Hematology — NIH ICB classification under blood / oncology-adjacent; physiologic sub-discipline of internal medicine studying blood, blood-forming tissues, and associated disorders. Foundations: (1) Hemoglobin oxygen-transport biophysics:…
hematology
Hemoglobin cooperativity: Hill equation Y = L^n / (K^n + L^n); n ≈ 2.8
Hemoglobin oxygen binding is the canonical allosteric-cooperativity example. Adair (1925) gave the earliest four-site saturation equation;…
CBC reference ranges and derived indices: MCV=Hct·1000/RBC (fL)
The Complete Blood Count (CBC) is the most commonly ordered clinical laboratory test. Core measured parameters: white blood cell count…
Coagulation cascade and INR = (PT_pt / PT_norm)^ISI (WHO 1983)
The coagulation cascade is a stepwise zymogen-to-protease activation network culminating in fibrin polymerization. Extrinsic pathway:…
Hill half-saturation: Y(L=K) = 1/2 for all n (cooperativity-invariant)
Sympy-exact witness of the Hill-equation half-saturation identity, true for any Hill coefficient n > 0. Setup: Y(L; n, K) = L^n / (K^n +…
CBC indices on Hct=45%, RBC=5, Hb=15: MCV=90, MCH=30, MCHC=100/3
Sympy-exact witness of the CBC-indices arithmetic on a canonical healthy-adult-male anchor patient. Setup: Hct = 45/100 (fraction), RBC =…
INR identities: INR(PT_pt=PT_norm) = 1; INR(PT_pt=2·PT_norm, ISI=1) = 2
Sympy-exact witness of the International Normalized Ratio idempotent and linearity identities. Setup: INR = (PT_pt / PT_norm)^ISI as a…
Erythrocyte senescence (cohort kinetics): f(a) = 1/T_life on [0, T_life]; ⟨a⟩ = T_life/2
Erythrocyte senescence cohort kinetics — the canonical steady-state age-distribution framework for red blood cells. Physical setup: under…
Platelet dynamics: dP/dt = λ − k·P (first-order linear ODE); P_ss = λ/k; τ = 1/k
Thrombopoietin (TPO)-regulated platelet steady-state dynamics — the canonical compartmental framework for circulating platelet population…
Transfusion mass-balance: Hb_post = (Hb_0·TBV + Hb_d·V_t)/(TBV + V_t); ΔHb_lin = V_t·(Hb_d−Hb_0)/TBV
Transfusion volume mass-balance — the conservation-law framework governing post-transfusion hemoglobin (Hb), hematocrit (Hct), and…
Erythrocyte mean age: ⟨a⟩ = T_life/2; at T_life=120 d ⟨a⟩=60 d; Var(a) = T_life²/12 (uniform)
Sympy-exact symbolic witness of the erythrocyte-cohort-kinetics first and second moments under the steady-state uniform-age distribution. …
Platelet steady-state: P_ss = λ/k; τ = 1/k; t_half = ln(2)/k; lim_{t→∞} P(t) = λ/k
Sympy-exact symbolic witness of the platelet-dynamics steady-state, relaxation, and half-life anchors. Setup: first-order linear ODE dP/dt…
Transfusion: ΔHb_lin = V_t·(Hb_d−Hb_0)/TBV; anchor (TBV=5000,V_t=250,Hb_d=20,Hb_0=0) ⇒ ΔHb_lin = 1 g/dL
Sympy-exact symbolic witness of the transfusion volume mass-balance anchors, including the clinically-taught '+1 g/dL per unit' rule in its…
Hemoglobin O2 binding curve (sigmoidal)
Hill 1910 / Bohr 1904: sigmoidal Hb-O2 binding via cooperativity n~2.8; right-shift by H+/CO2/2,3-BPG releases O2 in tissues; left-shift by…
Erythropoietin (EPO) + hypoxia sensing
Goldwasser 1977 / Semenza 1992 HIF-1: kidney peritubular cells sense O2 via HIF-stabilization; secrete EPO -> bone marrow RBC production;…
Coagulation cascade (Davie-Ratnoff 1964)
Davie-Ratnoff 1964 + MacFarlane 1964 coagulation cascade: intrinsic + extrinsic + common pathways; modern cell-based model adds platelet +…
Transfusion ABO + Rh systems (Landsteiner)
Landsteiner 1900 ABO + 1940 Rh discovery; cross-matching prevents hemolytic-transfusion-reaction; group-O universal donor; AB universal…
Anemia classification (MCV)
Wintrobe 1934 erythrocyte indices: microcytic <80 fL (Fe-deficiency / thalassemia), normocytic 80-100 fL (chronic-disease), macrocytic >100…
Immunothrombosis (Engelmann-Massberg)
Engelmann-Massberg 2013 immunothrombosis: innate-immune cells + platelets co-trigger coagulation in response to pathogens / DAMPs;…
Blood groups (Landsteiner 1900)
K Landsteiner 1900 (Nobel 1930) ABO-blood-groups + 1940 Rh-factor; modern modern foundational text + 2024 transfusion-medicine +…
EPO (Jacobson 1957)
L Jacobson 1957 + 1985 cloning + 2019 (Nobel HIF-pathway Kaelin-Ratcliffe-Semenza) hypoxia-EPO; modern modern foundational EPO-anemia.
HSC niche (Schofield 1978)
R Schofield 1978 stem-cell-niche; modern modern foundational text + 2024 single-cell HSC-niche-mapping + osteo-vascular endothelial.
Coagulation cascade (Davie-Ratnoff 1964)
E Davie-O Ratnoff 1964 + Macfarlane 1964 coagulation-cascade; modern modern foundational + DOAC apixaban / rivaroxaban + 2024 NEXTOAC.
Sickle cell (Pauling 1949)
L Pauling 1949 'molecular disease'; modern modern foundational + Ingram-1957 hemoglobin-S + 2023 Casgevy CRISPR-FDA cure.
Transfusion (Blundell 1818)
J Blundell 1818 first human-human transfusion; modern modern foundational + Janeway 1942 banking + 2024 universal-blood Akkari enzyme.