Delta shock index predicts injury severity,interventions,and outcomes in trauma patients:A 10-year retrospective observational study

BACKGROUND Most trauma occurs among young male subjects in Qatar.We examined the predictive values of the delta shock index(DSI),defined as the change in the shock index(SI)value from the scene to the initial reading in the emergency unit(i.e.,subtracting the calculated SI at admission from SI at the scene),at a Level 1 trauma center.AIM To explore whether high DSI is associated with severe injuries,more interventions,and worse outcomes[i.e.,blood transfusion,exploratory laparotomy,ventilator-associated pneumonia,hospital length of stay(HLOS),and in-hospital mortality]in trauma patients.METHODS A retrospective analysis was conducted after data were extracted from the National Trauma Registry between 2011 and 2021.Patients were grouped based on DSI as low(≤0.1)or high(>0.1).Data were analyzed and compared usingχ2 and Student’s t-tests.Correlations between DSI and injury severity score(ISS),revised trauma score(RTS),abbreviated injury scale(AIS),Glasgow coma scale(GCS),trauma score-ISS(TRISS),HLOS,and number of transfused blood units(NTBU),were assessed using correlation coefficient analysis.The diagnostic testing accuracy for predicting mortality was determined using the validity measures of the DSI.Logistic regression analysis was performed to identify predictors of mortality.RESULTS This analysis included 13212 patients with a mean age of 33±14 years,and 24%had a high DSI.Males accounted for 91%of the study population.The trauma activation level was higher in patients with a high DSI(38%vs 15%,P=0.001).DSI correlated with RTS(r=-0.30),TRISS(r=-0.30),NTBU(r=0.20),GCS(r=-0.24),ISS(r=0.22),and HLOS(r=0.14)(P=0.001 for all).High DSI was associated with significantly higher rates of intubation,laparotomy,ventilator-associated pneumonia,massive transfusion activation,and mortality than low DSI.For mortality prediction,a high DSI had better specificity,negative predictive value,and negative likelihood ratio(77%,99%,and 0.49%,respectively).After adjusting for age,emergency medical services time,GCS score,and ISS,multivariable regression analysis showed that DSI was an independent predictor of mortality(odds ratio=1.9;95%confidence interval:1.35-2.76).CONCLUSION In addition to sex-biased observations,almost one-quarter of the study cohort had a higher DSI and were mostly young.High DSI correlated significantly with the other injury severity scores,which require more time and imaging to be ready to use.Therefore,DSI is a practical,simple bedside tool for triaging and prognosis in young patients with trauma.

Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations

The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.

Initial-boundary value problem of nonlinear hyperbolic system for conservation laws with delta-shock waves

For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions.

THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX

We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.

色谱方程的广义黎曼问题:含有Delta激波

论文研究了非线性色谱方程的广义黎曼问题,并在x-t平面内,构造性地获得了上述广义黎曼问题的局部解.由于非线性色谱方程的黎曼解含有Delta激波,这与以往其它模型的广义黎曼问题(对应的黎曼解只有古典基本波)有很大区别.论文结果表明:在大多情况,广义黎曼解和对应的黎曼解结构相同;但当相关的黎曼解含有Delta激波时,Delta激波可能会转变成激波和接触间断的组合.论文结果有助于详细分析Delta激波的内部机理.

用分离的Delta函数法研究非对称Keyfitz-Kranzer系统中Delta激波的交互性

该文用分离的Delta函数法研究非对称Keyfitz-Kranzer系统中Delta激波的交互性.当初值是三个分段常数状态时,讨论Delta激波和接触间断的交互性,构造性的得到四种不同交互作用下的解.同时,获得当小扰动ε→0时,黎曼解是稳定的.

THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS

In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.

一维等温欧拉方程组的Delta激波解

讨论了一维等温欧拉方程组的黎曼问题。通过特征分析的方法,得到了相应黎曼问题的Delta激波解。

Radon Measure Solutions to Riemann Problems for Isentropic Compressible Euler Equations of Polytropic Gases

We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of satisfying the over-compressing entropy condition:(i)there is a unique delta shock solution,corresponding to the case that has two strong classical Lax shocks;(ii)for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave,or two shocks with one being weak,there are infinitely many solutions,each consists of a delta shock and a rarefaction wave;(iii)there are no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves.These solutions are self-similar.Furthermore,for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data,there always exists a unique delta shock for at least a short time.It could be prolonged to a global solution.Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass(particle).Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified.This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases,that is strictly hyperbolic,and whose characteristics are both genuinely nonlinear.We also discuss possible physical interpretations and applications of these new solutions.

一类等熵欧拉方程组的流近似

研究了一类带有流扰动的一般压力等熵欧拉方程组的黎曼问题,获得了包含5种不同结构的黎曼解.证明了当包含压力的3-参数流扰动消失时,任何包含2个激波的黎曼解收敛于零压流系统的狄拉克激波解;任何包含2个稀疏波的黎曼解收敛于零压流系统的真空解.还证明了当包含压力的2-参数流扰动消失时,任何满足一定初值条件的2-激波黎曼解收敛于一类Chaplygin型气体方程组的狄拉克激波解.最后,对狄拉克激波和真空状态的形成过程进行了数值模拟.

休克指数在产后出血中应用的研究进展

产后出血(postpartum hemorrhage)是产科常见的严重并发症,也是全球孕产妇死亡的首要原因,降低其不良结局发生率的关键在于早期快速识别和及时干预,但临床诊断标准大多是基于对出血量的视觉估计,出血的严重程度很可能会被低估,易导致临床对产后出血的延迟诊断及治疗。近年来,多项研究提出休克指数(shock index,SI)可以提示血流动力学的不稳定性,用于预测产后出血的发生、发展及不良结局,尤其在医疗资源匮乏的地区,其应用价值更大。而与其相关的休克指数差值(delta-shock index,ΔSI)可以进一步个体化评估出血情况。虽然SI作为产后出血的预测指标有一定的局限性,但总体而言,其临床价值是值得肯定的。

带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限

研究了带有Chaplygin压力的耦合Aw-Rascle(CAR)交通模型的黎曼问题.通过令耦合模型两侧压力同时消失,得到上述黎曼解的极限,并证明了该极限具有相同初值的无压气体动力(Pressureless Gas Dynamics,PGD)模型的黎曼解.更进一步,证得极限后的delta激波解的权重和速度与PGD模型的delta激波解的权重和速度完全一致.此外,由解的渐近行为,可以观察到稀疏接触间断到接触间断的转化.

Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation

In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.

关于一个非线性几何光学中的非严格双曲守恒律系统的研究(英文)

研究了一个产生于非线性几何光学中的非严格双曲守恒律系统.该系统具有强非线性流函数项,且狄拉克激波可能同时出现在解的两个状态变量中.通过未知函数的一个变换,该系统的非线性流函数项得到弱化,从而其黎曼问题被完全解决.

关于δ初值的Chaplygin压交通流AR模型的Riemann问题

研究Chaplygin压交通流AR模型初值含Dirac δ函数的Riemann问题.在广义Rankine-Hugoniot条件和熵条件下,构造性地获得了包含δ激波的整体广义解,明确地显示出四种不同的结构.结果表明,在Riemann初值这里构造的扰动下,Riemann解是稳定的.

广义Chaplygin气体交通流方程组的Riemann问题(英文)

构造性的得到了广义Chaplygin气体交通流AW-Rascle(AR)模型Riemann问题的解.它包括三种解:前两种解包含R(疏散波)+J(接触间断)和S(激波)+J(接触间断),最后一种解是包含满足广义Rankine-Hugoniot和熵条件的Delta激波解.

阿片δ_1受体激动剂对出血性休克大鼠心肌损伤的影响

为观察出血性休克后复苏开始前给予阿片δ1受体激动剂2-Methyl-4aa-(3-hydroxyphenyl)-1,2,3,4,4a,5,12,12aα-oc-tahydroquinolino[2,3,3-g]isoquinoline dihydrobromide(TAN—67)对大鼠心肌缺血缺氧性损伤的影响。将24只成年雄性SD大鼠,随机分为三组,每组8只,实验分假手术组、休克对照组、TAN-67组。休克对照组和TAN-67组大鼠放血使MAP降至40mmHg,休克持续60min,注射生理盐水或TAN-67后,回输自体血进行复苏,观察复苏2h内MAP和心功能(LVP、±dp/dtmax)的变化。实验结束时取心肌组织行病理学电镜检查。并分析各组线粒体损伤。休克对照组复苏后各时点血流动力学指标呈逐渐下降趋势。TAN-67组复苏后同一时点各项指标均显著高于对照组(P<0.05)。病理学电镜检查和线粒体损伤结果,TAN-67组心肌损伤较对照组减轻。结果表明TAN-67有利于急性出血性休克大鼠血流动力学复苏,对心肌损伤有保护作用。

一维具有阻尼和摩擦项的可压缩流体欧拉方程组当压力消失时黎曼解的极限

该文研究带有复合源项的一维可压缩流体欧拉方程组的黎曼问题,其中源项可以是摩擦项,也可以是阻尼项,也可以是阻尼和摩擦两者都具有.与齐次型不同,非齐次守恒律方程组的黎曼解是非自相似的.当绝热指数γ→1即压力消失时,讨论带有复合源项的一维可压缩流体欧拉方程组的黎曼解中集中现象和真空状态的形成,证明包含两条激波的黎曼解收敛于零压下的delta激波解,包含两条稀疏波的黎曼解收敛于零压下的两条接触间断解,其中连接两条接触间断解的中间状态是真空状态.

Wave Interactions of the Aw-Rascle Model for Generalized Chaplygin Gas

In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.

Chaplygin气体Euler方程组Riemann问题解的结构稳定性（英文）

研究了Chaplygin气体Euler方程组Riemann解的结构稳定性.当修正Chaplygin气体的压力趋于Chaplygin气体压力时,可压Euler方程组Riemann解的结构是稳定的.特别地,当修正Chaplygin气体的压力趋于Chaplygin气体压力时,Chaplygin气体Euler方程组Riemann问题的δ激波解是由后向激波和前向激波形成的Riemann解的极限.