Surface registration is a one of the crucial and actual problems of computer aided surgery. This paper presents the modification of the non-rigid Iterative Closest Point Algorithm which takes into account an anisotropic noise model and landmarks as guided correspondence at the transformation step in every iteration. The presented approach was validated on human abdominal briefing surface data from a time-of-flight camera. We took the median of the resulting measures and the outcome is presented: the median of means of surfaces distance was at the same level for both variants of the ICP algorithm and is comparable with the isotropic variant, the median of mean landmark position errors decreased by 0.93 units (over 20% improvement) and the median of percentage of single correspondences in target point cloud increased by 11.96%. The results showed that the introduction of the anisotropic model of noise for the ToF camera allows for the improvement the percentage of target cloud points which had only one correspondent over 10% impartment and additional weighting of markers also improves the measure of the quality of finding real correspondents over 20% improvement. In the examined dataset, where the average initial distance between the clouds of points in the inspiratory and expiration is equal to approx. 7.5 mm, a more than 10% improvement in the quality of the correspondence improves the accuracy of matching the surface within 1 mm which is a significant value in application of minimally invasive image guided interventions. Nowadays there’s more and more research carried out in the field of precise and automatized acquisition of human organs as 3D models. Such models can be used to diagnose a pathological state of an organ or enhance therapeutically procedures. A common use of 3D models of human body organs is minimally invasive surgery. Certain cases of working with 3D models require registration of point clouds for achieving an outcome in form of transformation values. That is where registration algorithms play a major role. Next in the few paragraphs we introduce Iterative Closest Point algorithm, then the rigid and non-rigid variants of the ICP algorithm and their recently published applications are presented.One of the common known registration algorithms is the ICP algorithm introduced by . The oririgid Iterative Closes Point lead to the creation of two pathways of algorithm development. One alternative was presented by [non-rigid application and ICP non-rigid algorithm modifications.Modifications of the ented by  and the ented by , in whicnon-rigid application for surface registration algorithms. A non-rigid surface registration algorithm which uses feature points and deformation constraint was presented by [In this section we present other recently announced and available ented by . The algented by  describeented by . By consented by  reviews ented by . In the ICP non-rigid algorithm modifications we also have found some propositions. First novel enhancement to Iterative Closest Point Algorithm is provided by [As regard recently published vided by . The artvided by . The proThe aim of this article is to present a modification of non-rigid Iterative Closest Point Algorithm by introducing an anisotropic noise model for the Time of Flight camera. Our article extends/continues research carried out by . We presIn this section we present previous works that have been our inspiration during creation of our modifications of non-rigid ICP algorithm.The non-rigid ICP is a variant of the classical rigid ICP which was presented by . The newWhen multiplying the vertex vector and its transformation matrix the bottom row of the rotation matrix corresponds to the ‘one’ values in the vertices vectors and allows the translation of the point. The other values of the transformation matrix allow the rotation in x, y and z axes.d—distance function cost, W—N × N identity matrix, D—N × 4N source cloud points, U—N × 3 correspondent target cloud points, X—4N × 3 transformation matrix.An iteration of the algorithm starts with a search for correspondences between points of both the source and target clouds. This stage is the same as in rigid ICP algorithm. Euclidean or normal-shooting approach is available to find closest point pairs. After finding corresponding pairs of points we can define the distance term that has been proposed by  as folloIn Eq.  the matrNext two additions to the global cost function were presented as an improvement to the classical approach.landmark term which is similar to the distance term, but applied to landmark vertices. Matrices DL and UL are composed in the same way as the ones in correspondents distance term, except these matrices are filled with only vertices provided as pairs of landmarks. The beta parameter has been initially set to ‘one’. The landmark term is as follows:l—landmark distance function cost, DL—source cloud landmarks, UL—correspondent target cloud landmarks, X—transformation matrix.One of them is the s—stiffness function cost, M—node-arc incidence matrix, G—4 × 4 weighting matrix, X—4N × 3 transformation matrix.Second of them is the stiffness term, which sets the rigidness of the source cloud. It needs to be provided with a topology matrix M which describes either 4-connected or 8-connected neighborhood relations between adjacent points in a mesh. The stiffness term is defined in following way:G can initially be set as the identity matrix. The operation done on the M and G matrices is the Kronecker product.The matrix M should be defined such that each column represents a point in source cloud and rows represent single connectivity relation between these points. The relation is directional. In the column representing the starting point, a value of ‘− 1’ was used and in the column of the destination point, a value of ‘1’ was used. The rigidness of the cloud depends directly on the Alpha parameter. The matrix Finally we create the global cost function which is composed of the three terms described above. The global cost function is presented in following way:The matrix equation defined above is a quadratic function with an unknown variable X. It is possible to minimize that function by setting its derivative to zero and solving the acquired linear equations system. The minimum of the global cost function, with X as input variable, is located at:Resulting transformations are applied to the source cloud points and it becomes the new initial input cloud for the algorithm. After that, a new iteration begins. The algorithm is repeated until either maximal iteration count has been achieved or clouds distance measure reaches a preset precision.Another innovative approach in terms of enhancement of the rigid ICP algorithm was proposed by . This veThe time-of-flight localization error model assumes that the camera which the model was acquired from generates a point localization noise. It is a common issue with cameras and it is greater in the axis that connects the point and the camera origin than in perpendicular axes. The noise strength is set using variances that can be established arbitrarily or in accordance with the camera specification. Variance values are placed in a variance matrix which next is used to calculate covariance matrices k−1—rotation matrix.It is important to notice that presented values of the cross-covariance matrix and the covariance matrix of source cloud are only initial. These values change with each iteration and the covariance matrix needs to be recalculated based upon the rotation values and values of the covariance matrix achieved in the previous iteration:Cross-covariance matrix allows the algorithm to calculate the weighting matrix W.It is then used to modify the correspondents matching stage of the classical ICP algorithm. Article  assumes new—modified Euclidean point distances, W—weighting matrix, x—source cloud points coordinates, y—target cloud points coordinates.The modification of the Euclidean distances by application of the weighting matrix leads to a new set of distances used to find correspondent points in source and target clouds:Another alternation of the ICP algorithm presented in  is relatAs mentioned in the introduction, this article is a continuation for work presented by . This apz = 10 mm. The standard deviations of localization errors in x and y axes were set to 0.02 mm. The localization error was set equally for both input point clouds.First, the corresponding points pairs finding stage was changed. Instead of using the plain Euclidean distance norm presented by , we modiThe covariance matrices and the cross-covariance matrix were calculated as presented in “As mentioned, the source cloud covariance matrix has to be recalculated after each iteration of algorithm because of updated positions of source cloud points . Due to Using  algorithAnother modification was that instead of leaving the weighting matrix W as the identity matrix, we set the weights of the points which were landmark points placed in matrix D to value ‘4’. For the rest of the points, weights were set to value ‘0.25’. This change increased the contribution of landmark points in the algorithm.z = 10 mm, σx, σy = 0.02 mm. The purpose of this was only to visually present how finding the corresponding points is affected using the approach presented by [The artificial data used for testing were two square, flat meshes containing 625 points each, created in Matlab environment . These sented by .To show what effect had the modified weighting of the landmark points on the outcome of the algorithm, the surfaces without noise have been drawn from each other creating sort of a step pattern. The alpha parameter starts at a value of 100 and decreases every 20 iterations with rate of 0.5*alpha. The maximal iteration count for testing on artificial data was 100 iterations.It is crucial to mention that in case of artificial data, there were known correspondences of cloud points. This means that the points of one cloud correspond by their number to the points of the other cloud e.g. the first point of source cloud corresponds to the first point of target cloud, both being a part of a regular and square mesh.For measuring the suitability of our approach for human based scenarios, the algorithm was tested by registering point clouds containing data of abdominal skin surfaces during inhale and exhale phases of breathing Fig.  recordedThe mentioned article explains usage of non-rigid Iterative Closest Point for tracking patients abdominal surfaces. This approach presents a solution for a hard case of surface registration problem. The abdominal skin changes from convex to concave during breathing phases which under geometric distance constraint, in worst case, may lead to attraction of outlying points in source cloud to closest points in the center of target cloud. No extreme folding of point surfaces should be present in this type of deformation tracking, yet the greatest change in amplitude is present for central points in cloud. The surfaces were acquired with time-of-flight camera Swiss Ranger SR4000, which has an absolute accuracy of about 1 cm. The markers used as landmark points in our algorithm were placed on the abdominal skin before the acquisition so that they were imaged with the designated object. The markers used were square-shaped and had a size of 15 mm. The frequency of the camera was set to 30 MHz, which allowed for acquisition of within a 5 m radius. The patient was at the distance of from 1 to 1.5 meters from the camera.Our approach was tested on 10 cases of abdominal skin surface pairs each containing 9 markers distributed in a 3 × 3 mesh. From every marker, we extracted 4 landmark points which gave us 36 landmark points overall. Markers placed on patients abdominal skin were found using a tracking algorithm basing on maximization of normalized cross correlation value . Such alMean distance of the surfaces in millimeters (M1)—is measured as distance from source point clouds and their closest correspondents in target cloud (preferred minimum).Landmark distance in numbers of units (M2)—is the localization error of landmarks measured as sum of columns and rows by which source cloud landmark has been misaligned compared to its corresponding landmark, during registration (preferred minimum). This measure was also present in , named aPercentage of target cloud points which had only one correspondent (M3)—the target cloud points may have multiple correspondents in source cloud, which is not desired. Great amount of points that have only one correspondences indicate that the clouds have been registered evenly/uniformly (preferred maximum).For measuring how well the algorithm was able to register surfaces containing real data, we used three measures:Verifying the matching of landmark points and measuring their final distance is important because the landmark points, carry real correspondence information of the points which is set arbitrarily before the acquisition. For making this measure credible, only 9 points out of the landmarks set to play the role of landmarks were used for registration.The remaining 27 landmark points were used as measurement points for the landmarks registration accuracy. For the 9 landmarks, the first point from each of the markers groups was chosen.In this section we present results of testing our modification of ICP algorithm on artificial and real clinical data.For analyzing improvements of each modification of non-rigid ICP algorithm separately, we used correspondence maps, which present counts of source cloud correspondents attracted by target cloud points in color scale. The points seen on the map are the target cloud points viewed from above.First modification of non-rigid algorithm was using anisotropic approach of  for seekAs we can notice, using anisotropic localization error for finding corresponding point pairs into consideration shows that every point of target cloud has single corresponding point of source cloud, while isotropic localization error has more points that have no or up to 3 corresponding points matched.Another alternative is to remove the minimization of landmark term and make landmark points in the distance minimization term arbitrary. Below Fig. , correspAs tests on artificial data showed, our approach of the anisotropic ICP algorithm allowed for an improvement of measures M2 and M3, while measure M1 was at a satisfying level of 10E−08. Table We grouped the results by ICP algorithm method, each having three measures of registration quality M1, M2 and M3 (2.6) in columns. Rows represent various point cloud pairs used for testing. Additional, initial distance of cloud pairs and the median value of each quality measure for each method has been presented. The left part presents results for non-rigid isotropic ICP algorithm, the middle one shows results for non-rigid anisotropic ICP variant and right one shows the outcome of our non-rigid anisotropic with enhanced landmark weighting approach.There was no improvement in measures M2 and M3 only in point cloud pairs C8 and C9, respectively. In other cases, testing showed a major advantage over the plain isotropic approach. Measure M1 is at the same level for all variants. The measure M2 is almost equal for both the isotropic and anisotropic approach (except for cloud pairs C7 and C4 where there is a difference). Measure M3 was the best for the non-rigid anisotropic alternative. This is due to using [Unfortunately, combining it with our idea of placing landmark points in distance term minimization equation as arbitrary correspondences and setting higher weights for these pair lowered the amount of single correspondences. In summary, this approach is a compromise between increasing landmarks attraction force of other points and having the most single correspondences between clouds of all.Next Fig. , we presAs mentioned, measure M1 is at similar level for all variations of algorithm, measures M2 and M3 have improved for almost all approaches of ICP algorithm.Next, two pairs of point clouds were chosen for registration quality analysis. The first one was the one with the greatest initial distance—C1, and the other was the one with the least initial distance—C8. First, correspondence histograms are presented, which give information about how many points of target surface had certain counts of correspondents in the source surface , mean landmark position error (M2), and percentage of target cloud points having one corresponding source cloud point (M3). We took the median of the resulting measures and the outcome was as presented: median mean of surfaces distance (M1) was at acceptable level of 10E−08 for both variants of ICP algorithm, median of mean landmark position errors (M2) decreased by 0.93 number of units, median of M3 measure increased by 11.96%.Comparison of results of our algorithm modification with results from  showed aIn cloud pairs C8 and C9, there was no improvement. The mean landmark position error (M2) was greater in C8 and the percentage of target cloud points having one in source cloud (M3) was smaller in C9. Overall there is a compromise between the measures M2 and M3. In case of cloud pair C8, there was a significant improvement of measure M3 and worsening of measure M2. In case of cloud pair C9 the opposite occurred. This may be due to differences in the placement of landmarks in both the source and target cloud. In the case of cloud C8, measure M3 increased because the displacement of landmarks during breathing phases was minor, which lead to points in the source cloud not changing distances inside the mesh. Point cloud pair C9 shows a major displacement of landmarks between abdominal skin surfaces acquired during the inhalation and exhalation phase. This stretched the mesh and increased distances between points of the source cloud mesh. In turn, that created areas of different point density. It is more likely that a single point in the target cloud will attract a group of densely localized points rather than one point. Unlike the results of the previous, article , in whicAs stated in , the lanModifications based on  were intFor comparison with article , we calcIn the presented approach the mean marker error is also reduced from 5.63 to 2.64. which indicated less offset between registered point clouds. In [The paper presents a modified previously presented version of the non-rig Iterative Closest Point Algorithm by introducing an anisotropic noise model for the Time of Flight camera. This allowed to improve the results of the match quality measures. The results showed that the introduction of the anisotropic model of noise for the ToF camera allows for the improvement the percentage of target cloud points which had only one correspondent over 10% impartment and additional weighting of markers also improves the measure of the quality of finding real correspondents over 20% improvement. In the examined dataset, where the average initial distance between the clouds of points in the inspiratory and expiration is equal to approx. 7.5 mm, a more than 10% improvement in the quality of the correspondence improves the accuracy of matching the surface within 1 mm which is a significant value in application of minimally invasive image guided interventions.In the future, the proposed method can be developed with the use of other noise models and verified in other applications.


In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the  At elevated temperature, creep crack growth (CCG) is one of the most common failure mechanisms in many engineering applications, e.g. structural components, similar and dissimilar metal welds etc. This problem has received much attention over the last forty years due to the importance in designing structures with high integrity and safety. Hence, developing analytical models for steady-state crack growth which can be calibrated against detailed Finite Element models is of great interest. Further, an assessment of the effect of different material parameters and damage development processes on the crack growth behaviour can be provided using such models.J-integral, Rice C(t) that describes the strain, strain-rate and stress fields within a creep zone that forms about the crack tip. Their analysis also provides a characteristic time for the transition to the steady state stress field (i.e. the time for C(t) to equal C(t) and C(t). Bassani et al. (C(t). Further, the C(t) parameter is found to be more suitable for characterizing a stationary crack and C(t), Studying creep crack growth has a long history in the literature. A major feature of these studies is the development of a parameter that characterizes the crack tip fields as well as crack propagation. Under steady state creep conditions, the so called and Rice  studied d Riedel  proposed. Saxena  proposedi et al.  compared, Riedel  suggesteMcDowell  includedUnder creep conditions, cracks in polycrystalline materials advance as a result of the growth of damage ahead of the crack tip . In the vicinity of a macroscopic primary crack tip, secondary micro-cracks are formed as a result of intensive void growth and coalescence and/or an accumulation and growth of micro-cracks. These secondary cracks propagate and coalesce creating the new crack surfaces, allowing the primary macroscopic crack to advance along an interface or interconnected grain-boundaries. The growth of damage can influence the constitutive properties of the material and therefore the details of the near crack tip stress and strain-rate fields. Early models of creep crack growth either assumed that the stress . In this case, the In the following sub-sections we describe the constitutive relationships for the bulk continuum response and introduce a number of different models to describe the response ahead of the crack tip within the damage zone. We concentrate on mode I crack growth and only present relationships for the opening mode, although a description of the shear response is also required for the computational studies presented later. We consider the crack growth process in Sect. n is the rate sensitivity parameter. Consider a body containing a crack and subjected to a constant far field loading, see Fig. Crack propagation is assumed to be determined by an interface model such that the propagation takes place along a fictitious interface surface, In order to analyse the problem the mentclass2pt{minimIn the following sub-section we present a number of different constitutive relationships for the damage zone response.In this section, we present models for the damage zone. We limit our description to mode I loading. More general relationship for mode II and mixed mode loading are described elsewhere \documentP in Fig. As noted earlier, under a constant applied moment the crack velocity will, after an initial transient, achieve a steady state, in which it reaches a constant value n, m and the detailed form of model for the damage zone. Substituting for n and m or H. For more general cracked geometries The are two characteristic length scales in this problem, the geometric length scale entclass1pt{minimaused Eq.  to substsing Eq.  gives thIn order to determine the crack growth rate we need to evaluate the quantity n of Eq. .The initial-boundary value problem described in Sect. The geometry of the double cantilever beam (DCB) specimen shown in Fig. The damage zone elements are modelled with zero initial thickness such that the top and bottom face nodes coincide. The mesh has 11,634 elements, of which 11,279 are bulk elements and 355 are damage zone elements. A uniform refined element region is created adjacent to the crack and its propagation for controlling the interface element length p and The numerical analysis was performed for different combinations of the dimensionless parameters defined above to confirm that the functional form of Eq.  is validSeveral analyses have been performed for different combinations of the dimensionless parameters and damage zone properties. The crack tip position, transient and steady state crack propagation velocity have been obtained for all the combinations. For the simple interface model the parameters Figure Figure H and It proves instructive to concentrate initially on the response for the simple damage zone model of Sect. from Eq. :34\documBefore evaluating the computational results in detail it is instructive to examine the response in the limits of small and large n and n and When an interface is very stiff in comparison with the bulk material the deformation along the interface is negligible and it does not influence the stress state in the body. The tractions seen by the damage zone are determined by the stress distribution in the bulk material, and can be expressed in terms of the tchinson . It follfrom Eq.  as37\doco in Eq. , as38\dowith Eq. , the \doThe other limit is when the interface is too compliant in comparison with the bulk material which can be regarded as rigid. Hence, in the case of an infinite DCB specimen, the equilibrium between the applied moment and the traction along the infinite damage zone suggests that the traction will tend to zero and there will be no crack propagation. on the other hand, when the specimen is finite a non zero traction along the finite damage zone. The deformation along the damage zone can directly be related to the angular deflection at the end of the beam. Thus, the separation at the crack tip is obtained ascing Eq.  we obtai0 in Eq.  as47\docwith Eq. , the \doE is Young’s modulus and Another limitation comes from the time scale of the crack propagation as mentioned in Sect. d Julian  studied ring Eq.  as51\docElasticity is only relevant in the computational models and this relationship can be used to assess whether the conditions employed in the FE models are consistent with the assumptions of the analytical model presented in Sect. p of Eq.  is thereIn order to evaluate the proposed framework, ned from  for \docmentclasspt{minimaOver the range of the data, the results can be fit using two separate power-law relations. Under plane stress conditions this relation is mentclasspt{minimainto Eq.  gives thinto Eq. , the velsing Eq.  to provimentclasspt{minimaequality  is satisWe can repeat the analysis for plane strain conditions, see Fig. mentclasspt{minimamentclasspt{minimaIn order to investigate the effect of the detailed form of the damage zone model on the crack growth response, entclass1pt{minima see Eq. . We choowith Eq. . As befoentclass1pt{minima point-wise a linear relationship between these two functions withRather than express The computational results approach the analytical results for small values of nd Ashby ] the craThe main objective of this paper is to identify simple constitutive models for the damaging process ahead of a crack tip in a creeping material and to identify a simple structural configuration which can be analysed rigorously to provide new insights into the relationship between damage models and the crack growth process, including the role of different characteristic material and geometric length scales. As a result, the simple geometry and loading conditions considered are not representative of laboratory test components. None-the-less, it proves instructive to explore how the models presented here can be calibrated against available experimental data, to determine the characteristic material and geometric length scales in these experiments and explore where this data lies with respect to the general trends identified in Figs. n, m, A and B. The steady creep response under a constant uniaxial stress In this section, we consider the low alloy steel , while mentclasspt{miniman and m. The In this study, a combined theoretical and computational study for crack growth under steady state conditions is presented. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process such that the constitutive relation is described by a traction-separation rate law. Further, three different damage zone models are investigated: a simple critical displacement model; empirical Kachanov damage type models; and a micromechanical model. The path independence of the In this paper we have used simple material models for the matrix and damage zone response to analyses crack growth in a simple geometry. Nonetheless, the calculations provide a useful framework for evaluating the effect of different damaging processes on crack growth and evaluating data for more complex laboratory specimens.


PO2, PCO2, and pH of a small sample of arterial blood. It was soon recognized that the commonest cause of hypoxemia was ventilation‐perfusion inequality, and that this could also be responsible for CO2 retention. In the early days, the understanding of the mechanisms of pulmonary gas exchange relied on graphical analysis because the oxygen and carbon dioxide dissociation curves are nonlinear and interdependent which precluded algebraic methods. However, with the introduction of digital computing, problems that had hitherto been impossible to tackle became amenable to study. A key advance was the development of the Multiple Inert Gas Elimination Technique. Now, noninvasive methods for measuring gas exchange show promise, and the whole subject continues to develop.Pulmonary gas exchange is the primary function of the lung, and during my lifetime, its measurement has passed through many stages. When I was born, many physiologists still believed that the lung secreted oxygen. When I was a medical student, the only way we had to recognize defective gas exchange was whether the patient was cyanosed. The advent of the oximeter soon showed that this sign could be very misleading. A breakthrough was the introduction of blood gas electrodes that could measure the  I have spent much of my life thinking about pulmonary gas exchange. Looking back, I see enormous changes in the topic, and looking forward I anticipate fascinating new developments. During my lifetime, knowledge has progressed from the incorrect belief that the lung secreted oxygen, to sophisticated computer analyses of gas exchange. Many students (and perhaps their mentors) do not appreciate the speed of change in respiratory physiology, and gas exchange is an engaging example.I embarked on pulmonary gas exchange at the age of about 30 sec, although naturally I do not recall this. It is just as well that I do not remember, because being born must be the most cataclysmic event in most peoples’ lives. What with gas exchange changing from placental to pulmonary within a few seconds, the enormous respiratory efforts required to expand the poorly inflated lung, the dramatic decrease in pulmonary vascular resistance, the closure of the ductus arteriosus, and the traditional whacks on the behind, it is a mercy that all this is forgotten.My next few years were uneventful, but when I was 7 years old, a landmark in the history of pulmonary gas exchange occurred. This was the publication of the second edition of J. S. Haldane's book titled Respiration  and the barometric pressure was only 380 mm Hg, which is half the sea level value. We exercised to our maximal level and the results are shown in Figure 2 that rose from about 45 to 53 mm Hg as the work level was raised. The explanation for the dramatic fall in oxygen saturation under these conditions was diffusion limitation across the blood gas barrier. It is usual to explain the diffusion limitation at low alveolar PO2 values to the reduced head of pressure of oxygen, but a more accurate analysis shows that the main reason is that the slope of the oxygen dissociation curve is very steep. It was possible to relate the observed results to theoretical predictions based on reasonable values for the diffusing capacity of the lung. In re‐reading the article after 50 years, it is a little alarming to see that one of the saturation measurements in myself was 33% and this was measured in duplicate.Figure These are particularly interesting measurements because virtually the only situation where substantial decreases in arterial oxygen saturation are seen in normal subjects during heavy exercise is at very high altitude. It is remarkable that the results were obtained under such difficult conditions with such a primitive instrument. Long before, Barcroft  had pred2 was therefore 43 mm Hg, and the alveolar PO2 from the gas samples was only 35 mm Hg. However, the calculated arterial PO2 was lower because of diffusion limitation across the blood gas barrier, the value being about 28 mm Hg. The arterial PCO2 based on the alveolar value was extraordinarily low at about 7.5 mm Hg. We were able to derive the arterial pH based on this PCO2 because the base excess was measured on two of the climbers. The pH exceeded 7.7  as the actual lung.While these important advances were being made, another group including Richard Riley and Andre Cournand at Bellevue Hospital in New York City were also studying defective gas exchange. Riley started by considering the gases in blood partly because, as indicated earlier, he was responsible for developing the method for determining the PO2, and the alveolar gas equation that relates the alveolar PO2 to the inspired PO2, the arterial PCO2, and the R value. The justification for using the arterial PCO2 for the alveolar value was that the blood R line is almost horizontal, and therefore the arterial PCO2 must be close to the ideal value  we are working on a noninvasive method of assessing pulmonary gas exchange in patients with lung disease. This exploits advances in technology that enable the continuous measurement of inspired and expired POMeasurements show that this oxygen deficit is very small in young normal subjects, and it increases slightly with age as would be expected. Studies in a series of patients with various types of lung disease show that the oxygen deficit increases greatly and it is a very sensitive index of abnormal gas exchange. The test is very quick and simple to do. The patient breathes through a mouthpiece for 2 or 3 min until a state of gas exchange has been established, and the device then immediately displays the oxygen deficit. It is too early to say whether this new development will be useful clinically, but the prospects are encouraging (West et al. 2, PCO2, and pH in a sample of arterial blood. A consequence of this was recognizing the importance of ventilation‐perfusion inequality, and we now know that this is responsible for most of the hypoxemia and CO2 retention in lung disease. The advent of digital computing has made a dramatic change in our understanding of pulmonary gas exchange, and one of the results has been the Multiple Inert Gas Elimination Technique that has clarified many areas that were previously obscure. Finally, it seems possible that a noninvasive measurement of pulmonary gas exchange is in the wings. The whole area has been enormously exciting, and it was a privilege to be active during these developments.The measurement of pulmonary gas exchange, which is the fundamental function of the lung, has passed through many stages during my lifetime. When I was born, some physiologists believed erroneously that oxygen was actively secreted by the lung. When I was a medical student, the only way we had for detecting defective gas exchange was whether the patient was cyanosed. However with the development of the oximeter, it was soon shown that cyanosis was a very poor metric. A breakthrough was the development of electrodes that could measure PONone declared.


The stereotactic frame represents the mainstay of accuracy for targeting in stereotactic procedures. Any distortion of the frame may induce a significant source of error for the stereotactic coordinates.To analyze the sources of distortion of the Leksell frame G induced by fixation to the patient's head and to evaluate the clinical impact of frame distortion on the accuracy of targeting in stereotactic procedures.We analyzed the torques exerted on the fixation screws after frame placement in a series of patients treated stereotactically by an experienced team. We studied the risk for frame bending in an experimental model of stereotactic frame fixation, with increasing torque of fixation screws in a homogeneous and heterogeneous distribution of torques between the four screws. We assessed the impact of expanding dimensions of bending of the Leksell frame both on surgeries utilizing the stereotactic frame, and on radiosurgical procedures with the Gamma Knife.Frames were fixed clinically at a range of torques of 0.147–0.522 Nm (mean = 0.348 Nm). The torques did not vary significantly with time. Heterogeneity between the two opposite pairs of screws is often limited, but can reach 96.3%. Distortion of the frame may occur even at minimal levels of torque. Heterogeneity between the two opposite pairs of screws will significantly raise the amount of frame distortion. We found a direct correlation between measures of the frame distortion and extend of the deviation from the stereotactic target in clinical models of stereotactic procedures.Stereotactic frames were subjected to distortion due to the torque used for frame fixation. The risk of distortion increased with the torque used and the heterogeneity between the torques of the fixation screws. Distortion of the frame was a significant source of inaccuracy of targeting for stereotactic procedures in clinical practice. This accuracy is achieved by the use of a stereotactic frame, which is firmly fixed to the patient's head. The stereotactic frame with a localizer fixed to it allows the registration of the patient's anatomy for the three‐dimensional coordinate system defined by the frame for accurate placement of surgical instruments or for targeting radiosurgical irradiation. To obtain high accuracy during this stereotactic procedure, the stability of all elements of the system is crucial. Among other things, the mechanical stability of the stereotactic frame is a critical issue since it represents the central element for the definition of stereotactic coordinates and the support for targeting.Treuer et al.The aim of our study was to analyze in which circumstances the Leksell stereotactic frame G  could be mechanically deformed during a stereotactic procedure. The present work focused on the Leksell frame distortions that could be induced by the torques exerted during fixation of the frame on the patient's head Fig. . We anal2This study was approved by the local Institutional Review Board by the Ethical Committee of our institution (ref. P2015/207). Informed consent was obtained in all patients included in this study.Our study consists of three different parts. In the first part, we analyzed the clinical expertise of routine procedures of frame fixation by an experienced team and defined the normal range of torques exerted on the Leksell frame by fixation to the patient's head. In the second part, we study the risk of frame distortions created by the use of different levels of torque exerted on the frame with the four fixation screws. In the third part of this study, we studied the clinical impact of frame bending on two different stereotactic applications of the Leksell frame G.2.A®, Morangis, France), self‐calibrated, which allows measurements of torque with an accuracy of 3%. Using this screwdriver, we measured the torque exerted individually by the four screws at the end of the frame fixation procedure in 75 patients. We made the same measurements at the end of the stereotactic procedure, before frame removal. The measurements were expressed in Newton‐meter (Nm); conversion to inch‐pound is: 0.1 Nm (Newton‐meter) = 0.885 inch‐pound; 4 inch‐pounds = 0.452 Nm. The torques T1, T2, T3, and T4 (recorded at end of frame fixation) and T5, T6, T7, and T8  were measured as the torque of the left anterior, right anterior, right posterior, and left posterior screw, respectively.Our team had a 20‐year experience with more than 4000 applications of stereotactic head frame in a routine clinical setting of stereotactic and functional neurosurgery and Gamma Knife radiosurgery. For this clinical study, we used a high‐precision digital torque screwdriver . We connected the Target Simulator on a stereotactic frame not stressed by any significant torque. We settled the stereotactic arch on the frame and we utilized a Sedan biopsy needle of 2.5 mm diameter to reach the target . We placed the Leksell frame on the head of an anthropomorphic phantom and we applied different conditions of torque in order to create increasing distortions of the stereotactic frame. A series of 30 measurements were performed when the frame was not distorted and with five levels of frame distortions at 0.5, 0.85, 1.0, 1.5, and 2.0 mm: we run each experiment multiple times, and Table 4 represents the average of these measurements. We evaluated the targeting inaccuracy induced by distortion of the frame using the following method: we compared the stereotactic coordinates of a target located in the head based on two different stereotactic CT scans. The first one was the conventional stereotactic 1‐mm 3D CT scan acquired after having placed the CT Indicator box of Elekta®  on the frame, as used in a clinical routine. The location of the fiducial marker sets on the tomographic images was used by the Stereotactic Reference Definition program of Leksell GammaPlan 11.0 to define the stereotactic coordinates of tomographic images. The indicator box was docked on the frame; so that bending of the frame would unavoidably influence the stereotactic coordinates issued from the box. The second stereotactic CT scan was the stereotactic Cone Beam CT (CBCT) of the Gamma Knife Icon.® ICONTM system once the head frame has been docked on the couch with the frame adapter. So, the CBCT‐related stereotactic coordinates are independent of frame bending. We analyzed the difference of stereotactic coordinates of the target provided by these two imaging methods with GammaPlan software . We co‐registered both data sets and obtained two sets of stereotactic coordinates of the target. The difference in stereotactic coordinates will represent the inaccuracy of targeting induced by frame distortion in real clinical conditions. The ICON procedure using CBCT as reference will give corrections of coordinates in the three directions and vectorial correction that must be applied to correct the inaccuracy of targeting.This experimental study focused on the influence of distortion of the Leksell frame on the radiation targeting of the Leksell Gamma Knife Icon33.AThe standard procedure of frame fixation recommended by ElektaTo evaluate the applied torque as a function of time, we measured four torques at T1 to T4 at the end of the frame fixation procedure, and again at the end of the stereotactic treatment several hours later, just before frame removal. We calculated the mean value of the four torques measured at each time point. The median ratio between the two values was 0.99 (SD 0.1), and ranged from 0.73 to 1.19.We also studied the difference between the torques that were applied by the neurosurgeon during frame placement by measuring the difference in torque (∆T) between the two different couples of diagonally opposed screws, T1–T3 and T2–T4. We found a mean and a median difference of torques of 0.086 and 0.068 Nm (SD 0.066), respectively. The maximum ∆T observed was 0.325 Nm. In addition to measurements in absolute values, we analyzed the value of ∆T as a percentage of the mean values of the four torques applied. We observed a mean and median ∆T of 26.4% and 22.4% (SD 21.8%) respectively, with a maximum ∆T of 96.3%.3.B®, including new frames as well as frames with several years of use.We applied our experimental protocols of frame distortion with homogeneous torques and heterogeneous torques to 7 different Leksell frames G. All these frames were certified to be within industry standards for accuracy during the 6‐month maintenance provided by Elekta Instruments3.B.12 = 0.94258. In the range of torques exerted routinely under clinical conditions, frames could have maximum distortions reaching 0.75 mm. However, the mean torque usually applied for frame attachment provided a frame bending in the range of 0.14–0.33 mm based on our measurements.The results of the homogeneous torque exerted are presented in Table 3.B.22 = 0.9906 [Fig. The results of the heterogeneous torque exerted are shown in Table 3.C3.C.12 of 0.99709. The equation of the trend line was y = 0.7357x + 0.036.When the Target Simulator was applied to the stereotactic frame not strained by any significant torque, we observed that the needle reached the target with submillimetric precision. For the six values of frame bending 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 mm, we measured the distance of the tip of the stereotactic cannula from the target. The values recorded were 0.3, 0.8, 1.1, 1.5, 1.8, and 2.2 mm Fig. . The tre3.C.2X‐axis, −0.55 in Y‐axis, and −0.18 in Z‐axis. When increasing distortions were applied to the frame, the differences in stereotactic coordinates were increasing, as shown in Table 2 of 0.96825. The equation of the trend line is y = 0.6721x + 0.7299.The measurements performed when the frame was not distorted showed that the difference in stereotactic coordinates was a translation of −0.31 mm in Results of the analysis of gafchromic films of the irradiated target obtained after the correction proposed by the Gamma Knife ICON system had or had not been applied, have confirmed the accuracy of the correction applied. Figure 4Stereotactic procedures require a high level of spatial accuracy. The most classical and efficient way to reach this high level of precision is the use of a rigid stereotactic frame fixed firmly to the patient's head. The frame will give the stereotactic coordinates for surgical or radiosurgical procedures. The stereotactic frame by itself is assumed not to be a source of inaccuracy. Our experiences with Leksell frames G, both clinical and experimental, showed that frames are bendable. We demonstrated that the distortion of the frame is related to the torques applied to the frame during frame fixation to the patient's head. The magnitude, as well as the asymmetry of the torque used, could be a source for frame bending. Other variables not studied in this work, such as the length of fixation posts, the kind of screws used, the angle between screw and skull, etc…, could also influence frame distortion and its potential clinical consequence for stereotactic inaccuracy.Elekta does not stipulate detailed recommendations for the torque exerted for an adequate frame fixation. In the “Instructions for Use”Maciunas et al.In our clinical study, we tested the variation of the torques exerted by frame application on the patient's head with time. We found no significant difference in the torque measurements taken at the beginning and at the end of the stereotactic procedure. The torque applied by the neurosurgeon on each of the four screws during frame application remained unchanged during the stereotactic procedure, no rebalance between the forces applied to the frame occurs. The analysis of our experience in frame application showed that the torques put on the four screws for head fixation could be different and that significant differences in the torque exerted on the two opposite pairs of screws might lead to a significant distortion of the frame.® . Safaee et al. did not provide any reference for the assertion that frames could be distorted by overtightening.Little information on the technique for application of stereotactic head frames could be found in the literature. Safaee et al.The consequences of frame distortion in terms of inaccuracy of targeting in clinical practice represent highly critical information for the quality of stereotactic frame‐based surgical and radiosurgical procedures. The results of our experience using the Target Simulator of Elekta as an experimental model of frame distortion show that distortion of the Leksell frame has a direct and significant impact on the accuracy of targeting for stereotactic procedures using the stereotactic arch. The fixations of the stereotactic arch applied on both sides of the frame are in their turn distorted by frame bending, which will as a consequence influence the accuracy of targeting of the stereotactic instruments. We found a linear relationship between the amount of frame distortion and the extent of deviation from the target.We performed some experiments to evaluate the accuracy of the stereotactic coordinates issued from CT and MR acquisitions when the Leksell stereotactic frame was subjected to some distortion constraint. We demonstrated that frame distortion will affect significantly the accuracy of the CT‐ and MR‐based stereotactic coordinates. The MR and CT indicator boxes were attached to the frame and when the frame is bent, the imaging series will provide inaccurate stereotactic coordinates. There is a linear relation between the importance of frame distortion and the level of deviation of the stereotactic coordinates issued from imaging acquisition.For surgical procedures using the Leksell stereotactic arch, the two sources of inaccuracy in targeting will occur: the stereotactic error from imaging acquisition and the stereotactic error from the fixation of the stereotactic arch to the bent frame while for Gamma Knife radiosurgical procedures, only the error from imaging acquisition will occur.We have shown from our experiment with gafchromic films that the correction proposed by the Gamma Knife ICON system allows correcting efficiently the inaccuracy of targeting induced by frame bending. The stereotactic CBCT of the Gamma Knife ICON apply an accurate correction algorithm. Stereotactic radiosurgery with all devices would probably in the future include systematically a stereotactic 3D imaging acquisition before or even during irradiation to check for inaccuracy of targeting, even when a conventional rigid stereotactic frame is used.5The Leksell stereotactic frame G may be subject to distortion induced by the torque exerted by frame attachment to the patient's head. This bending is significantly related to the level of torque applied, and especially to differences of torques applied by the fixation screws. Frame distortion may occur at the levels of torque commonly used clinically. We recommend using torque wrenches for frame fixation, reducing the levels of torque and balancing the torques applied by the four fixations in order to reduce frame distortions. A significant clinical impact of frame distortion on stereotactic procedures or radiosurgical treatments was observed both in surgical and radiosurgical procedures. Image acquisition with the CT‐ or MR‐box and fixation of the stereotactic arch on a distorted frame represented the two sources of inaccuracy in stereotactic targeting. The use of an undeformable box at the end of the application of the frame and use of the CBCT of the Gamma Knife Icon could avoid the consequences of frame distortion as a source of targeting inaccuracy in clinical use.The authors report no conflict of interest concerning the materials or methods used in this study or the findings specified in this paper.


Risk factors include, but are not limited to, diabetes and intravenous drug use. The hypotheses for the primary objectives of this study were that the opioid epidemic would cause a younger population of patients to be seen with osteomyelitis and the treatment for this population has special considerations including longer hospitalization for proper intravenous antibiotics. This retrospective chart review compared 2,150 cases of osteomyelitis in the Hospital Corporation of America  West Florida Division. A sample group of osteomyelitis with diabetes was compared to a group with reported opioid use. The results showed a significantly younger age at which the osteomyelitis was occurring in opioid drug users and a significantly longer hospitalization for the treatment. With the rising costs of healthcare and the continuing growth of drug abuse, the 11.501-year younger age difference (95% confidence interval ,  Osteomyelitis is an infection involving the bone. A study by Kremers showed the incidence to be 21.8 per 100,000 person-years during 1969-2009 , p-value <0.001; Table A total of 2,150 patients were identified for meeting the inclusion criteria. The data were divided into the subgroups of diabetics and opioid drug users for comparison. The diabetic group contained 2,038 patients. The opioid drug group contained 112 patients. The diabetic group averaged an age of 56.65 years with a standard deviation of 9.433 years and averaged a length of stay of 9.59 days with a standard deviation of 9.389 days. The opioid group averaged an age of 45.15 years with standard deviation of 12.079 years and averaged length of stay of 14.49 days with a standard deviation of 16.877. The independent samples The strengths of this study include comprehensive data from HCA Healthcare that was from a large database and analyzed with professional research assistance. This study has growth potential by including more divisions of HCA Healthcare, as similar data are available for greater validity. Further analysis of years from previous decades to observe if the percentages of opioid-associated osteomyelitis are increasing would be another potential way to expand this study, however; that data was not available in the data bank. Finally, this study could be expanded to look at the treatment received by the groups as hypotheses were made as the causes for variations in length of stay.There were several limitations to the research project. Being a retrospective chart review, improper or missed documentation may limit the ability to collate data. Opiate use may be underrepresented in the population observed due to intentional or unintentional misrepresentation of opiate use history by patients. Opioid use is self-reported and in the social history of documentation. With this in mind, of our 2,150 cases of osteomyelitis, only 5.2% were reported and documented opioid use. It was also hard to compare the location of the osteomyelitis being treated which could be amenable to certain treatment protocols. With these limitations in mind, the group for osteomyelitis with opioid use was much smaller, and the results above were obtained.This retrospective chart review significantly showed that patients with osteomyelitis and opioid use were, on average, younger in age and required a longer hospitalization than those with osteomyelitis and diabetes. As previously discussed, osteomyelitis is a chronic comorbidity of the diabetes and correlates to the older age of that population of patients. These patients are able to have catheters placed to allow for discharge from the hospital and outpatient management with antibiotics for the necessary time period. Related comorbidities found in longstanding diabetic patients include compromised circulation in the extremities which may necessitate a procedure such as an amputation that also decreases the length of hospitalization. The studied osteomyelitis cohort who used IV drugs was younger than the diabetic osteomyelitis group. The lack of central catheter line availability for outpatient management in this cohort leads to prolonged hospitalization. For most medical problems, younger patients require less treatment in a hospital, but this is a special population. And because they are generally younger with healthy limbs, procedures such as amputations are avoided if at all possible. Although this rational is a hypothesis, it would account for the results seen. This leaves prolonged hospitalizations and close monitoring as the best treatment option which costs more healthcare dollars for the younger population of patients.


Coalescence and splitting of liquid marbles (LMs) are critical for the mixture of precise amount precursors and removal of the wastes in the microliter range. Here, the coalescence and splitting of LMs are realized by a simple gravity‐driven impact method and the two processes are systematically investigated to obtain the optimal parameters. The formation, coalescence, and splitting of LMs can be realized on‐demand with a designed channel box. By selecting the functional channels on the device, gravity‐based fusion and splitting of LMs are performed to mix medium/drugs and remove spent culture medium in a precise manner, thus ensuring that the microenvironment of the cells is maintained under optimal conditions. The LM‐based 3D stem cell spheroids are demonstrated to possess an approximately threefold of cell viability compared with the conventional spheroid obtained from nonadhesive plates. Delivery of the cell spheroid to a hydrophilic surface results in the in situ respreading of cells and gradual formation of typical 2D cell morphology, which offers the possibility for such spheroid‐based stem cell delivery in regenerative medicine. The coalescence of LMs was conducted mainly through a magnetic attraction for opening and closing of the particles shell of LM, or manual injection with a microsyringe to achieve the LM‐based reactions.Here, we introduced a centrifugal force‐ and gravity‐based method to achieve rapid formation, coalescence, and splitting of the LMs for 3D culture of stem cells in vitro, drug/nutrient addition, and waste medium removal using a highly automated process to ensure that the cellular microenvironment of such 3D cell culture was maintained under optimal conditions for long‐term. An additional benefit of the method is the versatility for various kinds of LMs. The method was systematically investigated to obtain optimal parameters to realize both coalescence and splitting. The size of the cell spheroid generated from the system could be controlled within a wide range, from the micrometer to sub‐millimeter scales. The prepared cell spheroids showed highly compact cell‐to‐cell cross‐contacts and formed the in vitro tissue, which is more valuable for the simulation of a real in vivo tissue than the 2D cell monolayers. More importantly, the obtained stem cell spheroid (SCS) from the coalescence and splitting system (CSS) showed much higher cell viability than that of the traditional culture method, which is probably attributed to the high gas permeability of the LMs. The CSS shows potentials as a bioreactor for controlled long‐time in vitro tissue cultures used in regenerative medicine, drug screening, and tissue engineering.22 microspheres were prepared by hydrolysis and condensation of TEOS, followed with grafting of a layer of trimethoxymethylsilane. The resultant powders are white and water‐repellent with a water contact angle (5 µL) of ≈152°  image and transmission electron microscopic (TEM) image in Figure The SiO2° Figure1a. WheFigureTaking the advantages of the gravity and centrifugal forces, we develop the automatic CSS Figure2, via 3Figure2 quickly formed an LM. The centrifugal force‐driven circular motion with a gradually increasing radius ensured both the uniform coverage of powders on the medium and transportation of the as‐formed LMs to the ultimate destination. Figure The 3D view and unfolded view of the device is shown in 4To coalesce the LMs, the liquid inside the LMs should overcome the energy barrier generated from the outer hydrophobic powder to get into contact with each other. The energy barrier between the LMs can hardly be overcome via normal compression because the shell of an LM is composed with multiple layers of silica nanoparticles. The hydrophobic layers of silica nanoparticles of two LMs prevent all of the formation of liquid bridges. (see Movie S1 in the Supporting Information). After liquid‐to‐liquid contact occurred, the coalescence of the LMs would be a spontaneous process since they always tried to reduce their total surface area so that the total surface free energy of the system would be reduced accordingly to realize a lowest energy state, i.e., quasi‐spherical shape .2 shell with multiple layers. After collision with the substrate, the LM showed a serious deformation and became pancake shaped within only 3 ms. The serious deformation and complicated flow inside the LM made a small number of the outer layer of hydrophobic particles without direct contact and trapping on the water–air interface be splashed out. The peeling off of the shell particles mainly occurred at the moments of either impact of LM with the substrate at the lowest pancake thickness at the border region of the LM  or bounce process at the center of the LM . The major part of the hydrophobic particles on the shell would make themselves adapt the shape variation of the inner droplet and surface area increase of the droplet. As is known, a droplet shows its lowest surface area at the spherical shape. The deformation of the LM made the surface area of the LM increase, therefore producing the defects, especially when the LM deformed into a pancake shape, as showed by side view and bottom view in Figure S4b,c in the Supporting Information. The LM showed pancake shape at the maximum deformation of the impact process and the diameter of the pancake shape is measured to be 3.8 mm, which is 1.4 mm larger than that of the 6 µL LM at its spherical stage . Figure S4c in the Supporting Information gives the bottom view of the impact process at its spreading stage, the pancake shape at the maximum deformation, and the retraction stage. The increase of the surface area at the pancake state causes the shortage of the hydrophobic particles to have a full coverage of the droplet, making rich surface defects and bare regions.To investigate the coalescence caused by LMs impact, we first investigated the process of an LM impacting a solid substrate, which is also demonstrated by Marston and co‐workers.The surface defects and bare regions are highly dependent on the inner flow field of the LMs. The simulation results of the impact between a droplet and hydrophilic glass were presented . This simulation is established using the phase field method in COMSOL Multiphysics to investigate the velocity field during the impact process, where a droplet and surrounding air are modeled as two separate phases. We use 2D axisymmetric computational domain due to the axisymmetry of the whole process. The droplet with a radius of 1 mm is initially positioned at a 5 cm distance above the substrate with zero initial velocity. The droplet freely falls downward under the influence of the gravity force and reaches the substrate at an impact velocity. Open boundary conditions are applied at both the top and side, simulating an infinite domain. A wetted wall boundary condition is used for the substrate with a contact angle of 152°. The successive images in Figure S4d,e in the Supporting Information show the inner flow field variation tendency during the process of drop‐solid contact to pancake shape. The inner velocity field near the spherical edge shows increased intensity and finally reaches its maximum value at the pancake shape as the time elapse . Apart from the sharply increased surface area, the nonuniform flow field inside the droplet may also contribute to the generation of the surface defects.FigureTo overcome the energy barrier caused by the outer layer of hydrophobic particles, we use the gravity‐induced collision to overcome the energy barrier and coalesce the LMs. As shown in The coalescence process could also be realized by a sliding impact process as is shown in Figure Fresh medium and drug additions, as well as coculture of different types of cells, could be achieved by the coalescence of LMs Figure f. The di5FigureApart from the coalescence of two small LMs into a larger one, the inverse process Figure5a, whiWaste medium removal was achieved by separating the formed LMs using a gravity‐driven cutting process after certain culture period Figure f. After 6The application of LM as a chemical reactor has been reported previously and here we demonstrated this application in Figure S7 in the Supporting Information. The aqueous solution‐based reactions with mild reaction condition can be precisely performed by our coalescence process to form nanomaterials. For example, the synthesis of the Ag NPs was proposed in the LM via an impact‐induced coalescence process and could be easily extracted for further usage. The specific information was presented in Figure S7 in the Supporting Information. Another application we must emphasize is the LM‐based SCS culture by applying our technique.FigureIn a conventional 3D cell culture protocol, cell spheroids are commonly obtained with either nonadhesive plates or the hanging drop method. For nonadhesive plates, the flow of the process includes the addition of culture medium containing stem cells, centrifugation of the medium to form aggregates at bottom of the well, incubation of the stem cells to form spheroids, replenishment of the medium with a pipette, and collection of the spheroids by pipetting using wide bore pipette tips, as shown in Figure4 cells mL−1, spheroids were rarely formed and the size of the cell aggregates was approximately the size of single stem cell. When the cell density was greater than 105 cells mL−1, the 3D SCS was well formed, as shown in Figure 5 cells mL−1 and 450 µm at a cell density of 106 cells mL−1 ‐5‐(3‐carboxymethoxyphenyl)‐2‐(4‐sulfophenyl)‐2H‐tetrazolium (MTS) assay. As shown in Figure 5 cells mL−1) also showed a compact configuration. The shape of the cells varied, enabling them to conform to the environment. The cells inside the spheroid were in different shapes. The shape diversity inside a spheroid can affect the differentiation direction of stem cells. For instance, the chondrogenesis requires the stem cell to be spherical shape whereas the osteogenesis requires the stem cell to be spindle shape.In addition to the apparent cells, the internal cell‐to‐cell communication in the spheroid was inspected by capturing images with a confocal laser scanning microscope (CLSM) layer‐by‐layer with a gap of 9 µm, as shown in Figure S10 in the Supporting Information. Cells inside the spheroid .6 cells mL−1 was visible to the naked eye after the LM on medium/PBS solution was subjected to a simple shaking process, as indicated by the arrows in Figure2 and O2 are indispensable for the cell metabolism, the LM is gas‐permeable and contains numerous microscale pores on the LM surface  that enable the medium inside the LM to participate in gas exchange with the surrounding environment, whereas the standard nonadhesive plate only participates in gas exchange on the upper surface of the medium, as schematically illustrated in Figure The SCS derived from our system at a cell density of 10The obtained 3D spheroid with high‐viability may show their potential for regenerative medicine, such as tissue repairing. As demonstrated in Figure TableThe comparison of 3D cell culture tools is described in detail in 7In summary, the coalescence and splitting of LMs by applying simple mechanical force were systematically investigated to obtain the optimal parameters for the processes. By selecting the functional channels on the device, gravity‐based fusion and splitting of LMs were performed to mix precise volume of medium/drugs and remove spent culture medium, thus ensuring that the microenvironment of the cells was maintained under optimal conditions. The size of the cell spheroid was controlled within a wide range, up to sub‐millimeter in size. The cultured SCS showed highly compact cell‐to‐cell cross‐contacts, which are more valuable for the simulation of a real in vivo tissue than the 2D cell monolayer. The high gas permeability and the liquid repellent properties of the formed LMs endow the “in vitro tissue” with good cell viability, which is crucial for stem cell differentiation and tissue engineering. After transferring and delivering the cell spheroid to a hydrophilic surface, the cells were respread and transformed into typical 2D cell morphology gradually, which may offer the possibility for spheroid‐based stem cell delivery. The system offers researchers a new choice for producing SCSs with a large size, high cell viability, and strong internal cell‐to‐cell contact, which is a useful in vitro model to study the formation and growth mechanism of tissues in vivo. The coalescence and splitting of LMs show the great prospect for ultrafast, tiny, and stoichiometric chemical reactions, synthesis of functional nanomaterials, and cell spheroid culture in biomedical engineering.The authors declare no conflict of interest.SupplementaryClick here for additional data file.SupplementaryClick here for additional data file.SupplementaryClick here for additional data file.SupplementaryClick here for additional data file.SupplementaryClick here for additional data file.


In this paper, a fully statistical investigation of the control of family structure as random effects is analyzed and discussed, using both the genome-wide association studies (GWAS) data and simulated data. Three modeling strategies are proposed and the analysis results suggest the hybrid use of results from all possible models should be combined in practice. It is well known that genome-wide association studies (GWAS) may lead to spurious findings if one fails to address the dependence among individuals such as that resulting from family structure. If the true dependence structure is known, the best practice is to explicitly incorporate this information into the analysis. However, the true dependence structure is rarely available. Consequently, different strategies have been proposed to address this issue –13.Statistically, we use multilevel models to model complicated family structures. Multilevel models, also known as variance component models, random effects models, or hierarchical linear models, have seen rapid growth and development in many different fields . MultileLinear mixed-effect regression models assume the family effect to be a random effect. The covariance structure for the random effect is generally assumed to correspond to that implied by a polygenic model, incorporating the genetic relationship (kinship) between each pair of individuals. Although the use of this linear mixed-effect regression model was originally proposed for pedigrees with known relationships –5, this The data set we use for this analysis is collected under the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study. It was designed to identify genetic determinants of lipid response to two interventions: (1) a high-fat meal challenge and (2) fenofibrate treatment for 3 weeks . The datX and random effects Z as follows:y is the vector of observations, with mean Xβ; β is an unknown vector of fixed effects; μ is the vector of unknown random effects, with mean 0 and the variance–covariance matrix proportional to the kinship matrix; and ϵ is an unknown vector of random errors, with mean 0 and the variance–covariance matrix assumed to be proportional to the identity matrix. X and Z are design matrices and Im and In are identity matrices.Using a linear mixed-effect model, we model the response to both the fixed effects y is given byThe variance–covariance matrix of Analysis of variance is one of the popular methods in the statistical literature to estimate the variance components X in eq. , and one that uses only one randomly drawn representative individual from each family (referred as the representative option). While these 3 modeling options differ in the covariance matrix for the random effects, the fixed-effect parts remain the same. Figure In a mixed-effect model, one needs to consider a covariance matrix for the random effects. In this study, family structures provide additional information on potential dependence among individuals. We attempt three different strategies to account for family structures. First, we recreate the Irvin study : modelinX in eq. ] and theZ in eq. ] as randl, as in . We madeOption 1, in expectation, is equivalent to using centroids for each family, which is not always feasible for all data types.Under the assumption that the assumed model is correct, the important single-nucleotide polymorphisms (SNPs) identified by these 3 modeling options should have a nested structure as in Fig. lmekin function in R package coxme for the estimation of the mixed effect model and compare the results from the 3 modeling options. This is done by using user-specified variance functions. We use the 3 random effect structures explained previously in Fig. We use the p values from option 1 are lower than those from options 2 and 3. Figure We first apply the 3 modeling options for fitting linear mixed effects model to the GAW20 data. For each SNP, as in Irvin et al. , we testTo average out random variation resulting from change, we randomly choose 5 sets of representatives (one from each family for each set). Figure representative, green for kinship, and blue for independence.)For each run, one individual was randomly drawn from each family, which led to different results. The results from the kinship and the independence options remain unchanged.  is based on an incorrect assumption. We observe from Fig. kinship option) provides the best performance, with the largest overlap with the true signals. Second, in the third Venn diagram we obtained, we see the same phenomenon as in the real data analysis; that is, the findings from the representative option is further away from the independent option to the kinship option. Conversely, the overlapped results from the representative option and the independence option have, on average, slightly lower false discovery rates. This suggests a potential hybrid modeling option that combines results from the independence option and the representative option when the kinship coefficients are not available.To understand what we observed in the real data analysis, we carry out a simple simulation study to further compare the three coping options. We ran independently 3 sets of simulations, in which we draw samples under the model assumed in eq.  to eq. (representative option) is greater than that of ignoring dependence among all individuals in a study (the independence option). More research should be conducted to understand this phenomenon. From the results of a simple simulation, we suggest that both strategies should be used in practice and that the focus should be on SNPs that are identified by both.In this paper, we evaluate different modeling options for coping with data with family structure in the context of genetics studies. Our analysis suggests the need for adjusting for kinships. When kinship information is not known, we compare two opposite strategies, one that treats all individuals in the study as independent and the other that approximately uses the family centroid by randomly sampling 1 representative from each family. Our results suggest that the cost of ignoring other members from a family (the


ACR) for its PET accreditation program unnecessarily limit how tight the tolerances can be made on the accuracy requirements for the concentrations measured in the resultant images.The phantom filling procedures currently specified by the American College of Radiology (New procedures are proposed to improve the accuracy and consistency of the concentrations within the phantom at the time of imaging. These improvements are gained by exchanging the difficult process of accurately measuring a dose with the more easily achieved accurate measurements of time and liquid volume to control final radioactivity concentrations. A comparison of the results when following the two filling procedures is made.ACR was approximately halved by following the new procedures.The variability in metrics specified by the PET images. These changes also render this phantom data more suitable for inter‐PET‐scanner harmonization and improve its utility for comparing image reconstruction methods.These improvements allow tighter thresholds to be applied when evaluating image quality and quantitative accuracy of the  Such programs perform an important service providing peer review of a facility's staff qualifications, imaging equipment, quality control procedures and ultimate image quality. As part of their nuclear medicine accreditation program, the ACR has published detailed instructions describing the acquisition and analysis of PET phantom data to be submitted for review by the ACR during the accreditation process. These instructions specify the phantom to be used (an Esser PET Phantom with a Flangeless Deluxe Jaszczak Lid) along with specific target fluorine‐18 radioactivity concentrations based on the injected dosage typically used by the site. The sites are also instructed to use their standard protocols for image acquisition and reconstruction. The overall goal of the phantom filling instructions is to achieve specific levels of radioactivity both within the main chamber and within the cylindrical subregions of the phantom at the time of imaging. However, because the instructions specify a fixed dilution volume and assume that the two main dose measurements are made simultaneously, the accuracy of the radioactivity concentrations achieved is unnecessarily limited.18F]FDG concentrations seen in patients at the time of imaging. The absolute level of radioactivity is important because the signal‐to‐noise ratio in PET data is not only a function of the counting noise associated with the true coincidences but also on the noise introduced by the subtraction of the scatter and random coincidences. In particular, the noise stemming from the random coincidences are heavily dependent on the absolute amount of radioactivity present, this is because the number of random coincidences increases quadratically with radioactivity whereas true coincidences vary linearly with radioactivity . Thus, in establishing a reference for the image noise level encountered within a given PET imaging system, it is imperative that the radioactivity at the time of imaging be considered and carefully controlled.The intent in providing this level of detail is to achieve radioactivity concentrations that are consistent with [18F‐FDG injection. Moreover, it is specified that the acquisition protocol and reconstruction parameters match that which is typically used at the institution for a standard whole‐body study.The ACR accreditation instructions set target amounts of radioactivity that are proportional to the patient doses used by the candidate institution for a clinical whole‐body FDG PET scan. For example, if a given institution would typically give a 10 mCi dose to a patient, then the ACR instructions are to fill the main “background” chamber of the phantom with 830 uCi of F‐18 and to fill the “hot” cylinders with radioactivity having a concentration of 350 nCi/ml (350 uCi diluted in 1000 ml). The instructions also stipulate that the phantom should be imaged precisely 60 min after the background dose is measured, much like the recommended delay following the patient's If consistent radioactivity levels can be achieved, the reconstructed images of this phantom can serve as a reference via which interscanner and interinstitutional comparisons of image quality can be made. The quality of (and noise within) the images does not directly describe the quality and noise of a patient image, but one can roughly predict that if an institution following a given set of clinical procedures produces higher quality phantom images than that of another institution following different procedures or with a different PET camera system, then their patient images will likely be better as well . Similarly, these images can serve as references  when attempting to harmonize image quality between PET camera systems through adjustments in dose, acquisition time, and reconstruction parameters.In addition to facilitating these intercamera comparisons, the ACR phantom serves as a routine check of the quantitative accuracy of the camera system. By following the recommended procedures (which includes specifying a 70 kg patient injected with the standard dose used at the facility), the expected background radioactivity should have an SUV of unity. The ACR‐specified tolerance on this background level (tellingly) is a generous ±15%. The anticipated variability implicit in this specification is significantly greater than one would normally expect for a repeated measurement of a large region of background radioactivity and it is the thesis of this manuscript that this and other tolerances could be made much tighter if certain procedural deficiencies were to be addressed.18F doses, especially given the delay between the two measurements. Measuring a dose drawn into a syringe generally involves a series of radioactivity measurements with small adjustments in the amount of radioactivity between each. If it is too low, more is added. If it is too high, radioactivity is discarded. Any error in the measurement of the first dose (“dose A” in ACR's parlance) will directly result in an error in the magnitude of the measurements taken from the hot cylinders. Any error in either the timing or the magnitude of the second dose (“dose B”) will directly be reflected as an error in the SUV of background activity at the time of imaging. No adjustment is made within the ACR instructions to account for the time that it takes to get the second dose correct. If this measurement is for some reason delayed or takes an extended time to get right, then this will result in errors in both the absolute activity in the cylinders and in contrast relative to the background. This uncertainty in the true contrast is particularly problematic when seeking to assess image quality using contrast‐to‐noise and related metrics.The difficulty stems from the need, when following the ACR procedures, to precisely draw up the specified 2t (in minutes), before imaging is adjusted to achieve the desired radioactivity concentration in the background at the time of imaging, using the formula shown in eq. (1).Two simple modifications of the ACR phantom filling procedure can improve the accuracy of the radioactivity levels achieved within the phantom. Specifically, I propose that dose B should be measured first and need only be approximate. The dose should still be measured precisely, along with a precise recording of the time of measurement, but any radioactivity near the target level is acceptable. Instead, the time delay, dt is the target dose , dm is the (approximate) dose that was actually measured and T1/2 is the half‐life of 18F in minutes . Note that the constant, 60, in the formula refers to the original specified delay time in minutes.dm, it is possible to reduce or increase the wait time for your convenience. For simplicity and clarity, it is assumed here that the entire drawn dose can be transferred into the background of the phantom with negligible residual . If this is not the case, adjustments to the formula can be made to compensate for the residual radioactivity.It is also worth noting that by purposefully increasing or decreasing v, according to the formula shown in eq. 2.Following the measurement and transfer of dose B into the phantom, dose A can once again be drawn up approximately and without significant time pressure. In this instance, the desired concentration (at the newly designated time of imaging) will be achieved by controlling the dilution volume, ti‐tm is the difference in minutes between the target imaging time and the time at which dose A was measured. And where dm is again the approximately measured dose (this time of dose A) and dt is the target dose A specified by the ACR. Note that here the constant, 1000, refers to the original dilution volume specified by the ACR in milliliters.dm, it is possible to reduce the volume of radioactivity generated  to avoid having to store or dispose of a large volume of radioactive liquid. The reductions in volume, however, should not be pushed too far in order that sufficient volume is available to fill all the cylinders and also to maintain the high percent accuracies associated with measuring large volumes with (for example) a graduated cylinder. In addition to a graduated cylinder, a container to mix the dose and a spreadsheet to perform the calculations are helpful when performing these procedures.It is also again worth noting that by purposely reducing the measured dose By following this procedure, it is expected that the ACR specified radioactivity concentrations within background and hot cylinders of the Esser phantom can be achieved both more accurately and with greater consistently than is possible when following the ACR specified procedure. To test this hypothesis, both phantom filling procedures  were tried during the quarterly QA at my institution, on the same PET camera (a GE D690) but at different times. The quantitative accuracy and consistency of the resultant images were then compared.3The ACR target SUV levels in the background and hot cylinder regions of the phantom are 1.0 and 2.45, respectively. At my institution we routinely use a 12 mCi patient injection. This corresponds to activity concentrations at the time of imaging for the phantom of 117.4 nCi/ml and 287.5 nCi/ml, respectively. The ACR analysis procedures stipulate that two metrics, the background mean SUV and the SUVmax of the 25 mm diameter hot cylinder, be reported. The tolerances on these metrics prescribed by the ACR are 0.85–1.15 and 1.8–2.8, respectively. While following the ACR prescribed filling method during the quarterly QA over a period of 2 yr  the coefficient of variance about the expected value was 5.1% for the ACR specified mean of the background region and 7.2% for the max value within the hot cylinder. The ACR specified tolerance for the mean SUV is therefore consistent (approximately) with a three‐sigma variation about the target value. The ACR specified tolerance on the SUVmax of the hot cylinder, however, is quite asymmetric ranging from 26.5% below to 14.3% above the target value. This presumably is to allow for reductions in the max value owing to high partial voluming on  some scanners. Based on the variability seen in this set of phantoms, the tolerance corresponds to a −3.7 to +2.0 sigma acceptable range.When following the newly proposed phantom filling procedure  the variances measured went down to 2.5% for the background mean and to 4.1% for the cylinder maximum, approximately half the variability seen when following the ACR instructions. These improvements allow tighter thresholds to be applied when evaluating both image quality and quantitative accuracy of the PET images.4The phantom specified for ACR accreditation has several potential uses beyond accreditation including the harmonization of image quality across PET camera systemsI have no conflicts of interest related to this work.


In peripheral nerve surgery, repair of the femoral nerve (FN) requires identification of normal nerve elements both proximal and distal to the level of the injury. We identified FN branches to the sartorius (SRT) and quadriceps muscles in 16 embalmed specimens and calculated the length of each branch to its point of entry into its respective muscle. The SRT and rectus femoris (RF) muscles were mobilized but not transected to mimic the surgical approach. Ratios of the length of each motor branch as a unit of the total length of the thigh, defined as the FN at the inguinal ligament to the superior margin of the patella were also calculated. The proximal branch to RF spanned a ratio of .19 ± .11 (mean ± standard deviation) from the FN at the inguinal ligament to its endpoint. The ratio of the distal branch to the RF was .29 ± .08. The ratio of the proximal SRT branch was .20 ± .05. The distal branch to SRT was located at a ratio of .43 ± .11. The proximal branch to vastus lateralis (VL) was .26 ± .08. The distal branch to VL was .39 ± .07. The ratio of the motor branch to vastus intermedius (VI) was .30 ± .05. Lastly, the branch to vastus medialis (VM) was .55 ± .06. The motor branch to SRT frequently emerged as a bifurcation of itself and saphenous nerve within the adductor canal. Knowledge of the relative location of the motor branches of the FN in the thigh can be helpful to surgeons during the nerve exploration and repair.  In peripheral nerve surgery, repair of injured nerves requires identification of the normal nerve elements both proximal and distal to the level of injury. In the case of the femoral nerve (FN), identification of the branching pattern just distal to the inguinal ligament and the distal motor branches where many FN injuries requiring surgical repair occur can be extremely difficult. Injuries in this location often have associated vascular injuries with prior repair and subsequent significant scarring, complicating surgery. We sought to identify the FN branches in the thigh at their point of muscle entry and calculate the location relative to the length of the thigh.Anatomy and morphologyWe identified and dissected the FN unilaterally (nine left and seven right) on 16 embalmed cadavers,  from the Penn State College of Medicine with ages at death ranging from 71 to 95 years (mean = 84).The FN was located at the inguinal ligament (FNIL). The sartorius (SRT) and RF muscles were mobilized but not divided and vascular structures were preserved in order to more closely approximate the surgical approach. Upon identification of the FNIL, its motor branches to the SRT, RF, vastus medialis (VM), vastus intermedius (VI) and vastus lateralis (VL) were traced and dissected to the point of entrance into the muscle. The saphenous nerve was also identified and isolated from structures within the adductor canal. We did not attempt to identify the pectineus motor branch given its location posterior to the femoral sheath and its minor clinical significance in FN repair.MeasurementsMeasurements of the distance between the bony anterior superior iliac spine (ASIS) and the ipsilateral pubic tubercle (PT) and between the ASIS to the FNIL were taken. The ratio of the relative location of the FNIL was calculated. The distances from the FNIL to the superior border of the patella and between the FNIL to the motor point of the SRT and each of the quadriceps muscles were also measured. A ratio of the FNIL to motor point distance relative to the FNIL to patella distance was then calculated for each muscle. A pin was placed in the FNIL and a string passed to the point at which each motor branch reached the anterior compartment muscles. The measurement for distance down the leg as a percentage was (FNIL-Motor point)/(FNIL-Patella). The measurements were determined by a combination of calipers and rulers.The mean medial-lateral distance from the ASIS to the PT was 13.03 ± 1.40 cm (mean ± standard deviation)  and the ASIS . This inThe FNSRT and RF muscles were found to have two branches each. This is similar to the findings of others, although some report a single motor branch to the RF that branches into two separate sub-branches -5. The mIn our series and others, the branch to VM was the most distally located approximately half way down the thigh . The braThe VL branches were also easily identified lateral and deep to the RF muscle coursing laterally with the descending branches of the lateral circumflex femoral vessels lying at a distance between 25% and 40% distally down the thigh. Our findings correspond to other authors -9. The VThe identification of the nerve to VI was in part more difficult given its deep and more medial location compared with the VL branches as we were trying not to sever the RF branches on the medial side of the muscle and thus approached the VI branches from the lateral side of the RF. Similarly, the distal to proximal dissection of the VL branches and the branch to the VI was challenging in those specimens with thicker RF fascia or septum between the RF and VL. In the face of prior injury, this would likely add further complexity and should be taken into consideration in the clinical setting.Anatomical texts often describe the separation of the FN into an anterior or medial division that innervates the SRT muscle and gives off the medial and intermediate cutaneous nerves of the thigh, and a posterior or lateral division that gives off motor branches to the quadriceps muscles and the saphenous nerve . A clearOur study has some limitations. We did not have multiple independent investigators to measure the distances which would have strengthened the validity of the results. Future clinical and cadaver studies attempting to identify the location of the motor branches prior to exploration to assess the validity of our findings are needed and planned. Overall, we feel that the ratio measures are easier for clinicians to remember and for this reason are more useful than numerical values that may vary with patient size. The FN motor branches in the thigh could be identified with mobilization but preservation of the SRT and RF muscles. Our findings were similar to prior reports with more aggressive muscle dissection. The medial location of the RF and SRT branches should be considered when mobilizing these muscles in the surgical setting. Knowledge of the relative location of the motor branches of the FN in the thigh can be helpful to surgeons during nerve exploration and repair.