide by NAIF.The purpose of high-level data processing is to determine whether Psyche contains remanent magnetization consistent with formation by a dynamo paleofield, and if so, to constrain the strength and pattern of this magnetization. This will yield at least one and up to three different data products. First, we will constrain the asteroid’s dipole moment and, in particular, establish whether it exceeds the threshold specified by the level 1 requirement that would indicate Psyche has magnetization like that known for iron meteorites at spatial scales of 40 km or greater. If a remanent dipole moment is detected, then depending on the ratio of the remanent field to the noise and on how spatially complete are the measurements, we will optionally create a magnetic anomaly map and possibly even estimate higher-order multipole field terms.Given that the flight system magnetic field is suppressed during the production of The dipole moment of the asteroid will be estimated from ons Fig.  indicateSimilarly, we can obtain a constraint on Psyche’s dipole moment by recasting [Eq. ] in termThe simplest situation will be if the spacecraft never passes through a magnetopause boundary even during Orbit D, such that hip [Eq. ] and ourhip [Eq.  indicateDue to the variability of the solar wind and the body’s rotation, we expect the magnetospheric topology to significantly change over time. While large planetary magnetospheres have extended regions with a quasi-fixed topology, a small magnetosphere of a quickly rotating body would continuously change its configuration as it reconnects to the external fields. Because of the periodicity of the rotation and the fact that similar wind condition would repeat during the mission, we will collect data from various times and bin them as a function of spacecraft locations in the PBF and PSO frames. This should enable us to construct several separate mean configurations for further study. For orbits that pass into and out of the magnetosphere, we will use the binned data to map the magnetopause surface. Magnetopause crossings can be identified from observing abrupt changes in the angle of from Eq. .Orbits for which the spacecraft spends a large fraction of the orbit inside the magnetosphere will yield s to Eq. : 11\docuWe can use the above estimates of the moment to model the solar wind interaction with the asteroid using hybrid simulations  and associated higher order Gauss coefficients would provide bonus science. As discussed below, the Gauss coefficient power spectrum could constrain the depth of the magnetization and its horizontal spatial scale. Combined with anomaly maps, the magnetic power spectrum could enable a correlation between the NRM and possible geologic terranes . This could in turn constrain the age and source of the NRM  and in turn constrain the thermal and magnetic evolution of the asteroid. For example, the demonstration that Psyche’s magnetization was unidirectional or not could be used to distinguish between external field sources like the nebular field and internal field sources like a dynamo, assuming scrambling of the magnetization by impact-induced block rotation can be excluded Sect. .Obtaining a magnetic anomaly map would require that Psyche’s dipole moment was sufficiently large that the spacecraft spends a large fraction of time in a magnetosphere . In this case, a map could be obtained of  Blakely . Note th Blakely  can be eThe power of the magnetic field is defined as the mean-squared average of the magnetic-field intensity at a given radius wn Lowes . To assewn Lowes . The modThe number of spherical caps and their mean-squared magnetization are part of a factor that multiplies the theoretical power spectra and that does not otherwise affect the power spectrum shape  Fig. B. Near dce) Fig. C. The lace) Fig. . Fig. 13These example spectra show that if the Gauss coefficients of Psyche can be determined for degrees beyond the dipole term, that it should be possible to constrain the size and depth of the magnetic sources. We emphasize that the theoretical power spectra of Wieczorek  were devData products will be archived as daily Common Data Format (CDF) files with Planetary Data Systems (PDS) Small Bodies Node using the PDS4 standards. Data products at the Raw, Partially Processed and Calibrated levels will be archived continuously throughout the mission as the data are received from the spacecraft and processed through the Magnetometer data pipeline. Data products up to the Calibrated data level will have a measurement cadence of The pre-flight calibration campaign focused on determining the scale factors, orthogonality and offsets, of the SUs and EUs Sect. . HoweverDuring initial checkout activities occurring just after launch, the Magnetometer will be turned on and passively measure the flight system magnetic field as other subsystems are progressively turned on and cycled through their various modes and power states. The data collected during initial checkout will be used to build calibration tables that include both the expected field contribution from each subsystem as well as coupling coefficients based on the changes in the observed field resulting from the subsystems. These tables will later be updated using information collected throughout cruise and during a flyby of Mars. During orbital operations, the calibration table will be used along with ancillary data indicating what subsystems are being commanded to inform the removal of flight system generated fields using gradiometry and frequency filtering of the differenced field Sect. .In addition to the passive monitoring of the flight system components, there will be a dedicated solar wind monitoring interval during initial checkout for determination of the zero-level field, ep Sect. . Solar wep Sect.  for whicep Sect. .In particular, time sequences of the ambient field can be used to estimate the zero-level field for each SU-EU pair as those values that minimize the variance of the squared magnitude of the measured field The solar panels are expected to be the main subsystem contributing to the flight system field in the frequency range es Sect. . FurtherWe will therefore characterize the solar array-generated fields at each SU as a function of ta Sect. . These cThe Psyche Magnetometry Investigation is designed to search for a remanent field around asteroid (16) Psyche that would provide evidence of past dynamo action. Evidence for a core dynamo would demonstrate that the asteroid was partially or fully differentiated rather than being an unmelted accretionary aggregate, thereby addressing one of the key mission science objectives. Using our knowledge of the age and intensity of NRM in meteorites and a nascent but growing understanding of dynamo generation on planetesimals, we conclude that a demonstration that Psyche has a moment of at least