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医学·健康
26
engines
药代动力学 · 房室模型
Pharmacokinetics · compartment models
IV/口服/静滴 · C(t)、t½、AUC · 一室/二室双指数 · 线性+半对数
IV bolus / oral / infusion · one- vs two-compartment · half-life · AUC
剂量-反应 · Emax / Hill · 治疗指数
Dose-response · Emax / Hill · therapeutic index
Emax·Cⁿ/(EC50ⁿ+Cⁿ) · EC50 / Hill n · 治疗指数 TD50/ED50
Sigmoidal Emax model on a log-dose axis · competitive shift · therapeutic window
SIR / SEIR 传染病房室模型
SIR / SEIR compartmental epidemic model
RK4 积分 SIR/SEIR · R0=β/γ · 群体免疫 1−1/R0 · 峰值
Numerically integrate the ODEs (RK4) · R₀, herd immunity, epidemic curve
Kaplan-Meier 生存曲线
Kaplan-Meier survival curve
乘积极限 S(t)=∏(1−d/n) · 删失 ✚ · 中位生存期
Product-limit estimator with right-censoring · median survival · group comparison
ROC 曲线与诊断性能
ROC curve & diagnostic performance
双分布 + 阈值 · 敏感度/特异度 · AUC + 混淆矩阵 PPV/NPV
Overlapping normal distributions · threshold sweep · AUC · confusion matrix
Davenport 酸碱图
Davenport acid-base diagram
pH–[HCO₃⁻] · PCO₂ 等压线 · 呼吸/代谢酸碱 ± 代偿
[HCO₃⁻] vs pH · PCO₂ isobars from Henderson–Hasselbalch · live classification
肾清除率、GFR 与肾血浆流量
Renal clearance, GFR & ERPF
C=U·V/P · GFR(菊粉)/ERPF(PAH) · 重吸收 vs 分泌
C = U·V/P · compare to GFR for reabsorption vs secretion · nephron schematic
Starling 力与毛细血管滤过
Starling forces & capillary filtration
Jv=Kf[(Pc−Pi)−σ(πc−πi)] · 净滤过压 · 滤过/重吸收/水肿
Jv = Kf·[(Pc−Pi) − σ(πc−πi)] · NFP along the capillary · edema flag
肺功能 · 流量-容积环
Spirometry · flow–volume loop
流量-容积环 + 容积-时间 · FEV1/FVC · 阻塞/限制/正常
FEV₁/FVC and lung volumes classify obstructive vs restrictive · loop shape follows the numbers
心电图 · 波形与判读
ECG · waveform & interpretation
高斯合成 P-QRS-T · 25 mm/s 网格 · 心率/PR/QRS/QTc · 心律
Synthesize P–QRS–T from the intervals · rate and rhythm read off the numbers
三大营养素热量 · Atwater 系数
Macronutrient calories · Atwater factors
蛋白/碳水 4·脂肪 9 kcal/g · 供能比 · AMDR
Grams of each macro → kilocalories, shares and AMDR check
BMI 计算器 · 体质指数
BMI calculator · body mass index
BMI=kg/m² · WHO 分级 · 健康体重区间
Weight relative to height, with the WHO category bands
Total Daily Energy Expenditure (TDEE) · nutrition calculator
Total Daily Energy Expenditure (TDEE) · nutrition calculator
Mifflin-St Jeor 基础代谢 · ×活动系数 · 增减目标
Mifflin-St Jeor basal rate × an activity factor
Glycemic Load (GL) · nutrition calculator
Glycemic Load (GL) · nutrition calculator
GL=GI×碳水/100 · 高/中/低分级
GL = glycemic index (GI) × available carbs per serving ÷ 100
Pharmacokinetics · drug half-life
Pharmacokinetics · drug half-life
C(t)=C0·e^(−kt) · t½=ln2/k · 重复给药达稳态
First-order elimination: C(t) = C₀·e^(−k·t) · t½ = ln2 / k · k = ln2 / t½
Blood-glucose homeostasis · negative feedback
Blood-glucose homeostasis · negative feedback
血糖↑→胰岛素→摄取↓ · 低糖→胰高血糖素 · 负反馈
high glucose → insulin → uptake / glycogen storage → glucose falls · low glucose → glucagon → glycogen breakdown → glucose rises
Thyroid axis · HPT negative feedback
Thyroid axis · HPT negative feedback
TRH→TSH→T3/T4 · 负反馈抑制 · 甲减/甲亢
hypothalamus TRH → pituitary TSH → thyroid T3/T4 ⊣ T3/T4 feed back to inhibit TRH & TSH
The nephron: how urine is made
The nephron: how urine is made
肾小球滤过+肾小管重吸收+分泌 · GFR · 尿浓缩
Filtration (blood → filtrate) · Reabsorption (filtrate → blood) · Secretion (blood → filtrate)
Blood acid–base balance
Blood acid–base balance
pH=6.1+log([HCO3]/(0.03·PCO2)) · 酸/碱中毒分类
Henderson–Hasselbalch: pH = 6.1 + log₁₀( [HCO₃⁻] / (0.03 · PCO₂) ) · normal pH 7.35–7.45
The baroreceptor reflex
The baroreceptor reflex
压感器测MAP→自主神经→HR/血管张力 · 负反馈稳压
Negative feedback: ↓MAP → ↓baroreceptor firing → ↑sympathetic → ↑HR, ↑contractility, vasoconstriction → MAP restored
Gas exchange at the alveolus
Gas exchange at the alveolus
肺泡O2→血、CO2→肺泡 · 分压梯度扩散 · Fick
Fick's law: net diffusion ∝ area × (partial-pressure gradient) / membrane thickness
Spirometry: lung volumes & capacities
Spirometry: lung volumes & capacities
TV/IRV/ERV/RV · VC · TLC · FEV1/FVC阻塞vs限制
VC = TV + IRV + ERV · TLC = VC + RV · FEV1/FVC distinguishes obstructive vs restrictive
Pulse oximetry (SpO₂)
Pulse oximetry (SpO₂)
660/940nm氧合/脱氧血红蛋白吸收比→SpO2 · 脉搏波
SpO₂ from the red/IR ratio-of-ratios R = (AC/DC)₆₆₀ / (AC/DC)₉₄₀
Cardiac rhythm & defibrillation
Cardiac rhythm & defibrillation
窦性 vs 室颤/室速 · 电击同步除极复窦 · 确定性波形
sinus rhythm vs ventricular tachycardia / fibrillation · when a shock helps
The audiogram · hearing threshold
The audiogram · hearing threshold
听阈dB HL对频率 · 正常≤25 · 高频/传导性损失
dB HL across 250–8000 Hz · normal ≤ 25 dB HL · plotted inverted
Accommodation of the eye's lens
Accommodation of the eye's lens
睫状肌变晶体曲率 · 近凸远扁 · 1/f=1/do+1/di · 老视
1/f = 1/dₒ + 1/dᵢ · image distance dᵢ fixed at the retina (≈ 17 mm)