MEDICINE AND SURGERY "F"
Course of LABORATORY MEDICINE
Anemias and hemoglobinopathies
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is a pathological condition characterized by reduced hemoglobin content in the blood. Physiological values of hemoglobin concentration range between >13 g/dL for adult males to >11 g/dL for infants and pregnant women. Hemoglobin concentrations below approx. 9 g/dL are symptomatic, and cause fatigue, dispnea and tachycardia. The increased cardiac work associated to reduced oxigenation of the blood perfusing the myocardium may cause angina pectoris and, occasionally, myocardial infarction. Blood transfusion is indicated when hemoglobin is <7 g/dL.
Anemia is neither a disease, nor a diagnosis
: it is a clinical condition that may be present in many different diseases, and may have a number of causes (summarized in the table below). An essential distinction is made between those conditions that
impair the biosynthesis of red blood cells
and those that
reduce the red blood cell lifespan
TABLE 1: SOME DISEASES CAUSING ANEMIA
Cause of anemia
Test(s) for diagnosis
Acute or chronic hemorrages, internal or external
Demonstration of blood loss (e.g. fecal occult blood; hematuria; hematemesis)
Hemolysis, toxic or allergic
Demonstration of hemoglobinuria and reduced erythrocyte lifespan
Bone marrow aplasia
Biopsy of the bone marrow
Leukemias (and lymphomas)
Demonstration of neoplastic cells in the blood (or the bone marrow)
Demonstration of lack of one of the subunits of hemoglobin in the erythrocytes (by electrophoresis); demonstration of abnormal hemoglobin genes
Chronic kidney diseases
Low erythropoietin levels in the serum; renal failure
Folate or vitamin B12 deficiency
Erythrociytes of increased size (megalocytes); measurement of serum levels of folate; deficit of the intrinsic factor in the gastric secretion
Low iron level in the serum
High lead concentration in the serum
Reduced erythrocyte lifespan:
Abnormal electrophoretic mobility of hemoglobin; demonstration of abnormal hemoglobin genes
Spherocytosis and ellissocytosis
Direct observation by optical microscopy
Genetic defects of red cell enzymes
Demonstration of abnormal enzyme genes (e.g. Glucose 6-phosphate dehydrogenase in favism)
It is important to remark that some diseases cause anemias because of more than a single reason: e.g. thalassemias cause premature death of the red cells but also defective erythropoiesis (hence these diseases appear twice in the table).
The lifespan of erythrocytes does not exceed 120 days, on average: thus every month the bone marrow has to replace one fourth of the circulating red cells. In some diseases causing ineffective erythropoiesis (i.e. destruction of abnormal erythrocytes during their differentiation in the bone marrow) an abnormal expansion of the marrow is observed: e.g. this is the case with beta-talassemia and the so-called "brush" skull. Diseases in which the biosynthesis of DNA is impaired (e.g. deficiency of folate or of vitamin B12) cause a delay in the differentiation of red blood cells, that result fewer, larger and paler (because of lower hemoglobin content) than in the healthy condition.
Anemias caused by reduced erythrocyte lifespan cause a compensatory increase in the rate of red cells production in the marrow, and release of an increased fraction of reticulocytes (immature erythrocytes) in the blood; by contrast reticulocytes are scarce or absent in anemias due to bone marrow aplasia.
As stated above, anemia is not a diagnosis (or it is a very imprecise one), but an easily recognized pathological condition. The identification of the disease underlying a condition of anemia is a differential diagnosis among the conditions listed in table 1, and requires the demonstration of the essential features of the disease. Some relevant cases are individually discussed below.
β - THALASSEMIA (Cooley disease)
. Thalassemias (or talassemias) are diseases caused by an imbalance of the synthesis of the alpha and beta subunits of hemoglobin. Since hemoglobin is a tetrameric protein, composed by two α and two β subunits, it is necessary that during the maturation of the erythrocyte, the two types of subunit are produced in equal amounts. Thalassemias are genetic diseases due to mutations of the genes of the α or the β subunit of hemoglobin, that may occur in the promoter region of the gene (lowering its transcription efficiency) or in the coding sequence (usually because of the mutation of a coding codon to a stop codon). The aploid human genome contains two copies of the α subunits gene and only one copy of the β subunit gene, on different chromosomes.
Thalassemia has autosomal recessive Mendelian transmission, and α thalassemia (in which the alpha subunits are lacking) is uncommon due to the redundancy of the alpha genes; thus β thalassemia is the most common of thalassemias. β talassemia in the heterozygous state, causes mild anemia and reduced volume erythrocytes (microcytosis). This form is asymptomatic or nearly so and is called talassemia minor. In the homozygous state the erythrocytes of the patient contain mostly unpaired alpha subunits, that precipitate inside the cell, forming Heinz bodies. This significantly shortens the lifespan of the affected erythrocytes and causes a very severe anemia. If untreated, β thalassemia major (Cooley disease) is fatal before puberty. In some cases the severity of a beta thalassemia major may be reduced by the hereditary persistence of foetal hemoglobin (made up by two α and two γ subunits, thus being independent of the biosynthesis of beta subunits). Diagnosis is made by finding the microcytosis in a blood smear and is confirmed by sequencing of the β globin gene. A frequently associated finding is the expansion of the bone marrow, with increased thickness of the bones where it is contained (e.g. the skull) and its protrusion in the periostium (e.g. in the vertebrae). In some regions or countries along the coast of the Mediterranean sea beta thalassemia is (or was) quite common, due to the fact that the minor, heterozygous form offers protection against malaria, which was formerly endemic in the region. The reason of protection probably lies in the reduced resistence of the affected erythrocytes which, when infected by the Plasmodium may undergo hemolysis before the parasite has completed its intraerythrocyte development, leading to an abortive infection.
An important indication may be obtained by electrophoresis; this is because the α and β subunits of hemoglobin have different electrophoretic mobility, and in the blood of a thalassemic patient one may observe normal human hemoglobin, and an excess of either subunit, revealed as an additional band with lower (α subunits excess in β-thalassemia) or higher mobility (β subunits excess in α-thalassemia).
. Folate is a vitamin required for the biosynthesis of nucleotides, hence of DNA, and deficiency of folate slows down the proliferation of stem cells of various tissues. The effect is particularly evident for red blood cells because of their rapid turnover, hence the anemia. Due to the reduced rate of replication the erythrocytes are few, large and pale and immature forms (reticulocytes) in peripheral blood are increased. Folate deficiency may occur in pregnant women, due to the high requirement of the vitamin by the foetus, and oral supplementation is indicated.
VITAMIN B12 DEFICIENCY (pernicious anemia, Brill disease)
The biological function of vitamin B12 is somewhat similar to that of folate, since it is a methyl group donor required for the biosynthesis of nitrogen bases of DNA. The pathogenetic mechanism of the anemia and the microscopic appearance of the red cells is also similar, i.e. this is a magalocytic, megaloblastic anemia. At variance with folate deficiency, pernicious anemia also causes neurological symptoms: paraesthesias, irritability, depression, and dementia. The disease is fatal if untreated.
Vitamin B12 deficiency is rarely due to insufficient dietary apport, although this can occur in strict vegan diets. More often vitamin B12 deficiency is due to atrophic gastritis, that impairs the production of the
(a protein required for the absorption of the vitamin) by the gastric mucosa. Because of this peculiarity, which is not shared by any other vitamin, oral administration of vitamin B12 may prove ineffective and intramuscular administration is required.
Diagnosis is suspected on clinical grounds (anemia associated to atrophic gastritis and neurological symptoms) and on the microscopic examination of a blood smear. It is confirmed by the measurement of vitamin B12 concentration in the serum (normal range 20-90 ng/dL). The preferred method for measurement is by radioimmunoassay. Some drugs may interfere with this test: e.g. Colchicine, Neomycin, Para-aminosalicylic acid, and Phenytoin.
IRON DEFICIENCY (sideropenic anemia)
Mammals have no physiological way to eliminate iron, and the iron content in the organism is regulated by its uptake in the gut. Iron is lost with hemorrages and iron deficiency may occur in the presence of insufficient uptake or increased loss by chronic or acute hemorrages. Fertle women have increased iron requirements. The anemia is microcytic (small erythrocytes) and diagnosis is confirmed by low values of sideremia (normal range in male adults: 65-175 ug/dL; female adults 50-170 ug/dL), and low iron saturation of circulating transferrin (normal concentration 200-360 mg/dL; normal saturation > 60%).
REDUCED HEME BIOSYNTHESIS
Insufficient production of the heme is observed in
chronic lead poisoning
. From a clinical view point these anemias are hypochromic and lack specific chracteristics; however the clinical picture entails several other symptoms (e.g. photosensitivity of the skin in eryhtropoietic porphyrias) that may suggest the diagnosis. Specific laboratory tests are available: measurement of heme precursors in the blood and urine for poprhyrias, measurement of lead in the blood, urine and tissues for lead poisoning.
INSUFFICIENT PRODUCTION OF RED BLOOD CELLS
Insufficient production of red blood cells is caused by diseases that destroy the bone marrow:
idiopathic bone marrow aplasia
(e.g. leukemias, lymphomas, etc.). Often these anemias are accompanied by deficiency of other cell types in the blood (reduced platelet count, reduced count of white cells); in leukemias the blood contains tumor-specific cells. The presenting symptom may often be a thrombocytopenic purpura. Diagnosis is suspected because of the results of hemochromocytometric analysis, and is confirmed by bone marrow biopsy.
DIFFERENTIAL DIAGNOSIS OF ANEMIAS
Anemias provide a very useful example to illustrate
. Let's suppose that we have a patient suffering of faticability and dispnoea. We prescribe a standard blood test in which Hb concentration and erythrocyte count are performed (see the lecture on the standard blood tests); usually together with erythrocye count the laboratory provides also an estimate of the mean erythrocyte volume, which tells us if the patient's condition is microcytic, normocytic or macrocytic. From this point onwards the clinical reasoning follows a linear path:
1) If Hb is low (< 13 g/dL) the patient has anemia.
2) In anemias the erythrocyte count is usually low, thus this datum adds little to your knowledge.
3) If the other blood cells are also low we have
, which usually points to a disease of the bone marrow.
4) If the mean red cell volume is
, the patient's anemia is macrocytic. The most important causes of macrocytic anemia are selective nutritional deficiencies, causing decreased production of erythrocytes: (i) folate deficiency; (ii) vitamin B12 deficiency; (iii) scurvy (deficiency of vitamin C); (iv) copper deficiency. The two former conditions are the most frequently observed. The next possible step in the diagnosis pathway is the measurement of vitamins and copper concentrations in the serum and the urine (see the lecture on vitamins). However, given that the administration of vitamins and minerals has virtually no contraindications, it is reasonable to prescribe vitamin and mineral supplements and see if this has the desired effect of curing the anemia (diagnosis
, literally "from the intervention that cures the disease"). It is also important to reevaluate the anamnesis, and possibly to ask the patient some more specific questions. Folate deficiency is more common during pregnancy, vitamin B12 is observed in vegans, etc. A very important consideration is that vitamin B12 is absorbed after binding to the intrinsic factor, a protein produced by the gastric mucosa; atrophic gastritis, gastric cancer, gastric surgery, etc. may be causes of vitamin B12 deficiency
resistent to oral administration of the vitamin
(intramuscular administration may be required).
5) If the mean red cell volume is
, the patient's anemia is microcytic. The most important causes of microcytic anemia are: (i) iron deficiency; (ii) thalassemias (consider in particular heterozygous β-thalassemia, β-thalassemia minor); (iii) inherited defects of the erythrocyte (e.g. spherocytosis);(iv) chronic lead (or other heavy metal) poisoning. Your next diagnostic step is to measure iron concentration in the blood (sideremia, serum transferrin), and to search for the relevant genetic diseases by gene sequencing. If the anamnesis suggests a possible professional intoxication, this should be tested by laboratory analyses. Caution: iron deficiency anemia may be the only sign of a chronic internal hemorrage, e.g. due to a bleeding colon cancer; a search of blood in the feces is indicated.
6) If the mean red cell volume is normal the patient anemia is normocytic. This is the largest group, and includes several possible diseases. Consider three possible cases: (i) chronic internal hemorrage (not associated to iron deficiency); (ii) increased destruction of red cells (reduced lifespan), possibly due to allergies, hemoglobinopathies, or other inherited conditions (e.g. defects of glucose-6-phosphate dehydrogenase); (iii) decreased production of red cells by the bone marrow because or aplasia, leukemias, lymphomas, etc. Clearly an important normocytic anemia requires a broad-scope investigation of several possible conditions. Normocytic anemia associated to reduced platelet count or pancytopenia strongly suggests a disease of the bone marrow.
7) If the mean red cell volume is
marginally increased or decreased
, and you do not feel confident in defining the patient's anemia macrocytic, normocytic, or microcyti, you apply the procedures of two cases, i.e. you carry out the analyses suggested for both macrocytic and normocytic anemias ( or microcytic and normocytic anemias).
Diagnosis is an iterative process
: an alteration in the patient's parameters suggests a list of diagnostic possibilities, each of them requiring specific tests and investigations. It is important that our list is as complete as possible, because omissions may lead to incomplete searches and missed diagnoses.
Hemoglobinopathies are hereditary defects of hemoglobin subunits (the alpha and beta polypeptide chains), usually due to single site mutations. They are inherited as Mendelian recessive traits. Hereditary defects of hemoglobin, due to the high solubility and rich functional behaviour of the protein, are somewhat exceptional with respect to those of other proteins and enzymes. Indeed the most usual effect of random point mutation in proteins is a drastic decrease of stability and solubility and the mutant protein is absent or present at very low concentration in the cell. In hemoglobin this is by no means the only possible effect of mutation and hemoglobinopathies can be classed into at least five groups:
1) Mutations which cause diminished stability. The intracellular Hb precipitates and form Heinz bodies adhering to the red cell membrane. The resulting damage of the membrane reduces the lifespan of the erythrocyte, causing an hereditary anemia.
2) Mutations which cause
increased oxygen affinity
. The mutant Hb uploads oxygen in the lungs but delivers few oxygen to the tissues, causing chronic ischemia. The ischemic kidney produces more erythropoietin to stimulate the bone marrow and these conditions are often associated to polycytemia (increased blood cell count), increased hematocrit, and increased Hb content.
3) Mutations which cause
reduced oxygen affinity
. The mutant Hb is not fully saturated with oxygen in the lung capillaries and the blood oxygen content is decreased in spite of a normal arterial oxygen pressure. The patient has cyanosis, but the amount of oxygen released to the tissues is normal and no ischemia is present (in general); the red cell count and hemoglobin content are usually normal or nearly so. The patient has fatigue because oxygen transport under strenuous muscular effort is reduced (a consequence of the reduced arterial oxygen content).
4) Mutations which cause
iron oxidation (methemoglobinemias)
. Mutation of the proximal or distal Histidine of either subunit to Tyrosine causes the heme iron to oxidize to the ferric state. Other mutations that increase the polarity of the heme pocket or allow water to flow in have the same effect. Methemoglobin (Hb with the heme iron in the ferric state) has low oxygen affinity and carries oxygen only on the hemes of the normal subunits, the ferric heme iron being unreactive. Thus the oxygen carrying capacity is halved. The patient presents a characteristic brown cyanosis of the mucosae (black mouth), due to the brownish colour of metHb; other symptoms are as in the case of reduced affinity Hbs, and polycytemia may be present to compensate for the reduced oxygen carrying capacity.
5) Mutations that cause other effects. This is a residual category that includes many different conditions. An important one is sickle cell Hb, the mutation of the sixth residue of the beta chain from Glu to Val. This mutation causes deoxyHb to polymerize and the resulting Hb polymer distorts the red cells, which assume a characteristic sickle shape. Sickled cells may stack in the venulae blocking the circulation: painful microinfarctions follow.
MOLECULAR MECHANISMS OF HEMOGLOBINOPATHIES
Hemoglobin is among the most deeply understood proteins, and hemoglobinopathies have significantly contributed to the study of structure-function relationships in hemoglobin. The macromolecule is a heterotetramer made up of two α and two β subunits arranged in a α
tetramer. The α and β subunits are globular proteins and are made up of 8 (or 7) α-helices. The subunits are arranged in the tetramer in a distorted tetrahedral geometry, and two types of α-β contacts occur. The α
-β1 contact involves helices B, G and H from both participating subunits; the α
-β2 contact involves helix C and the interhelical FG corner from both participating subunits. The regulation of oxygen affinity and cooperativity largely depends on (i) the residues lining the heme pocket of each subunit, (ii) the residues at the α
interface, which is responsible for the quaternary structural change associated to cooperative oxygen binding, and (iii) the two C-terminal residues of each subunit, that in deoxy Hb pack in proximity of the α
interface. The above listed regions of the macromolecule are thus those where single aminoacid mutations tend to exhert the most important functional effects. Examples of high oxygen affinity mutants are: Hb McKees Rocks, that bears the deletion of the last two C-terminal residues of the β, and Hb Chesapeake in which α Arg 92(FG3) is replaced by Leu; both mutations destabilize the low affinity T quaternary conformation and favor the transition to the high affinity R conformation. Examples of low oxygen affinity mutants are Hb Presbyterian that bears the mutation β 108 Asn to Lys, in proximity of the FG corner, and Hb Kansas that bears the mutation β 102 Asn to Thr; in the former the affinity is reduced because of stabilization of the T quaternary structure, in the latter presumably because G4 Asn is a heme contacting residue.
Several hemoglobinopathies, together with other hereditary diseases of the red cell (e.g. glucose 6 phosphate dehydrogenase deficiency, thalassemias) cause the red cell to become fragile and reduce its lifespan. While this effect usually results in an anemia,
it may protect the heterozygous patient from malaria
, because the damaged red cell does not support the full erythrocytic cycle of the parasite leading to an abortive effect. Because of this reason, in regions where malaria is or was endemic, an abnormally high frequency of any of these conditions may be observed (so called "polymorphism due to heterosis", i.e. higher fitness of the heterozygous carrier state that either the healthy or affected homozygous individual).
DIAGNOSIS OF HEMOGLOBINOPATHIES
The diagnosis is suspected on the basis of the clinical information, and confirmed by the finding of a hemoglobin with abnormal electrophoretic mobility. Protein sequencing and finger-printing are nowadays obsolete, and the diagnosis of the specific mutation depends on the sequencing of the genes coding for the α and β subunits.
Questions and exercises:
1) Megalocytic megaloblastic anemia is due to:
iron deficiency or thalassemias
reduced biosynthesis of DNA and lowered cell replication rate, possibly caused by folate or vitamin B12 deficiency
2) Microcytic anemia may be due to
iron deficiency or thalassemias
reduced biosynthesis of DNA and lowered cell replication rate, possibly caused by folate or vitamin B12 deficiency
3) The normal concentration of hemoglobin in the blood of an healthy adult is:
> 8 g/dL
> 12 g/dL
> 16 g/dL
4) Pancytopenia, i.e. reduced count of all cell types in blood may be due to:
lesions of the bone marrow (e.g. leukemias, lymphomas, aplasia)
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Thank you Professor (lecture on bilirubin and jaundice).
The fourth recorded part, the one on hyper and hypoglycemias is not working.
Bellelli: I checked and in my computer it seems to work. Can you better specify
the problem you observe?
This Presentation (electrolytes and blood pH) feels longer than previous lectures
Bellelli: it is indeed. Some subjects require more information than others. I was
thinking of splitting it in two nest year.
Bellelli in response to a question raised by email: when we compare the blood pH
with the standard pH we do not mean to compare the "normal" blood pH (7.4)
with the standard pH. Rather we compare the actual blood pH of the patient, with
the pH of the same blood sample equilibrated under standard conditions.
Thus, if we say that standard pH is lower than pH we mean that equilibriation with
40 mmHg CO2 has caused absorption of CO2 and has lowered the pH with respect
to its value before equilibration.
(Lipoproteins) Is the production of leptin an indirect cause of type 2 diabetes since
it works as a stimulus to have more adipose tissue that produces hormones?
Bellelli: in a sense yes, sustained increase of leptin causes the hypothalamus to adapt
and to stop responding. Obesity ensues and this in turn may cause an increase in the
production of resistin and other insulin-suppressing protein hormones produced by the
adipose tissue. However, this is quite an indirect link, and most probably other factors
contribute as well.
(Urea cycle) what is the meaning of "dissimilatory pathway"?
Bellelli: a dissimilatory pathway is a catabolic pathway whose function is not to produce
energy, but to produce some terminal metabolyte that must be excreted. Dissimilatory
pathways are necessary for those metabolytes that cannot be excreted as such by the
kidney or the liver because they are toxic or poorly soluble. Examples of metabolytes
that require transformation before being eliminated are heme-bilirubin, ammonia,
sulfur and nitrogen oxides, etc.
Talking about IDDM linked neuropathy can be the C peptide absence considered a cause of it??
Bellelli: The C peptide released during the maturation of insulin, besides being an indicator
of the severity of diabetes, plays some incompletely understood physiological roles. For
example it has been hypothesized that it may play a role in the reparation of the
atherosclerotic damage of the small arteries. Thus said, I am not aware that it plays a direct
role in preventing diabetic polyneuropathy. Diabetic neuropathy has at least two causes: the
microvascular damage of the arteries of the nerve (the vasa nervorum), and a direct
effect of hyperglycemia and decreased and irregular insulin supply on the nerve metabolism.
Diabetic neuropathy is observed in both IDDM and NIDDM, and requires several years to
develop. Since the levels of the C peptide differ in IDDM and NIDDM, this would suggest
that the role of the C peptide in diabetic neuropathy is not a major one. If you do have
better information please share it on this site!
In acute intermitted porphyria and congenital erythropoietic porphyria why do the end product
of the affected enzymes accumulate instead of their substrate??
Bellelli: First of all, congratulations! This is an excellent question.
Remember that a condition is which the heme is not produced is lethal in the foetus; thus
the affected enzyme(s) must maintain some functionality for the patient
to be born and to come to medical attention. All known genetic defects of heme
biosynthesis derange but do not block this metabolic pathway.
Congenital Erythropoietc Porphyria (CEP) is a genetic defect of uroporphyrinogen
III cosynthase. This protein associates to uroporphyrinogen synthase (which is present
and functional in CEP) and guarantees that the appropriate uroporphyrinogen isomer is produced
(i.e. uroporphyrinogen III). In the absence of a functional uroporphyrinogen III
cosynthase other possible isomers of uroporphyrinogen are produced together with
uroporpyrinogen III, mostly uroporphyrinogen I. The isomers of uroporphyrinogen
that are produced differ because of the positions of propionate and acetate side chains,
and this in turn is due to the pseudo symmetric structure of porphobilinogen. Only
isomer III can be further used to produce protoporphyrin IX. Thus in the
case of CEP we observe accumulation of abnormal uroporphyrinogen derivatives, which, as
you correctly observed are the products of the enzymatic synthesis operated by
The case of Acute Intermittent Porphyria (AIP) is similar, although there may be variants
of this disease. What happens is that either the affected enzyme is a variant that does not
properly associate with uroporphyrinogen III cosynthase or presents active site mutations
that impair the proper alignement of the phoprphobilinogen substrates. In either case
abnormal isomers of uroporphyrinogen are produced, as in CEP.
Also remark that in both AIP and CEP we observe accumulation of the porphobilinogen
precursor: this is because the overall efficiency of the biosynthesis of uroporphyrinogens is
reduced. Thus: (i) less uroporphyrinogen is produced, and (ii) only a fraction of the
uroporphyrinogen that is produced is the correct isomer (uroporphyrinogen III).
is it possible to take gulonolactone oxidase to synthesize vitamin C
instead of vitamin C supplement?
Bellelli: no, this approach does not work. The main reason is that
the biosynthesis of vitamin C, as almost all other metabolic processes, occurs intracellularly.
If you administer the enzyme it will at most reach the extracellular fluid but will not be
transported inside the cells to any significant extent. Besides, there are other problems
in this type of therapy (e.g. the enzyme if administered orally, may be degraded by digestive
proteases; if administered parenterally, may cause the immune system to react against a
non-self protein). In theory one could think of a genetic modification of the inactive human
gene of gulonolactone oxidase, but the risk and cost of this intervention would not be
justified. In addition to these considerations, except for cases of shipwreckage or
other catastrophes, a proper diet or administration of tablets of vitamin C is effective,
risk-free and unexpensive, thus no alternative therapy is reasonable. However, I express my
congratulations for your search on the biosynthesis pathway of ascorbic acid.
Resorption and not reabsorption would lead to hypercalcemia ie bone matrix being broken down.
Bellelli: I am not sure to interpret your question correctly. Resorption indicates destruction of the bone matrix and release of calcium and
phosphate in the blood, thus it causes an increase of calcemia. Reabsorption usually means active transport of calcium from the renal tubuli to the blood, thus
it prevents calcium loss. It prevents hypocalcemia, and thus complement bone resorption. To avoid confusion it is better use the terms "bone resorption" and "
renal reabsorption of calcium". If you have a defect in renal reabsorption, parthyroid hormone will be released to maintain a normal calcium level by means of
bone resorption; the drawback is osteoporosis.
In Reed and Frost model: I haven't understood what is the relationship
between K and R reproductive index. Thank you Professor!
Bellelli: in the Reed and Frost model K is the theoretical upper limit of
. R the reproductive index is the ratio (new cases)/(old cases) measured after
one serial generation time. R
is the value of R one measures at the beginning
of the epidemics, when in principle all the population is susceptible.
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