scholarly journals Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution

2017 ◽  
Vol 8 ◽  
pp. 117959721773030 ◽  
Author(s):  
Glen Atlas ◽  
John K-J Li ◽  
Shawn Amin ◽  
Robert G Hahn
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Human Study ◽  
Patient Specific ◽  
Sine Function ◽  
Integro Differential Equation ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Group 2 ◽  
Group 1

A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler’s formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly “adaptable” and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

THE FORWARD PDE FOR EUROPEAN OPTIONS ON STOCKS WITH FIXED FRACTIONAL JUMPS

2005 ◽  
Vol 08 (02) ◽  
pp. 239-253 ◽  
Author(s):  
PETER CARR ◽  
ALIREZA JAVAHERI
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Stock Price ◽  
Arrival Rate ◽  
European Options ◽  
Standard Assumption ◽  
Integro Differential Equation ◽  
Local Variance ◽  
Calendar Dates

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

scholarly journals The Effect of Patient-Specific Instrumentation Incorporating an Extramedullary Tibial Guide on Operative Efficiency for Total Knee Arthroplasty

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Oh-Ryong Kwon ◽  
Kyoung-Tak Kang ◽  
Juhyun Son ◽  
Dong-Suk Suh ◽  
Dong Beom Heo ◽  
...  
Keyword(s):  
Total Knee Arthroplasty ◽  
Knee Arthroplasty ◽  
Patient Specific ◽  
Surgical Time ◽  
Patient Specific Instrumentation ◽  
Significant Difference ◽  
Total Knee ◽  
Group 3 ◽  
Group 2 ◽  
Group 1

This retrospective study was to determine if patient-specific instrumentation (PSI) for total knee arthroplasty (TKA) leads to shortened surgical time through increased operating room efficiency according to different tibial PSI designs. 166 patients underwent primary TKA and were categorized into three groups as follows: PSI without extramedullary (EM) tibial guide (group 1, n=48), PSI with EM tibial guide (group 2, n=68), and conventional instrumentation (CI) group (group 3, n=50). Four factors were compared between groups, namely, operative room time, thickness of bone resection, tibial slope, and rotation of the component. The mean surgical time was significantly shorter in the PSI with EM tibial guide group (group 2, 63.9±13.6 min) compared to the CI group (group 3, 82.8±24.9 min) (P<0.001). However, there was no significant difference in the PSI without EM tibial guide group (group 1, 75.3±18.8 min). This study suggests that PSI incorporating an EM tibial guide may lead to high operative efficiency in TKA compared to CI. This trial is registered with KCT0002384.

Derivation of Fractional Differential Equations for Modeling Diffusion in Porous Media of Fractal Geometry

2008 ◽  
Author(s):  
Sergei Fomin ◽  
Vladimir Chugunov ◽  
Toshiyuki Hashida
Keyword(s):  
Differential Equation ◽  
Mass Exchange ◽  
Fractal Geometry ◽  
Double Porosity ◽  
Fickian Diffusion ◽  
Mass Transfer Equation ◽  
Diffusion In Porous Media ◽  
Fractional Differential ◽  
Group 2 ◽  
Group 1

Utilizing the double-porosity approach it is assumed that porous medium is constituted by two groups of pores in such way that major mass transport takes place mostly along the network of larger pores (group 1) and these larger (stem) pores are surrounded by the medium formed by the dead-end porous of fractal geometry (group 2). Solving analytically equation for the stem pore from the group 1 and accounting for the mass exchange with pores from the group 2, it is proved that diffusion in a stem pore should be described by the fractional differential equation. Based on this result, equation of mass flux that models non-Fickian diffusion in complex fractal medium is proposed. Applying this generalized form of mass transfer equation for modeling the contaminant transport in fractured porous aquifer leads to a fractional order differential equation, where mass exchange between blocks and fractures is modeled by the temporal fractional derivatives. This equation is solved analytically.

scholarly journals Preoperative Education Significantly Decreases Postoperative Opioid Use after Arthroscopic Meniscectomy

2019 ◽  
Vol 7 (7_suppl5) ◽  
pp. 2325967119S0035
Author(s):  
Steven M. Andelman ◽  
Nicholas Debellis ◽  
Daniel Bu ◽  
University of Connecticut ◽  
Chukwuma Nwachukwu ◽  
...  
Keyword(s):  
Patient Education ◽  
Opioid Consumption ◽  
Phone Call ◽  
Patient Specific ◽  
Opioid Use ◽  
Opioid Prescription ◽  
Narcotic Analgesia ◽  
Arthroscopic Meniscectomy ◽  
Group 2 ◽  
Group 1

Objectives: Arthroscopic meniscectomy is one of the most common procedures in orthopedic surgery and is thus a frequent reason for prescription of post-operative opioid narcotics. Recent emphasis has been placed on limiting the number of opioid pills given for post-operative analgesia, with the goal being to provide adequate post-operative pain control while minimizing the number of unused pills after surgery. A number of modifiable variables have been identified to prevent over-prescription of opioids including prescriber education and identification of patient-specific factors associated with increased opioid use. To date, no study has evaluated the role of patient education to decrease post-operative opioid use. The goal of this study is to determine the utility of pre-operative patient education in decreasing post-operative opioid consumption after arthroscopic meniscectomy. Methods: All patients 18 years and older from a group of five attending surgeons undergoing isolated arthroscopic unicompartmental meniscectomy were prospectively identified for inclusion in this cohort study. Patients were split into two groups: patients in Group 1 did not receive any specific education regarding opioid usage after surgery while patients in Group 2 received a formalized three-minute overview from a physician on both appropriate usage of opioid narcotics as well as options for non-narcotic post-operative analgesia. Patients were assigned to each group consecutively - all patients at the beginning of the study were assigned to Group 1 while all patients at the end of the study were assigned to Group 2. Post-operatively, patients in both groups were surveyed via phone call one, two, three, and four weeks after surgery to determine the number of opioid pills taken each week. Patient descriptive statistics and post-operative opioid consumption were analyzed and compared between the two groups. Results: 62 patients completed the study, with 32 in Group 1 (no pre-operative education) and 24 in Group 2 (received pre-operative education). There were no significant demographic differences between the two groups. Patients in Group 1 used an average of 16.71 (95% CI, 9.67-23.75) opioid pills after surgery while patients in Group 2 used an average 3.21 (95% CI, 1.78-6.06) opioids after surgery. Patients in Group 2 used 13.5 less opioid pills (p = 0.001) representing a 420.0% decrease in post-operative opioid consumption over a four-week course (Figure 1). 7 (21.9%) patients in Group 1 continued to take opioid pills four weeks after surgery, while only 1 (4.2%) patient in Group 2 did the same. Conclusion: Pre-operative patient education regarding appropriate usage of opioid and options for non-narcotic analgesia significantly decreases post-operative opioid consumption and the duration which patients take opioid pills after arthroscopic meniscectomy. Pre-operative education is quick and inexpensive method to decrease post-operative opioid prescription requirements. [Figure: see text]

Some Optimal Dividend Problems for a Surplus Process with Stochastic Interest

2010 ◽  
Vol 108-111 ◽  
pp. 1097-1102
Author(s):  
Wen Guang Yu
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Closed Form ◽  
Present Value ◽  
Integro Differential Equation ◽  
Surplus Process ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Stochastic Interest

In this paper, some results on the dividend payments prior to ruin in the classical surplus process with stochastic interest are derived. An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved. Furthermore, closed-form expressions for exponential claims are given.

Abundant closed-form solitons for time-fractional integro–differential equation in fluid dynamics

2021 ◽  
Vol 53 (3) ◽  
Author(s):  
Emad A. Az-Zo’bi ◽  
Wael A. AlZoubi ◽  
Lanre Akinyemi ◽  
Mehmet Şenol ◽  
Islam W. Alsaraireh ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fluid Dynamics ◽  
Closed Form ◽  
Integro Differential Equation

scholarly journals Severe COVID-19 pneumonia in an intensive care setting and comparisons with historic severe viral pneumonia due to other viruses

2021 ◽  
Author(s):  
Kiran Dadhwal ◽  
Rosalind Stonham ◽  
Stephen Poole ◽  
Kordo Saeed ◽  
Ahilanandan Dushianthan
Keyword(s):  
Intensive Care ◽  
Care Setting ◽  
Invasive Mechanical Ventilation ◽  
Viral Pneumonia ◽  
Patient Specific ◽  
Organ Support ◽  
Intensive Care Setting ◽  
Significant Difference ◽  
Group 2 ◽  
Group 1

Abstract Purpose Severe viral pneumonia is associated with significant morbidity and mortality. Recent COVID-19 pandemic continues to impose significant health burden worldwide and individual pandemic waves often leads to a large surge in the ICU admissions for respiratory support. Comparisons of severe SARS-CoV-2 pneumonia with other seasonal and non-seasonal severe viral infections are rarely studied in an intensive care setting. Methods A retrospective cohort study comparing patients admitted to ICU with COVID-19 between March-June 2020 and those with viral pneumonias between January-December 2019. We compared patient specific demographic variables, duration of illness, ICU organ supportive measures and outcomes between both groups. Results Analysis of 93 COVID-19 (group 1) and 52 other viral pneumonia patients (group 2) showed an increased proportion of obesity (42% vs 23%, p = 0.02), non-white ethnicities (41% vs 6%, p < 0.001) and diabetes mellitus (30% vs 13%, p = 0.03) in group 1, with lower prevalence of COPD/asthma (16% vs 34%, p = 0.02). In group 1, the neutrophil to lymphocyte ratio was much lower (6.7 vs 10, p = 0.006) and invasive mechanical ventilation (58% vs 26%, p < 0.001) was more common. Length of ICU (8 vs 4, p < 0.001) and hospital stay (22 vs 11, p < 0.001) was prolonged in group 1, with no significant difference in mortality. Influenza A and rhinovirus were the most common pathogens in group 2 (26% each). Conclusions Key differences were identified within demographics (obesity, ethnicity, age, ICU scores, co-morbidities) and organ support. Despite these variations, there was no significant differences in mortality between both groups. Further studies with larger sample sizes would allow for further assessment of clinical parameters in these patients.

scholarly journals Quality Characteristics and Clinical Relevance of In-House 3D-Printed Customized Polyetheretherketone (PEEK) Implants for Craniofacial Reconstruction

2020 ◽  
Vol 9 (9) ◽  
pp. 2818
Author(s):  
Neha Sharma ◽  
Soheila Aghlmandi ◽  
Shuaishuai Cao ◽  
Christoph Kunz ◽  
Philipp Honigmann ◽  
...  
Keyword(s):  
Dimensional Accuracy ◽  
Quality Characteristics ◽  
Patient Specific ◽  
Class Iii ◽  
Fused Filament Fabrication ◽  
Craniofacial Reconstruction ◽  
Printing Process ◽  
Alloplastic Materials ◽  
Group 2 ◽  
Group 1

Additive manufacturing (AM) of patient-specific implants (PSIs) is gradually moving towards in-house or point-of-care (POC) manufacturing. Polyetheretherketone (PEEK) has been used in cranioplasty cases as a reliable alternative to other alloplastic materials. As only a few fused filament fabrication (FFF) printers are suitable for in-house manufacturing, the quality characteristics of the implants fabricated by FFF technology are still under investigated. This paper aimed to investigate PEEK PSIs fabricated in-house for craniofacial reconstruction, discussing the key challenges during the FFF printing process. Two exemplary cases of class III (Group 1) and class IV (Group 2) craniofacial defects were selected for the fabrication of PEEK PSIs. Taguchi’s L9 orthogonal array was selected for the following nonthermal printing process parameters, i.e., layer thickness, infill rate, number of shells, and infill pattern, and an assessment of the dimensional accuracy of the fabricated implants was made. The root mean square (RMS) values revealed higher deviations in Group 1 PSIs (0.790 mm) compared to Group 2 PSIs (0.241 mm). Horizontal lines, or the characteristic FFF stair-stepping effect, were more perceptible across the surface of Group 1 PSIs. Although Group 2 PSIs revealed no discoloration, Group 1 PSIs displayed different zones of crystallinity. These results suggest that the dimensional accuracy of PSIs were within the clinically acceptable range; however, attention must be paid towards a requirement of optimum thermal management during the printing process to fabricate implants of uniform crystallinity.

In-vivo evaluation of the effect of cyanoacrylate on prosthetic vascular graft infection – does cyanoacrylate increase the severity of infection?

VASA ◽  
2020 ◽  
Vol 49 (4) ◽  
pp. 281-284
Author(s):  
Atıf Yolgosteren ◽  
Gencehan Kumtepe ◽  
Melda Payaslioglu ◽  
Cuneyt Ozakin
Keyword(s):  
Vascular Graft ◽  
Graft Infection ◽  
Vascular Graft Infection ◽  
Group 4 ◽  
Significant Difference ◽  
Group 3 ◽  
Group 2 ◽  
Prosthetic Vascular Graft Infection ◽  
Group 1

Summary. Background: Prosthetic vascular graft infection (PVGI) is a complication with high mortality. Cyanoacrylate (CA) is an adhesive which has been used in a number of surgical procedures. In this in-vivo study, we aimed to evaluate the relationship between PVGI and CA. Materials and methods: Thirty-two rats were equally divided into four groups. Pouch was formed on back of rats until deep fascia. In group 1, vascular graft with polyethyleneterephthalate (PET) was placed into pouch. In group 2, MRSA strain with a density of 1 ml 0.5 MacFarland was injected into pouch. In group 3, 1 cm 2 vascular graft with PET piece was placed into pouch and MRSA strain with a density of 1 ml 0.5 MacFarland was injected. In group 4, 1 cm 2 vascular graft with PET piece impregnated with N-butyl cyanoacrylate-based adhesive was placed and MRSA strain with a density of 1 ml 0.5 MacFarland was injected. All rats were scarified in 96th hour, culture samples were taken where intervention was performed and were evaluated microbiologically. Bacteria reproducing in each group were numerically evaluated based on colony-forming unit (CFU/ml) and compared by taking their average. Results: MRSA reproduction of 0 CFU/ml in group 1, of 1410 CFU/ml in group 2, of 180 200 CFU/ml in group 3 and of 625 300 CFU/ml in group 4 was present. A statistically significant difference was present between group 1 and group 4 (p < 0.01), between group 2 and group 4 (p < 0.01), between group 3 and group 4 (p < 0.05). In terms of reproduction, no statistically significant difference was found in group 1, group 2, group 3 in themselves. Conclusions: We observed that the rate of infection increased in the cyanoacyrylate group where cyanoacrylate was used. We think that surgeon should be more careful in using CA in vascular surgery.

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