Elephantoid oedema of the eyelids

We describe a male patient with rosacea who had a 2-year history of persistent bilateral oedema of the eyelids, leading to an elephantoid condition with blepharoptosis. An upper eyelid blepharoplasty was performed, but swelling progressively recurred over a few months. Based on the case history, clinical appearance and histological findings, rosaceous lymphoedema was considered to be the diagnosis. The latter is a bilateral, solid oedema of the mid-third of the face, regarded as a rare complication of rosacea. It is thought to occur as a result of chronic inflammation and lymphatic stasis, but its exact aethiopathogenesis remains elusive. Predominant eyelid involvement, causing severe visual impairment as in our patient, is unique.     

Finding long chains in kidney exchange using the traveling salesman problem

As of May 2014 there were more than 100,000 patients on the waiting list for a kidney transplant from a deceased donor. Although the preferred treatment is a kidney transplant, every year there are fewer donors than new patients, so the wait for a transplant continues to grow. To address this shortage, kidney paired donation (KPD) programs allow patients with living but biologically incompatible donors to exchange donors through cycles or chains initiated by altruistic (nondirected) donors, thereby increasing the supply of kidneys in the system. In many KPD programs a centralized algorithm determines which exchanges will take place to maximize the total number of transplants performed. This optimization problem has proven challenging both in theory, because it is NP-hard, and in practice, because the algorithms previously used were unable to optimally search over all long chains. We give two new algorithms that use integer programming to optimally solve this problem, one of which is inspired by the techniques used to solve the traveling salesman problem. These algorithms provide the tools needed to find optimal solutions in practice.As of May 2014 there were over 100,000 patients on the waiting list for a kidney transplant from a deceased donor. Many of these patients have a friend or family member willing to be a living kidney donor, but the donor is biologically incompatible. Kidney exchange, also called kidney paired donation (KPD), arose to allow these patients with willing donors (referred to as patient–donor pairs) to exchange kidneys, thus increasing the number of living donor transplants and reducing the size of the waiting list.In KPD, incompatible patient–donor pairs can exchange kidneys in cycles with other such pairs so that every patient receives a kidney from a compatible donor (Fig. S1). Additionally, there are a small number of altruistic donors who are willing to donate their kidney to any patient without asking for anything in return. In KPD, these donors initiate a chain of transplants with incompatible pairs, ending with a patient on the waiting list that has no associated donor (Fig. S2).Integrating both cycles and chains in KPD was proposed in ref. 1, allowing both chains and cycles to be of unlimited size. To ensure that every patient receives a kidney before her associated donor donates her kidney, cycles are conducted simultaneously (otherwise, if the intended donor is unable to donate to the patient whose associated donor already gave her kidney the pair not only did not receive a kidney, but also could not participate in future exchanges). Because organizing many surgeries simultaneously is logistically very complex, the first implementations of KPD by the New England Program for Kidney Exchange and other clearinghouses used only two-way cyclic exchanges. After a short period, clearinghouses have moved to allow three-way exchanges as well.In ref. 2 it was proposed to relax the requirement of simultaneity to the weaker requirement that every patient–donor pair receive a kidney before they give a kidney. Although for cycles this restriction still required all surgeries be performed simultaneously, it did allow for nonsimultaneous chains. Note that these nonsimultaneous chains still protected patient–donor pairs from irreparable harm but allowed for the possibility of donors’ backing out after their patient had received a transplant. Since the first nonsimultaneous chain was arranged (3) chain-type exchanges have accounted for a majority of the transplants in kidney exchange clearinghouses. [Approximately 75% of the transplants in the National Kidney Registry (NKR) and the Alliance for Paired Donation (APD) are done through chains.] Chains involving as many as 30 pairs have been performed in practice, capturing significant public interest (4). Very long chains are often planned in segments, in which the donor from the final pair in a segment is used to begin another segment after more patients arrive. Such donors are called “bridge donors.” Once the segment is executed, the bridge donors and altruistic donors are essentially identical for the purpose of planning future transplants and are collectively referred to here as “nondirected donors” (NDDs). The problem of determining how to optimally select a set of cycles and chains to maximize the number of transplants performed is the focus of this work.We refer to the problem of finding the maximum (possibly weighted) number of transplants for a pool of incompatible patient–donor pairs and NDDs as the kidney exchange problem (KEP). Optionally included in the problem are a maximum chain length and a maximum cycle length. Weights can be used to prioritize difficult-to-match patients. An example of a KEP instance is shown in Fig. S3. When there is no bound on the chain or cycle length, the problem can solved efficiently by reducing it to a maximum weighted perfect matching problem on a bipartite graph, as described in ref. 5. The special case in which only cycles of length two are used can be exactly solved very efficiently, because it is trivially equivalent to the maximum matching problem. In ref. 5, the case of this problem where only cycles of length two and three are used was shown to be NP-hard, meaning that it is unlikely there will be an algorithm that always finds the optimal solution quickly in every instance of the problem; see ref. 6 for a stronger negative result in this special case. However, integer programming (IP) techniques have been used by a variety of authors to solve special cases of the KEP without chains or with chains of bounded length, as first proposed in ref. 7. In ref. 5, by improving the IP formulation of ref. 7 and devising good heuristics the authors were able to solve KEP instances with thousands of donor pairs, but without chains. Alternate IP formulations were further explored for this special case in ref. 8. In ref. 1, a heuristic to produce feasible solutions when using chains and cycles of bounded length was suggested. However, no optimization algorithm was given, opening a major algorithmic challenge to reliably solve large-scale instances of the general KEP. The technique of ref. 5 was extended in refs. 9–12 to solve large instances with bounded cycles and bounded chains. However, the algorithm became impractical when the maximum chain length was beyond four or five, because the formulation required a decision variable for each chain up to the maximum chain length. As seen in Table S1, the number of chains of length up to k grows very quickly with k, at least when creating instances using patient–donor pairs drawn at random from the historical dataset (a more thorough explanation is given in Supporting Information). When both chains and cycles are bounded by length k, the relaxed version of the IP formulation (as a linear program) provides a good approximation to the original formulation (13, 14), and a large body of literature suggests that such problems can be effectively solvable in practice. However, this approximation property does not seem to hold if chains are unbounded (15), and hence this problem is likely to be much more challenging than the bounded case, as confirmed by our computational experiments.The primary challenge addressed in this paper is to find an algorithm to solve real instances of the KEP without bounding the maximum chain length. Solving this optimization problem is critical to the operations of KPD programs, which form long chains in practice but previously relied on heuristics that could lead to suboptimal solutions. We emphasize that we focus on real instances drawn from historical data, as opposed to synthetic instances, because the statistics of instances encountered in practice are quite complicated, making it difficult to generate representative random instances (a patient–donor pair waiting to be matched is on average more difficult to match than a patient–donor pair randomly selected from historical data, because the easy-to-match patients are on average matched more quickly). The second challenge we address in this paper is finding an algorithm that can solve instances using chains and cycles with an arbitrary bound on the maximum cycle length (with no maximum cycle length, the problem can be solved trivially). Although in practice cycles longer than three are rarely formed owing to logistical issues, there is some evidence that there may be benefits to considering longer cycles (16). Finally, in Supporting Information we demonstrate how our approach can be extended to efficiently deal with the case of bounded chain lengths as well as a stochastic version with “edge failures” (see refs. 17 and 18).We propose two new algorithms for the KEP that address these challenges. The first algorithm is a recursion based on a direct IP formulation for the KEP. Despite the NP hardness of the underlying problem, the algorithm is surprisingly effective in practice in most instances, as we will show in a later section devoted to the computational results. Additionally, the algorithm does not break down as the maximum cycle length is increased. On the contrary, as the bound on the maximum cycle length increases, the performance improves. At the same time there are several KEP instances of moderate size that have been encountered in practice on real data drawn from a particular KPD program that our algorithm was unable to solve. Thus, we have devised a second algorithm to reliably solve nearly all KEP instances of practical interest. The algorithm is motivated by an IP formulation of the so-called prize-collecting traveling salesman problem (PC-TSP), another NP-hard problem. The PC-TSP is a variant of the classical traveling salesman problem (TSP), one of the most widely studied NP-hard problems in combinatorial optimization. Although our PC-TSP–based algorithm was able to solve every instance we have encountered, somewhat surprisingly we have discovered that it is at times orders of magnitude slower than the direct recursive algorithm described above.The two algorithms described above allow us to optimally allocate kidneys transplanted in KPD with arbitrary chain lengths. These algorithms were capable of solving to optimality all real data instances we have encountered, using only a single desktop computer. Furthermore, several of the most active KPD programs are using our implementations of these algorithms in conducting their kidney exchanges, including Methodist Specialty and Transplant Hospital in San Antonio, Texas and the Northwestern University Medical Center in Chicago.The remainder of the paper is organized as follows. First, we formally define the KEP as an optimization problem on a graph. Then, we describe the recursive algorithm and PC-TSP–based algorithm for the KEP. Both algorithms are based on formulating associated IP problems. Next, we demonstrate the value of being able to find long chains by measuring the number of additional transplants they enable using simulations based on historical clinical data. We then compare the performance of our two algorithms in KEP instances found in actual data from the KPD programs, demonstrating the relative strength of the PC-TSP–based algorithm compared with the recursion-based algorithm. To provide some insight into the power of the PC-TSP–based algorithm we state a result showing that the formulation of the IP problem associated with the PC-TSP is stronger than the IP problem corresponding to the recursive algorithm. The proof of this result can be found in Supporting Information. Furthermore, we provide an example of a pathological instance of the KEP for which the recursive algorithm takes a very long time, whereas the PC-TSP–based algorithm solves this instance very quickly. Finally, we conclude with a summary of our results. Some technical results can be found in Supporting Information.     

Knowledge and attitude regarding human immunodeficiency virus/acquired immunodeficiency syndrome in dermatological outpatients

Background  Dermatologists are often the first-line specialists who recognize and diagnose human immunodeficiency virus (HIV) infection because of pathognomic skin signs. It is therefore important to investigate attitudes and knowledge regarding HIV/acquired immunodeficiency syndrome (AIDS) amongst dermatological patients in order to provide information for dermatologists and to draw their attention to the issues.
Objectives  Awareness of HIV/AIDS, its prevention, and hypothetical behaviour were surveyed in dermatological outpatients.
Patients/method  The anonymous cross-sectional survey was conducted with consecutive German-speaking outpatients aged 18–65 years, who registered at the dermatological outpatient's clinic (excluding venereology, genitourinary or HIV medicine) of the University of Munich (Germany).
Results  Three hundred forty-seven (77.5%) questionnaires were accepted for analysis. Most of the patients knew about HIV incurability (89.4%), HIV transmissibility during needle sharing (95.3%), or vaginal (87.4%) and anal intercourse (79.5%), as well as about HIV prevention by condom use (97.8%), and use of single needles (76.2%). However, knowledge gaps and misconceptions were detected regarding the risk of HIV transmission during oral sex, and the efficacy of sexual fidelity and avoidance of blood transfusions in HIV prevention. The lowest knowledge level (< 50% correct answers) was detected in patients aged 50–59 years, in unemployed, divorced/widowed, and in those without or with incomplete school education.
Conclusions  Patient education about HIV/AIDS in dermatological ambulant settings should be performed differentially with regard to socio-demographic factors, and focused on the topic of oral sexual HIV transmission and on some other specific misconceptions.

Conflicts of interest

None declared.     

Trapezoid fracture caused by assault

In this report we describe an open fracture of trapezoid and break in anterior cortex of capitate due to assault in a young adult male. Direct impact force of a sharp object to the first web space caused the above fractures. Open reduction and internal fixation of the trapezoid was carried out using Kirschner wires. Cut extensor tendons, extensor retaniculum, capsule, adductor pollicis muscle, first dorsal interosseous muscle, soft tissue and overlying skin were sutured primarily. Three months after the operation the patient has made a complete recovery. There is no similar case reported in the literature.