Small animal bone healing models : standards, tips, and pitfalls results of a consensus meeting

Small animal fracture models have gained increasing interest in fracture healing studies. To achieve standardized and defined study conditions, various variables must be carefully controlled when designing fracture healing experiments in mice or rats. The strain, age and sex of the animals may influence the process of fracture healing. Furthermore, the choice of the fracture fixation technique depends on the questions addressed, whereby intra- and extramedullary implants as well as open and closed surgical approaches may be considered. During the last few years, a variety of different, highly sophisticated implants for fracture fixation in small animals have been developed. Rigid fixation with locking plates or external fixators results in predominantly intramembranous healing in both mice and rats. Locking plates, external fixators, intramedullary screws, the locking nail and the pin-clip device allow different degrees of stability resulting in various amounts of endochondral and intramembranous healing. The use of common pins that do not provide rotational and axial stability during fracture stabilization should be discouraged in the future. Analyses should include at least biomechanical and histological evaluations, even if the focus of the study is directed towards the elucidation of molecular mechanisms of fracture healing using the largely available spectrum of antibodies and gene-targeted animals to study molecular mechanisms of fracture healing. This review discusses distinct requirements for the experimental setups as well as the advantages and pitfalls of the different fixation techniques in rats and mice.

Evaluation of modal analysis techniques using physical models to detect osseointegration of implants in transfemoral amputees

Non-invasive vibration analysis has been used extensively to monitor the progression of dental implant healing and stabilization. It is now being considered as a method to monitor femoral implants in transfemoral amputees. This paper evaluates two modal analysis excitation methods and investigates their capabilities in detecting changes at the interface between the implant and the bone that occur during osseointegration. Excitation of bone-implant physical models with the electromagnetic shaker provided higher coherence values and a greater number of modes over the same frequency range when compared to the impact hammer. Differences were detected in the natural frequencies and fundamental mode shape of the model when the fit of the implant was altered in the bone. The ability to detect changes in the model dynamic properties demonstrates the potential of modal analysis in this application and warrants further investigation.

Ocular surface changes with short-term contact lens wear

Contact lenses are a common method for the correction of refractive errors of the eye. While there have been significant advancements in contact lens designs and materials over the past few decades, the lenses still represent a foreign object in the ocular environment and may lead to physiological as well as mechanical effects on the eye. When contact lenses are placed in the eye, the ocular anatomical structures behind and in front of the lenses are directly affected. This thesis presents a series of experiments that investigate the mechanical and physiological effects of the short-term use of contact lenses on anterior and posterior corneal topography, corneal thickness, the eyelids, tarsal conjunctiva and tear film surface quality. The experimental paradigm used in these studies was a repeated measures, cross-over study design where subjects wore various types of contact lenses on different days and the lenses were varied in one or more key parameters (e.g. material or design). Both, old and newer lens materials were investigated, soft and rigid lenses were used, high and low oxygen permeability materials were tested, toric and spherical lens designs were examined, high and low powers and small and large diameter lenses were used in the studies. To establish the natural variability in the ocular measurements used in the studies, each experiment also contained at least one “baseline” day where an identical measurement protocol was followed, with no contact lenses worn. In this way, changes associated with contact lens wear were considered in relation to those changes that occurred naturally during the 8 hour period of the experiment. In the first study, the regional distribution and magnitude of change in corneal thickness and topography was investigated in the anterior and posterior cornea after short-term use of soft contact lenses in 12 young adults using the Pentacam. Four different types of contact lenses (Silicone hydrogel/ Spherical/–3D, Silicone Hydrogel/Spherical/–7D, Silicone Hydrogel/Toric/–3D and HEMA/Toric/–3D) of different materials, designs and powers were worn for 8 hours each, on 4 different days. The natural diurnal changes in corneal thickness and curvature were measured on two separate days before any contact lens wear. Significant diurnal changes in corneal thickness and curvature within the duration of the study were observed and these were taken into consideration for calculating the contact lens induced corneal changes. Corneal thickness changed significantly with lens wear and the greatest corneal swelling was seen with the hydrogel (HEMA) toric lens with a noticeable regional swelling of the cornea beneath the stabilization zones, the thickest regions of the lenses. The anterior corneal surface generally showed a slight flattening with lens wear. All contact lenses resulted in central posterior corneal steepening, which correlated with the relative degree of corneal swelling. The corneal swelling induced by the silicone hydrogel contact lenses was typically less than the natural diurnal thinning of the cornea over this same period (i.e. net thinning). This highlights why it is important to consider the natural diurnal variations in corneal thickness observed from morning to afternoon to accurately interpret contact lens induced corneal swelling. In the second experiment, the relative influence of lenses of different rigidity (polymethyl methacrylate – PMMA, rigid gas permeable – RGP and silicone hydrogel – SiHy) and diameters (9.5, 10.5 and 14.0) on corneal thickness, topography, refractive power and wavefront error were investigated. Four different types of contact lenses (PMMA/9.5, RGP/9.5, RGP/10.5, SiHy/14.0), were worn by 14 young healthy adults for a period of 8 hours on 4 different days. There was a clear association between fluorescein fitting pattern characteristics (i.e. regions of minimum clearance in the fluorescein pattern) and the resulting corneal shape changes. PMMA lenses resulted in significant corneal swelling (more in the centre than periphery) along with anterior corneal steepening and posterior flattening. RGP lenses, on the other hand, caused less corneal swelling (more in the periphery than centre) along with opposite effects on corneal curvature, anterior corneal flattening and posterior steepening. RGP lenses also resulted in a clinically and statistically significant decrease in corneal refractive power (ranging from 0.99 to 0.01 D), large enough to affect vision and require adjustment in the lens power. Wavefront analysis also showed a significant increase in higher order aberrations after PMMA lens wear, which may partly explain previous reports of "spectacle blur" following PMMA lens wear. We further explored corneal curvature, thickness and refractive changes with back surface toric and spherical RGP lenses in a group of 6 subjects with toric corneas. The lenses were worn for 8 hours and measurements were taken before and after lens wear, as in previous experiments. Both lens types caused anterior corneal flattening and a decrease in corneal refractive power but the changes were greater with the spherical lens. The spherical lens also caused a significant decrease in WTR astigmatism (WRT astigmatism defined as major axis within 30 degrees of horizontal). Both the lenses caused slight posterior corneal steepening and corneal swelling, with a greater effect in the periphery compared to the central cornea. Eyelid position, lid-wiper and tarsal conjunctival staining were also measured in Experiment 2 after short-term use of the rigid and SiHy contact lenses. Digital photos of the external eyes were captured for lid position analysis. The lid-wiper region of the marginal conjunctiva was stained using fluorescein and lissamine green dyes and digital photos were graded by an independent masked observer. A grading scale was developed in order to describe the tarsal conjunctival staining. A significant decrease in the palpebral aperture height (blepharoptosis) was found after wearing of PMMA/9.5 and RGP/10.5 lenses. All three rigid contact lenses caused a significant increase in lid-wiper and tarsal staining after 8 hours of lens wear. There was also a significant diurnal increase in tarsal staining, even without contact lens wear. These findings highlight the need for better contact lens edge design to minimise the interactions between the lid and contact lens edge during blinking and more lubricious contact lens surfaces to reduce ocular surface micro-trauma due to friction and for. Tear film surface quality (TFSQ) was measured using a high-speed videokeratoscopy technique in Experiment 2. TFSQ was worse with all the lenses compared to baseline (PMMA/9.5, RGP/9.5, RGP/10.5, and SiHy/14) in the afternoon (after 8 hours) during normal and suppressed blinking conditions. The reduction in TFSQ was similar with all the contact lenses used, irrespective of their material and diameter. An unusual pattern of change in TFSQ in suppressed blinking conditions was also found. The TFSQ with contact lens was found to decrease until a certain time after which it improved to a value even better than the bare eye. This is likely to be due to the tear film drying completely over the surface of the contact lenses. The findings of this study also show that there is still a scope for improvement in contact lens materials in terms of better wettability and hydrophilicity in order to improve TFSQ and patient comfort. These experiments showed that a variety of changes can occur in the anterior eye as a result of the short-term use of a range of commonly used contact lens types. The greatest corneal changes occurred with lenses manufactured from older HEMA and PMMA lens materials, whereas modern SiHy and rigid gas permeable materials caused more subtle changes in corneal shape and thickness. All lenses caused signs of micro-trauma to the eyelid wiper and palpebral conjunctiva, although rigid lenses appeared to cause more significant changes. Tear film surface quality was also significantly reduced with all types of contact lenses. These short-term changes in the anterior eye are potential markers for further long term changes and the relative differences between lens types that we have identified provide an indication of areas of contact lens design and manufacture that warrant further development.

A new model to analyze metaphyseal bone healing in mice

Background: Despite the increasing clinical problems with metaphyseal fractures, most experimental studies investigate the healing of diaphyseal fractures. Although the mouse would be the preferable species to study the molecular and genetic aspects of metaphyseal fracture healing, a murine model does not exist yet. Using a special locking plate system, we herein introduce a new model, which allows the analysis of metaphyseal bone healing in mice. Methods: In 24 CD-1 mice the distal metaphysis of the femur was osteotomized. After stabilization with the locking plate, bone repair was analyzed radiologically, biomechanically, and histologically after 2 (n = 12) and 5 wk (n = 12). Additionally, the stiffness of the bone-implant construct was tested biomechanically ex vivo. Results: The torsional stiffness of the bone-implant construct was low compared with nonfractured control femora (0.23 ± 0.1 Nmm/°versus 1.78 ± 0.15 Nmm/°, P < 0.05). The cause of failure was a pullout of the distal screw. At 2 wk after stabilization, radiological analysis showed that most bones were partly bridged. At 5 wk, all bones showed radiological union. Accordingly, biomechanical analyses revealed a significantly higher torsional stiffness after 5 wk compared with that after 2 wk. Successful healing was indicated by a torsional stiffness of 90% of the contralateral control femora. Histological analyses showed new woven bone bridging the osteotomy without external callus formation and in absence of any cartilaginous tissue, indicating intramembranous healing. Conclusion: With the model introduced herein we report, for the first time, successful metaphyseal bone repair in mice. The model may be used to obtain deeper insights into the molecular mechanisms of metaphyseal fracture healing. © 2012 Elsevier Inc. All rights reserved.

Influence of plate bending stiffness on mechanical properties of healing fracture, mouse femora

Mechanically well-defined stabilization systems have only recently become available, providing standardized conditions for studying the role of the mechanical environment on mouse bone fracture healing. The aim of this study was to characterize the time course of strength recovery and callus development of mouse femoral osteotomies stabilized with either low or high flexibility (in bending and torsion) internal fixation plates. Animals were euthanized and femora excised at 14, 21, and 28 days post-osteotomy for microCT analysis and torsional strength testing. While a larger mineralized callus was observed in osteotomies under more flexible conditions at all time points, the earlier bridging of the mineralized callus under less flexible conditions by 1 week resulted in an earlier recovery of torsional strength in mice stabilized with low flexibility fixation. Ultimate torque values for these bones were significantly higher at 14 and 21 days post-osteotomy compared to bones with the more flexible stabilization. Our study confirms the high reproducibility of the results that are achieved with this new implant system, therefore making it ideal for studying the influence of the mechanical environment on murine fracture healing under highly standardized conditions.

Reply to the discussion by Karen Johannesson on “Rare earth element geochemistry of scleractinian coral skeleton during meteoric diagenesis: a sequence through neomorphism of aragonite to calcite” by Webb et al., Sedimentology, 56, 1433-1463

Webb et al. (2009) described a late Pleistocenecoral sample wherein the diagenetic stabilization of original coral aragonite to meteoric calcite was halted more or less mid-way through the process, allowing direct comparison of pre-diagenetic and post-diagenetic microstructure and trace element distributions. Those authors found that the rare earth elements (REEs) were relatively stable during meteoric diagenesis, unlike divalent cations such as Sr,and it was thus concluded that original, in this case marine, REE distributions potentially could be preserved through the meteoric carbonate stabilization process that must have affected many, if not most, ancient limestones. Although this was not the case in the analysed sample, they noted that where such diagenesis took place in laterally transported groundwater, trace elements derived from that groundwater could be incorporated into diagenetic calcite, thus altering the initial REE distribution (Banner et al., 1988). Hence, the paper was concerned with the diagenetic behaviour of REEs in a groundwater-dominated karst system. The comment offered by Johannesson (2011) does not question those research results, but rather, seeks to clarify an interpretation made by Webb et al. (2009) of an earlier paper, Johannesson et al. (2006).

Orthopedic bone plates : evolution in structure implementation technique and biomaterial

With many important developments over the last century, nowadays orthopedic bone plate now excels over other types of internal fixators in bone fracture fixation. The developments involve the design, material and implementation techniques of the plates. This paper aims to review the evolution in implementation technique and biomaterial of the orthopedic bone plates. Plates were initially used to fix the underlying bones firmly. Accordingly, Compression plate (CP), Dynamic compression plate (DCP), Limited contact dynamic compression plate (LC-DCP) and Point contact fixator (PC-Fix) were developed. Later, the implementation approach was changed to locking, and the Less Invasive Stabilization System (LISS) plate was introduced as a result. Finally, a combination of both of these approaches has been used by introducing the Locking Compression Plate (LCP). Currently, precontoured LCPs are mainly used for bone fracture fixation. In parallel with structure and implementation techniques, numerous advances have occurred in biomaterials of the plates. Titanium and stainless steel alloys are now the most common biomaterials in production of orthopedic bone plates. However, regarding the biocompatibility, bioactivity and biodegradability characteristics of Mg alloys, Ta alloys, SMAs, carbon fiber composites and bioceramics, these materials are considered as potentially suitable for plates. However, due to poor mechanical properties, they have very limited applications. Therefore, further studies are required in future to solve these problems and make them feasible for heavy-duty bone plates.

Nonlinear H_infinity control of UAVs for collision avoidance in gusty environments

This paper proposes a nonlinear H_infinity controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed con- troller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.

4000 years of phenotypic change in an island bird: heterogeneity of selection over three microevolutionary timescales.

Pronounced phenotypic shifts in island populations are typically attributed to natural selection, but reconstructing heterogeneity in long-term selective regimes remains a challenge. We examined a scenario of divergence proposed for species colonizing a new environment, involving directional selection with a rapid shift to a new optimum and subsequent stabilization. We provide some of the first empirical evidence for this model of evolution using morphological data from three timescales in an island bird, Zosterops lateralis chlorocephalus. In less than four millennia since separation from its mainland counterpart, a substantial increase in body size has occurred and was probably achieved in fewer than 500 generations after colonization. Over four recent decades, morphological traits have fluctuated in size but showed no significant directional trends, suggesting maintenance of a relatively stable phenotype. Finally, estimates of contemporary selection gradients indicated generally weak directional selection. These results provide a rare description of heterogeneity in long-term natural regimes, and caution that observations of current selection may be of limited value in inferring mechanisms of past adaptation due to a lack of constancy even over short time-frames.

Experimental evaluation of the culture performance of three exotic and a ‘local’ Giant Freshwater Prawn (Macrobrachium rosenbergii, De Man 1879) culture strain in Fiji

Giant freshwater prawn (GFP; Macrobrachium rosenbergii) aquaculture has expanded rapidly since 1990. Most local culture industries, however, have developed in an unsystematic way. Fiji has a small culture industry producing the ‘Anuenue’ strain; however, performance of this strain has never been systematically evaluated. Recently, some Fijian farmers have reported declines in stock productivity. The current project evaluated the relative performance of three exotic strains with different genetic backgrounds from Malaysia, Indonesia and Vietnam, against the ‘local’ strain in Fiji in a 4 × 3 replicated pond trial experiment. A total of 5827 prawns were harvested after 143 days growout. Individual growth rate and relative survival of the Fiji strain were not statistically different from any of the introduced strains, but Vietnam strain was superior to that of the Malaysia strain. Genetic diversity showed significant differences in variability among strains, with the Malaysian strain displaying the lowest genetic diversity. Indonesia strain showed that females were reaching maturation earlier than other strains and were smaller in size. This study suggests that Malaysian and Indonesian strains would constitute a poor choice for Fiji, whereas the Vietnam strain consistently performed well on all criteria measured. High variation among replicate ponds within strains unfortunately confounded among-strain variation.

Ability of modal analysis to detect osseointegration of implants in transfemoral amputees : a physical model study

Owing to the successful use of non-invasive vibration analysis to monitor the progression of dental implant healing and stabilization, it is now being considered as a method to monitor femoral implants in transfemoral amputees. This study uses composite femur-implant physical models to investigate the ability of modal analysis to detect changes at the interface between the implant and bone simulating those that occur during osseointegration. Using electromagnetic shaker excitation, differences were detected in the resonant frequencies and mode shapes of the model when the implant fit in the bone was altered to simulate the two interface cases considered: firm and loose fixation. The study showed that it is beneficial to examine higher resonant frequencies and their mode shapes (rather than the fundamental frequency only) when assessing fixation. The influence of the model boundary conditions on the modal parameters was also demonstrated. Further work is required to more accurately model the mechanical changes occurring at the bone-implant interface in vivo, as well as further refinement of the model boundary conditions to appropriately represent the in vivo conditions. Nevertheless, the ability to detect changes in the model dynamic properties demonstrates the potential of modal analysis in this application and warrants further investigation.

Training program impact on thermoplastic immobilization for head and neck radiation therapy

Purpose: To determine whether uniform guidelines and training in the stabilization and formation of thermoplastic shells can improve the reproducibility of set-up for Head and Neck cancer patients. Methods and materials: Image based measurements of the planning and treatment positions for 35 head and neck cancer patients undergoing radical radiotherapy were analysed to provide a baseline of the reproducibility of thermoplastic immobilization. Radiation therapists (RT) were surveyed to establish a perception of their confidence in thermoplastic procedures. An evidence based staff training program was created and implemented. Set-up reproduction and staff perception were reviewed to measure the impact of the training program. Results: The mean (SD) 3D vectors of anatomical displacement, measured on the patient images, improved from 4.64 (2.03) for the baseline group compared to 3.02 (1.65) following training (p < 0.01). The proportion of 3D displacements of patient data exceeding 5 mm 3D vector was decreased from 37.1% to 5.7% (p < 0.001) and the 3 mm vector from 85.7% to 42.9% (p < 0.001). The post-training survey scores demonstrated improved confidence in reproducibility of set-up for head and neck patients. Conclusion: The Thermoplastic Shells Training Program has been found to improve the treatment reproducibility for head and neck radiation therapy patients. Uniform guidelines have increased RT confidence in thermoplastic procedures.

Natural improvements of geochemical conditions of acid sulfate soils caused by free tidal inundation and its effects on the mangrove seedlings

Acid sulfate soils (ASS) are one of the stressor factors that cause many mangrove restoration projects to fail. Achieving successful rehabilitation in an ASS affected area requires an understanding of the geochemical conditions that influence the establishment and growth of mangrove seedlings. This study evaluated the effect of tidal inundation on geochemical conditions on sub layer to better understand their impacts on the density, establishment, and growth of mangrove seedlings. This study also examined the geochemical conditions under which mangrove seedlings can establish naturally, and/or be replanted in abandoned aquaculture ponds. The study area was in an area of abandoned aquaculture ponds situated in the Mare District, adjacent to Bone Bay, South Sulawesi, Indonesia.The pH, pHfox, redox potential, organic content, water soluble sulfate, SKCl, SPOS, and grain size of the soil from the sediment core at + 10 - 15 cm depth near roots were measured using. Pyrite analysis were conducted for the top and sub sediments. The density, establishment, and the relative root growth of Rhizophoraceae were also determined. Free tidal inundation at abandoned pond sites improved the sediment quality. The high density, establishment, and growth of mangrove seedlings were characterized by freely drained areas with a higher pH (field and oxidisable), lower organic content, and high proportion of silt/clay. Higher density and growth also correlated to reduced environments. Sulfur species did not influence the density, establishment, and growth of the seedlings directly. The supply of propagules from the mangrove stands, or access from good waterways were also important for seedlings to establish naturally.

Seriously playful : the uses of networked spoof videos in China

This thesis examines online spoof videos in China. It shows the relationship between user-created content and change and how such videos are impacting on social memory. In the West, we are witnessing two outstanding trends in media. On the one hand, media are turning more "demotic" (Turner, 2006) and "participatory" (Jenkins, 2006), whereby lay audiences use popular media for identity formation, representation and association, reconfiguring the media and cultural landscape, and rendering invalid the old paradigm based on the dichotomy of audience and author, creator and consumer, expert and amateur. On the other hand, in both mainstream media and user-creation online there is a trend towards "silly citizenship", with comedy, send-ups and spoofs that used to reside in the margin propelled to the central stage in both pleasure and politics (Hartley, 2010), as is shown in the rising popularity of the Daily Show, Colbert Report, and spoof videos in elections ,e.g. the 2008 presidential election in US (Gray, Jones, & Thompson, 2009; Tryon, 2008). User generated content—and spoof subcultures—is now much a debated phenomenon in China. However, with different political (one party rule and censorship) and cultural (media regarded mainly as instrument for education and social stabilization instead of a critical fourth estate) configurations, will the social and cultural impacts of the two trends in the West be as the same in China? If not, what will be the specificities in the China context? The project starts with a historical review of popular culture and user-created content in China, before turning to spoof videos and looking at how they are produced and shared, travel and diffused on the Internet, and how the communities and sub-cultures forming and emerging around spoof videos are changing the overall cultural landscape in China. By acting as a participant observer in online video sharing sites and conducting face-to face as well as online interviews, I identify lead users and creators of spoof videos and the social networks emerging around them. I call these lead users "skill hubs" and their networks "liquid communities", foregrounding the fact that their appeal doesn’t come from their amicable personality, but rather from their creative skills; and that the networks surrounding them are in a permanent flux, with members coming and going as they see fit. I argue that the "liquidness" (Bauman, 2000) of these communities is what makes them constantly creative and appealing. Textual analysis of online videos, their comments and derivatives are conducted to tease out the uses that that can be made of spoof videos, namely as phatic communication, as alternative memory and as political engagement. Through these analyses I show that spoof videos constitute not only a space where young generations can engage with each other, communicate their anger and dissatisfaction, fun and hope, and where they participate in socio-cultural and political debates, but also create a space where they can experiment with their new skills, new ideas, and new citizenship. The rise of spoof videos heralds the beginning of a trend in popular culture in contemporary China towards the "canonization of the jester" and the dethroning of the establishment. I also argue that a historical perspective is needed to understand the current surge of use creativity and user activism in China, and that many forms of popular media we experience today have their antecedents in various stages of Chinese history. The entrenched "control-resistance" binary is inadequate in interpreting the rich, flux and multilayered Internet space in China.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.